**3. Methods**

### **3.1 Emergency resources demand prediction using case-based reasoning**

#### **3.1.1 Research background**

Public emergencies usually bring great negative impacts on economy and society, cause damage on casualties and property, bring destructions on ecological environment and human living environments, have adverse impacts on social order and public safety, and even arise social and political instability. Moreover, due to the change and influence of multiple factors, the type, occurrence probability and influence degree of public emergencies are increasing.

The demand on emergency resources refers to the minimum guarantee requirements for effective response to public emergencies. The so-called effective response refers to that the response on public emergencies should be efficient, and it also refers to that the emergency resources should be used with high efficiency. While the minimum guarantee requirements refer to that the smallest demands are needed when public emergencies are successfully solved. Obviously, an optimized idea is involved in the determination of emergency resource demand, meaning that under some given parameters such as type, intensity and influencing range of Emergency response, the smallest resource demand required for the successful response to public emergencies.

Currently, there are few researches on this aspect, in most cases the emergency decision maker subjectively decides whether the quantity, quality and type of emergency resources are rational and can meet the requirements of emergency. Besides, due to the particularity of emergency process, the effect of cost is smaller than that of time effect, so that in many cases, no efforts are spared to conduct the emergency rescue. But the method is easily to cause the irrational demand of emergency resources, so that it is unscientific and will cause groundless waste of numerous resources, meaning that a scientific prediction method is sorely needed to achieve the prediction on the demand of emergency resources.

Case-based reasoning (CBR) is a relatively new problem solving technique that is attracting increasing attention. For a long time, expert systems or knowledge-based systems (KBS) are one of the success choices in Artificial Intelligence (AI) research. The *first generation* KBS, and today's systems, are based upon an explicit model of the knowledge required to solve a problem. When it comes to so called *second generation* systems, a deep causal model was adopted to enable a system to reason using first principles [1]. But whether the knowledge is shallow or deep an explicit model of the domain must still be elicited and implemented often in the form of rules or perhaps more recently as object models. However, knowledge elicitation is a difficult process, often being referred to as the knowledge elicitation bottleneck; implementing KBS is a difficult and slow process requiring special skills; and once implemented they are difficult to maintain [2-6].

addition, the concrete case can be used to confirm the model's validity and practicability. The results of our repetitive experimental application of the model show that it works perfectly for its duty in improving the efficiency of emergency management and overcoming the problem of wasting emergency resource as well as low efficiency in

Public emergencies usually bring great negative impacts on economy and society, cause damage on casualties and property, bring destructions on ecological environment and human living environments, have adverse impacts on social order and public safety, and even arise social and political instability. Moreover, due to the change and influence of multiple factors, the type, occurrence probability and influence degree of public

The demand on emergency resources refers to the minimum guarantee requirements for effective response to public emergencies. The so-called effective response refers to that the response on public emergencies should be efficient, and it also refers to that the emergency resources should be used with high efficiency. While the minimum guarantee requirements refer to that the smallest demands are needed when public emergencies are successfully solved. Obviously, an optimized idea is involved in the determination of emergency resource demand, meaning that under some given parameters such as type, intensity and influencing range of Emergency response, the smallest resource demand required for the

Currently, there are few researches on this aspect, in most cases the emergency decision maker subjectively decides whether the quantity, quality and type of emergency resources are rational and can meet the requirements of emergency. Besides, due to the particularity of emergency process, the effect of cost is smaller than that of time effect, so that in many cases, no efforts are spared to conduct the emergency rescue. But the method is easily to cause the irrational demand of emergency resources, so that it is unscientific and will cause groundless waste of numerous resources, meaning that a scientific prediction method is

Case-based reasoning (CBR) is a relatively new problem solving technique that is attracting increasing attention. For a long time, expert systems or knowledge-based systems (KBS) are one of the success choices in Artificial Intelligence (AI) research. The *first generation* KBS, and today's systems, are based upon an explicit model of the knowledge required to solve a problem. When it comes to so called *second generation* systems, a deep causal model was adopted to enable a system to reason using first principles [1]. But whether the knowledge is shallow or deep an explicit model of the domain must still be elicited and implemented often in the form of rules or perhaps more recently as object models. However, knowledge elicitation is a difficult process, often being referred to as the knowledge elicitation bottleneck; implementing KBS is a difficult and slow process requiring special skills; and

sorely needed to achieve the prediction on the demand of emergency resources.

**3.1 Emergency resources demand prediction using case-based reasoning** 

emergency rescue.

**3.1.1 Research background** 

emergencies are increasing.

successful response to public emergencies.

once implemented they are difficult to maintain [2-6].

**3. Methods** 

Over the last few years an alternative reasoning paradigm and computational problem solving method has increasingly attracted more and more attention. Case-based reasoning (CBR) solves new problems by adapting previously successful solutions to similar problems. CBR is attracting attention because it seems to directly address the problems outlined above. CBR does not require an explicit domain model and so elicitation becomes a task of gathering case histories, implementation is reduced to identifying significant features that describe a case, an easier task than creating an explicit model, by applying database techniques largely volumes of information can be managed, and CBR systems can learn by acquiring new knowledge as cases thus making maintenance easier.

The work Schank and Abelson in 1977 is widely held to be the origins of CBR [7]. They proposed that our general knowledge about situations is recorded as scripts that allow us to set up expectations and perform inferences. Whilst the philosophical roots of CBR could perhaps be claimed by many what is not in doubt is that it was the work of Roger Schank's group at Yale University in the early eighties that produced both a cognitive model for CBR and the first CBR applications based upon this model [8]. Janet Kolodner developed the first CBR system called CYRUS [9-11]. An alternative approach came from Bruce Porter's work, at The University of Texas in Austin, into heuristic classification and machine learning resulting in the PROTOS system [12-13].

In the U.S., Edwina Rissland's group at the University of Massachusetts in Amherst developed HYPO [14]. This system was later combined with rule-based reasoning to produce CABARET [15].

In Europe, the first one is that of Derek Sleeman's group from Aberdeen in Scotland. They studied the uses of cases for knowledge acquisition, developing the REFINER system [16]. Mike Keane, from Trinity College Dublin, undertook cognitive science research into analogical reasoning [17]. Michael Richter and Klaus Althoff in the University of Kaiserslautern applied CBR to complex diagnosis [18]. This has given rise to the PATDEX system [19] and subsequently to the CBR tool S3-Case. In the University of Trondheim, Agnar Aamodt has investigated the learning facet of CBR and the combination of cases and general domain knowledge resulting in CREEK [20-21].

In the UK, CBR seemed to be particularly applied to civil engineering. A group at the University of Salford was applying CBR techniques to fault diagnosis, repair and refurbishment of buildings [22]. Yang & Robertson [23] in Edinburgh developed a CBR system for interpreting building regulations, a domain reliant upon the concept of precedence. Another group in Wales applied CBR to the design of motorway bridges [24].

Further, there are active CBR groups in Israel [25-26], India [27] and Japan [28].

#### **3.1.2 Methods for emergency resource demand prediction**

According to the characteristics of emergency resource demand prediction process, both the risk analysis and case-based reasoning method are introduced into the process, accordingly a case-based reasoning method for emergency resource demand prediction based on risk analysis is obtained, which improves the scientificity of emergency resource demand. The case-based reasoning flow for emergency resource demand prediction based on risk analysis is shown in Fig.2.

Theories and Methods for the Emergency Rescue System 127

The case-based reasoning is a comprehensive form of three types of human thoughts including imaginal thinking, logical thinking and creative thinking. From the view of reasoning method, the case-based reasoning is an analogy reasoning from one case (old case) to another case (new problem), while from the view of knowledge, the case-based reasoning is a method based on memory in which old experiences are used to guide the problems. The CBR is generally composed of four main processes, including retrieve, reuse,

Therefore, in this paper, the case-based reasoning prediction method associated with risk analysis process is used to conduct demand prediction on the quantity, quality and type of emergency resources. After conducting risk analysis on target area, characteristic values of risk in these are can be obtained, including possible incident type, incident results, occurrence probability of incident, etc., accordingly the case-based reasoning process can be

The case generally includes two parts, including case attribute description and case solution, of which the former one is the index structure of case and the latter one is the answer of case. While the emergency resource demand prediction is composed of three parts, including characteristic description of Emergency response, characteristic description of emergency rescue plan and description of emergency resource demand, all of which can be determined based on the results of risk analysis, namely risk probability and risk results.

 Characteristic description of Emergency response: it includes some characteristic information of Emergency response, including type, intensity, natural environment surround the occurrence site, population density, losses, duration time of hazard, etc., all of which depict and describe the characteristic attributes of Emergency response. Characteristic description of emergency rescue plan: it includes the characteristic attributes of emergency object, emergency rescue method, emergency procedure, etc. If there is a difference in the emergency object, way, technique and process of Emergency

Description of emergency resource demand: it includes the quantity, quality and type of

On the whole, in order to obtain complete data, the case should be described in detail as can as possible under the specific condition. Generally, one case can be composed of several attributes, all of which can be further divided, while the whole case library is composed of associated cases at different attribute levels. Therefore, in the emergency resource demand

*case (F, P, D)*  In the formula: *F*=(*f*1, *f*2,…, *f*n), *f*n is a characteristic attribute of Emergency response, which can be obtained according to the results of risk analysis; P=( *p*1, *p*2, …, *p*n), *p*n is a characteristic attribute of emergency rescue plan; D is the demand attribute of emergency

response of the same type, the material demands will be different too.

revise and retain [29-30], so that CBR is also called 4R.

used for emergency resource demand prediction.

1. Expression of case

emergency resources.

resource.

prediction, the case can be modeled as follows:

2. Case-based reasoning process of emergency resource demand

a. Characterization of emergency resource demand case

Fig. 2. Case-based reasoning prediction on emergency resource demand based on risk analysis.

The case-based reasoning is a comprehensive form of three types of human thoughts including imaginal thinking, logical thinking and creative thinking. From the view of reasoning method, the case-based reasoning is an analogy reasoning from one case (old case) to another case (new problem), while from the view of knowledge, the case-based reasoning is a method based on memory in which old experiences are used to guide the problems. The CBR is generally composed of four main processes, including retrieve, reuse, revise and retain [29-30], so that CBR is also called 4R.

Therefore, in this paper, the case-based reasoning prediction method associated with risk analysis process is used to conduct demand prediction on the quantity, quality and type of emergency resources. After conducting risk analysis on target area, characteristic values of risk in these are can be obtained, including possible incident type, incident results, occurrence probability of incident, etc., accordingly the case-based reasoning process can be used for emergency resource demand prediction.

1. Expression of case

126 Novel Approaches and Their Applications in Risk Assessment

Risk Identification

Risk Analysis

Probability analysis Consequence analysis

Risk Level

Problem Target case

Risk sequence in target area

Scenario Definition

Importance degree sequence of emergency resource

Historical case

Retrieve

Reuse

Exterior Environment

Metrological condition

Traffic condition

Infrastructure condition

Population condition

Case retrieve

Retain

Case library

method

Determining prediction object

Determining target area for prediction

Historical data and related data collection

Fig. 2. Case-based reasoning prediction on emergency resource demand based on risk analysis.

Prediction results of emergency resource demand

Determined Modified case

Revise

The case generally includes two parts, including case attribute description and case solution, of which the former one is the index structure of case and the latter one is the answer of case. While the emergency resource demand prediction is composed of three parts, including characteristic description of Emergency response, characteristic description of emergency rescue plan and description of emergency resource demand, all of which can be determined based on the results of risk analysis, namely risk probability and risk results.


On the whole, in order to obtain complete data, the case should be described in detail as can as possible under the specific condition. Generally, one case can be composed of several attributes, all of which can be further divided, while the whole case library is composed of associated cases at different attribute levels. Therefore, in the emergency resource demand prediction, the case can be modeled as follows:

#### *case (F, P, D)*

In the formula: *F*=(*f*1, *f*2,…, *f*n), *f*n is a characteristic attribute of Emergency response, which can be obtained according to the results of risk analysis; P=( *p*1, *p*2, …, *p*n), *p*n is a characteristic attribute of emergency rescue plan; D is the demand attribute of emergency resource.


Theories and Methods for the Emergency Rescue System 129

Generally, under different decision-making environments, the same characteristic factor has different effects on the decision output. Given that represents the value of case when the characteristic factor is b. If there is a large difference in distribution of in the case library C (C ={*c*1, *c*2,…,*c*n}), which indicates that the factor has great effect on classification identification, and it should be assigned a larger weight value. On the contrary, if there is a small difference in distribution of in the case library C (C ={*c*1, *c*2,…,*c*n}), which indicates that the factor has little effect on classification identification, and it should be

*n b*( )

( ) *C j <sup>i</sup> n b*

**1 2 2**

Therefore, each case in the case library can be classified into one type. Given the case *Ci* takes the value of when the characteristic factor is *bj*, the membership function of the

*n b*( )

case to the characteristic factor *bj* can be expressed as , and the formula below can

() () **1**

*n j C j j nb n b n*

*i*

( ( ) ( ))

*Cj j*

*n b nb*

*n*

**1**

Thus, the mean square deviation is expressed as the formula below:

( )

*j*

*b*

The weight *wj* of each characteristic factor can be obtained by the formula below:

( )

*b*

*j*

*i*

*n*

**<sup>1</sup>** *<sup>i</sup>*

the weight of characteristic factor, and the formula below can be obtained:

*j*

 **1**

*j m*

*j*

**1**

*j i m*

*m*

**1**

*b*

After the weight of characteristic factor is obtained, the similarity function is combined with

( ( ) ( ))

*sim T C i n*

*jT j C j*

*jT j C j*

*wn x n x*

*wn x n x*

(, ) , ,, , ( ( ) ( ))

*i*

*i*

 **12** 

( ) , ,,

 **12** , *<sup>j</sup>*

*w jm*

(6)

*n b*( )

(7)

(8)

(9)

c. Weight calculation of characteristic factor

assigned a smaller weight value.

( ) *n bj*

be obtained:

Given that there are n cases in the case library, the case i is expressed as *C*i (*i*=1,2,…,n). Its characteristic factor set *B*={*b*1, *b*2,…,b m}. Therefore, the membership function of case *Ci* to the characteristic factor *b*j (*j*=1,2,…,m) is expressed as ( ) *C j <sup>i</sup> n b* , and the characteristic vector corresponding to the case *Ci* in the case library is as follows:

$$V\_{C\_i} = \langle \mathfrak{n}\_{C\_i}(\mathfrak{b}\_1), \mathfrak{n}\_{C\_i}(\mathfrak{b}\_2), \dots, \mathfrak{n}\_{C\_i}(\mathfrak{b}\_{\mathfrak{m}}) \rangle = \langle \mathfrak{n}\_{C\_i}(\mathfrak{b}\_j) \Big| \mathfrak{j} = \mathbf{1}, \mathfrak{2}, \dots, \mathfrak{m} \rangle \tag{1}$$

Given that the characteristic vector set of prediction plan is *T*, which can be expressed as the formula below:

$$V\_T = \langle \mathfrak{n}\_T(\mathfrak{b}\_1), \mathfrak{n}\_T(\mathfrak{b}\_2), \dots, \mathfrak{n}\_T(\mathfrak{b}\_{\mathfrak{m}}) \rangle = \langle \mathfrak{n}\_T(\mathfrak{b}\_j) \Big| j = 1, 2, \dots, \ \mathfrak{m} \rangle \tag{2}$$

#### b. Emergency resource demand case retrieve-similarity calculation

According to the organization form of case, the nearest neighbour method is used. The nearest neighbour method is a method in which the cumulative sum of characteristic weights of the input case that is matched with the existing case in the case library is used to retrieve the case, namely that:

$$\frac{\sum\_{l=1}^{n} \mathbf{w}\_{l} \text{sim}(\mathbf{b}\_{l}^{I}, \mathbf{b}\_{l}^{R})}{\sum\_{l=1}^{n} \mathbf{w}\_{l}} \tag{3}$$

In the formula above: w is the important weight value of characteristic factor, *sim* is the similarity function, *bI* and *bR* is the input case value and retrieve case value of characteristic factor *i*.

In the similarity matching of cases using the characteristics of case, the effect of each characteristic is different, so that in the similarity calculation, it is necessary to assign different weights to each characteristic factor.

Given that the influencing weight set of the characteristic factor set B={*b*1, *b*2,…,b m} is {*w*1, *w*2,…,wm}, and the following condition is satisfied:

$$\sum\_{j=1}^{m} \mathbf{w}\_j = \mathbf{1}, \quad j = \mathbf{1}, \mathbf{2}, \dots, \quad m \tag{4}$$

Consequently, the similarity can be calculated by the formula below:

$$\text{sim}(A, \mathcal{B}) = \frac{\sum\_{j=1}^{m} \mathbf{w}\_{j}(\mathfrak{n}\_{A}(\boldsymbol{\mathfrak{x}}\_{j}) \wedge \mathfrak{n}\_{\mathcal{B}}(\boldsymbol{\mathfrak{x}}\_{j}))}{\sum\_{j=1}^{m} \mathbf{w}\_{j}(\mathfrak{n}\_{A}(\boldsymbol{\mathfrak{x}}\_{j}) \vee \mathfrak{n}\_{\mathcal{B}}(\boldsymbol{\mathfrak{x}}\_{j}))} \tag{5}$$

In the formula (5), is the maximum lower limit, and is the minimum upper limit. 

#### c. Weight calculation of characteristic factor

128 Novel Approaches and Their Applications in Risk Assessment

Given that there are n cases in the case library, the case i is expressed as *C*i (*i*=1,2,…,n). Its characteristic factor set *B*={*b*1, *b*2,…,b m}. Therefore, the membership function of case *Ci* to the characteristic factor *b*j (*j*=1,2,…,m) is expressed as ( ) *C j <sup>i</sup> n b* , and the characteristic vector

(1)

{ ( ), ( ), ( )} { ( ) , , } **1 2** , , **1 2** *CC C ii i Cm C j <sup>i</sup> <sup>i</sup> V nbnb nb nb j m*

Given that the characteristic vector set of prediction plan is *T*, which can be expressed as the

(2)

{ ( ), ( ), ( )} { ( ) , , } **1 2** , , **1 2** *V nb nb nb nb TT T Tm T j j m*

According to the organization form of case, the nearest neighbour method is used. The nearest neighbour method is a method in which the cumulative sum of characteristic weights of the input case that is matched with the existing case in the case library is used to

In the formula above: w is the important weight value of characteristic factor, *sim* is the similarity function, *bI* and *bR* is the input case value and retrieve case value of characteristic

**1**

**1**

(, )

*w*

*w sim b b*

*n I R i ii i n i i*

In the similarity matching of cases using the characteristics of case, the effect of each characteristic is different, so that in the similarity calculation, it is necessary to assign

Given that the influencing weight set of the characteristic factor set B={*b*1, *b*2,…,b m} is {*w*1,

, ,,

*w j m*

**1 12** ,

( ( ) ( ))

*jA j B j*

*wn x n x*

*wn x n x*

*jA j B j*

( ( ) ( ))

In the formula (5), is the maximum lower limit, and is the minimum upper limit.

*j m*

**1**

*m*

*j*

**1**

(3)

(4)

(5)

corresponding to the case *Ci* in the case library is as follows:

b. Emergency resource demand case retrieve-similarity calculation

formula below:

factor *i*.

retrieve the case, namely that:

different weights to each characteristic factor.

*w*2,…,wm}, and the following condition is satisfied:

Consequently, the similarity can be calculated by the formula below:

*j*

*j*

*m*

**1**

(, )

*sim A B*

Generally, under different decision-making environments, the same characteristic factor has different effects on the decision output. Given that represents the value of case when the characteristic factor is b. If there is a large difference in distribution of in the case library C (C ={*c*1, *c*2,…,*c*n}), which indicates that the factor has great effect on classification identification, and it should be assigned a larger weight value. On the contrary, if there is a small difference in distribution of in the case library C (C ={*c*1, *c*2,…,*c*n}), which indicates that the factor has little effect on classification identification, and it should be assigned a smaller weight value. *n b*( ) *n b*( ) *n b*( )

Therefore, each case in the case library can be classified into one type. Given the case *Ci* takes the value of when the characteristic factor is *bj*, the membership function of the case to the characteristic factor *bj* can be expressed as , and the formula below can be obtained: ( ) *n bj* ( ) *C j <sup>i</sup> n b*

$$\overline{n}(\mathbf{b}\_j) = \frac{1}{\mathbf{n}} \sum\_{j=1}^{n} \mathbf{n}\_{C\_i}(\mathbf{b}\_j) \tag{6}$$

Thus, the mean square deviation is expressed as the formula below:

$$\delta(b\_j) = \left[ \frac{\sum\_{i=1}^n \left( n\_{C\_i}(b\_j) - \overline{n}(b\_j) \right)^2}{n} \right]^{\frac{1}{2}} \tag{7}$$

The weight *wj* of each characteristic factor can be obtained by the formula below:

$$\mathbf{w}\_{j} = \frac{\delta(\mathbf{b}\_{j})}{\sum\_{j=1}^{m} \delta(\mathbf{b}\_{j})}, \quad j = 1, 2, \dots, \ m \tag{8}$$

After the weight of characteristic factor is obtained, the similarity function is combined with the weight of characteristic factor, and the formula below can be obtained:

$$\text{sim}(T, C\_i) = \frac{\sum\_{j=1}^{m} \mathbf{w}\_j(\mathfrak{n}\_T(\mathbf{x}\_j) \wedge \mathfrak{n}\_{C\_i}(\mathbf{x}\_j))}{\sum\_{j=1}^{m} \mathbf{w}\_j(\mathfrak{n}\_T(\mathbf{x}\_j) \vee \mathfrak{n}\_{C\_i}(\mathbf{x}\_j))} \geq \eta, \quad i = 1, 2, \dots, n \tag{9}$$

Theories and Methods for the Emergency Rescue System 131

Ninghe and Jixian. It has a total area of 11,919.7 square kilometers, and a resident population of 1023.67 million. Table 1 shows the statistics of accidents this year in City T.

> **Accident rate 0/000**

**Mortality rate 0/000** 

**Injured rate 0/000** 

**10 thousand** 

10 32 27 1001 0.999 3.197 2.697 9 37 25 1001 0.899 3.696 2.498 1 9 3 1001 0.010 0.899 0.300 9 21 5 1024 0.879 2.051 0.488 \* Data derives from 2004~2007 Statistics of accident distribution in cities and provinces China in *Journal* 

As can be seen from the table, City T is a metropolis with a good security situation, but in order to take preventive measures, it is very important and very necessary to carry out the optimization of location planning of emergency logistics base stations in City T. Therefore, in this paper, taking City T as the object, the author makes use of multi-stage location planning optimization model to study the location planning of emergency resource base stations in this city and seek a reasonable location planning program to provide a decision

**Time Accident Death Injured Population/** 

Table 1. Statistics of accidents in recent years in City T\*.

making basis for the future construction and development of City T.

stations, and the other is to solve the problem of spatial distribution.

**3.2.2 Multi-stage location planning optimization model of emergency resource** 

An important role of emergency logistics base station is to provide adequate and timely emergency response resources to potential unforeseen accident or disaster sites. And the optimal planning of emergency logistics base station helps to make rational use and allocation of spaces and emergency resources, to reduce the risks the city, as well as conduce to the efficient, orderly and sustained operation of urban economy, social activities and

The optimization of location planning of emergency resource base station includes determining reasonable position and scale of emergency resource base station. Therefore, the optimization of the location planning of emergency resource base station should mainly start with two aspects, one is to determine the appropriate scale of emergency resource base

The first step is to use set covering model to determine the minimum number of emergency resource base stations which can meet the needs of all demand sites; and the second step is to use maximum coverage model to determine the optimal sites of the minimum number of emergency resource base stations among the options, to meet the needs of all demand sites

Coverage model is one of the most basic models of optimal planning of emergency resource base stations. The meaning of coverage refers to that the services scope of emergency

*of Security and Environment* 

**base station** 

construction activities.

to the maximum.

a. Scale optimization - set covering model

In the formula above, the similarity between target case *T* and *Ci* can be expressed as *sim*(*T*,*Ci*) (∈[0,1]), *η* is a threshold value, and the learning strategies of case are divided into following types:


All cases in accordance with the similarity calculation formula are the similar cases, among which the one with the maximum sim (*T*, *C*i) is the most similar case. Accordingly, the material demands of the most similar case are taken as the prediction results of material demand when the Emergency response occurs.

#### **3.2 Application of multi-stage location planning model in optimizing location of emergency resource base stations**

#### **3.2.1 Research background**

Urban Planning refers to the specific method or process of predicting urban development and managing various resources to adapt to its development, to guide the design and development of built environments. While modern urban planning is trying to study the impact which a variety of economic, social and environmental factors have on the change of land using patterns, and develop planning reflecting the continuous interaction. Currently, in the process of making urban planning, parties have paid more and more attention to urban safety planning, in which the optimization of location planning of emergency logistics base station is one of the very important contents[31-33].

Emergency Logistics refers to the special logistics activities through which the necessary emergency supplies are provided to minimize the loss caused by unforeseen accidents and disasters in the shortest time, while an important role of emergency logistics base station (also known as emergency resource base station) is to provide adequate and timely emergency response resources to potential unforeseen accident or disaster sites[34-37].

The optimization of location planning of emergency resource base station includes determining reasonable position and scale of emergency resource base station, and since the special construction of emergency logistics base station costs a lot due to its specialization, so the optimization of the location planning of emergency resource base station should mainly start with two aspects, one is to determine the appropriate scale or the reasonable amount of emergency resource base stations, the other is to solve the problem of spatial distribution, namely, location optimization[38-40].

City T, as largest coastal open city in Northern China, currently has jurisdiction over 15districts including Heping, Hedong, Nankai, Hexi, Hebei, Hongqiao, Tanggu, Hangu, Dagang, Dongli, Xiqing, Jinnan, Beichen, Wuqing, Baodi, and 3 counties such as Jinghai,

In the formula above, the similarity between target case *T* and *Ci* can be expressed as *sim*(*T*,*Ci*) (∈[0,1]), *η* is a threshold value, and the learning strategies of case are divided into

a. *sim*(*T*, *Ci*)=0, *i*∈[0, 1], the new case doesn't match with all cases in the case library,

b. *sim* (*T*, *Ci*)=1, *i*∈[0, 1], the new case is completely similar to certain case, and it can

d. *sim* (*T*, *Ci*)>*η*, *i*∈[0, 1], the solution for the case with maximum similarity (max[*sim* 

All cases in accordance with the similarity calculation formula are the similar cases, among which the one with the maximum sim (*T*, *C*i) is the most similar case. Accordingly, the material demands of the most similar case are taken as the prediction results of material

Urban Planning refers to the specific method or process of predicting urban development and managing various resources to adapt to its development, to guide the design and development of built environments. While modern urban planning is trying to study the impact which a variety of economic, social and environmental factors have on the change of land using patterns, and develop planning reflecting the continuous interaction. Currently, in the process of making urban planning, parties have paid more and more attention to urban safety planning, in which the optimization of location planning of emergency logistics

Emergency Logistics refers to the special logistics activities through which the necessary emergency supplies are provided to minimize the loss caused by unforeseen accidents and disasters in the shortest time, while an important role of emergency logistics base station (also known as emergency resource base station) is to provide adequate and timely emergency response resources to potential unforeseen accident or disaster sites[34-37].

The optimization of location planning of emergency resource base station includes determining reasonable position and scale of emergency resource base station, and since the special construction of emergency logistics base station costs a lot due to its specialization, so the optimization of the location planning of emergency resource base station should mainly start with two aspects, one is to determine the appropriate scale or the reasonable amount of emergency resource base stations, the other is to solve the problem of spatial

City T, as largest coastal open city in Northern China, currently has jurisdiction over 15districts including Heping, Hedong, Nankai, Hexi, Hebei, Hongqiao, Tanggu, Hangu, Dagang, Dongli, Xiqing, Jinnan, Beichen, Wuqing, Baodi, and 3 counties such as Jinghai,

**3.2 Application of multi-stage location planning model in optimizing location of** 

c. *sim* (*T*, *Ci*) <*η*, *i*∈[0, 1], the new case can be added into the case library;

following types:

 

and it can be added into the case library;

demand when the Emergency response occurs.

**emergency resource base stations** 

**3.2.1 Research background** 

(*T*, *Ci*) ]) is converted into the solution for new case.

base station is one of the very important contents[31-33].

distribution, namely, location optimization[38-40].

not added into the case library;


Ninghe and Jixian. It has a total area of 11,919.7 square kilometers, and a resident population of 1023.67 million. Table 1 shows the statistics of accidents this year in City T.

\* Data derives from 2004~2007 Statistics of accident distribution in cities and provinces China in *Journal of Security and Environment* 

Table 1. Statistics of accidents in recent years in City T\*.

As can be seen from the table, City T is a metropolis with a good security situation, but in order to take preventive measures, it is very important and very necessary to carry out the optimization of location planning of emergency logistics base stations in City T. Therefore, in this paper, taking City T as the object, the author makes use of multi-stage location planning optimization model to study the location planning of emergency resource base stations in this city and seek a reasonable location planning program to provide a decision making basis for the future construction and development of City T.

#### **3.2.2 Multi-stage location planning optimization model of emergency resource base station**

An important role of emergency logistics base station is to provide adequate and timely emergency response resources to potential unforeseen accident or disaster sites. And the optimal planning of emergency logistics base station helps to make rational use and allocation of spaces and emergency resources, to reduce the risks the city, as well as conduce to the efficient, orderly and sustained operation of urban economy, social activities and construction activities.

The optimization of location planning of emergency resource base station includes determining reasonable position and scale of emergency resource base station. Therefore, the optimization of the location planning of emergency resource base station should mainly start with two aspects, one is to determine the appropriate scale of emergency resource base stations, and the other is to solve the problem of spatial distribution.

The first step is to use set covering model to determine the minimum number of emergency resource base stations which can meet the needs of all demand sites; and the second step is to use maximum coverage model to determine the optimal sites of the minimum number of emergency resource base stations among the options, to meet the needs of all demand sites to the maximum.

a. Scale optimization - set covering model

Coverage model is one of the most basic models of optimal planning of emergency resource base stations. The meaning of coverage refers to that the services scope of emergency

Theories and Methods for the Emergency Rescue System 133

*x y i V*

*Maximize d y*

*i V*

 **()**

*i i*

Maximum coverage model can be used to seek the best possible using method of available resources, but does not guarantee to cover all demand sites. Therefore, maximum coverage model can be used to determine the optimal solution of maximum coverage on the base of

**{ , } ( )**

**{ , } ( )**

0 1

*x j W*

*y i V*

*j*

*x p*

*subject to*

*i*

*j W*

*j W*

*j*

*i*

*j i*

0 1

At present, our country is in an important opportunity period for economic and social development, which is also the crucial period to implement the third-step strategic deployment of the modernization construction; therefore, the important task of our country is to maintain the long-term harmonious and stable social environment and stable and united situation. As the most important link in emergency handling, the contingency plan strengthens the research in respect of optimized resource allocation, which has very important significance for promoting the technological level of dealing with unexpected accidents and emergency management capacity of our country, guaranteeing public safety in our country and establishing reasonable and efficient contingency plans for national

The emergency resource management process of unexpected public events is in fact a set of decisions and decision implementation processes under a series of goal constraint conditions. These series of decisions and decision implementation processes mean "when and which resources at which place to allocate, and what to do". It is necessary to invest in enhancing urban comprehensive emergency capability, which proposes the problems of optimized allocation and dispatch of limited emergency resources, and the problem solving relates to whether the limited resources can exert the greatest effect, whether the emergency rescue system can achieve the desired goal and so on. At present, the researches related to emergency resource allocation practically aim at single resource optimization, such as the emergency service vehicle dispatch or vehicle relocation problems. When the emergency service vehicle system receives the service demand, it dispatches its emergency response unit (such as police car, fire engine, ambulance and so on) to the service demand zone. After

the optimal solution of set coverage.

**3.3.1 Research background** 

public safety.

**3.3 Appropriate allocation of emergency resources** 

(11)

resource base stations set up should be able to cover all sites requiring service. And it is one of the common goals of optimal planning of emergency logistics base station to cover all demand sites with the minimum number of emergency logistics base stations.

Set covering model is simple, but highly practical. It can be used to determine the most efficient number the emergency resource base stations covering all demand sites. Since the investment in emergency resource base stations can be quite expensive, so decision-makers need to keep a minimum number of base stations at the same time of taking providing services of necessary level to each demand site into account, therefore, they need to determine the reasonable number of emergency logistics base station under the limitation of covering distance or covering time.

The binary decision variable *x*j is set as follows: When the candidate site *j* is selected, *x*j = 1; otherwise *x*j= 0. if the set of candidate sites which can cover all the demand sites *i* is *N*i = {*j*| *d*ij ≤ *S*} (or *N*i = {*j*| *t*ij ≤ *R*}), the minimum number of the necessary facilities which can cover all the demand sites may be decided by set covering model:

$$\begin{aligned} \min \quad & z = \sum\_{j \in J} x\_j\\ \text{s.t.} \quad & \sum\_{j \in N\_i} x\_j \ge 1 \quad \forall i \in I\\ & x\_j \in (0, 1) \quad \forall j \in J \end{aligned} \tag{10}$$

In which the objective function can minimize the number of base stations, the constraint 1 can ensure that each demand site is covered by at least one emergency resource base station, and it is one of the basic objectives of optimal planning of emergency resource base station. The constraint 2 limits the decision variables *x*j as integer variables between (0, 1).

Set covering model is of integer linear programming model, mathematically, it is a typical NP-hard model. Generally, its solution can be obtained through relaxing integer limiting requirement against *x*j, using the procedure of general linear programming, and in most cases, integer solution of general problems can be directly obtained.

b. Space layout optimization - maximum coverage model

After the first phase of finding model solution, the number of emergency resources base stations providing services to all the demand sites in the whole region can be determined. Being clear about the number of base stations, the goal of the second stage is to optimize the spatial layout of these emergency resource base stations, to enable them to meet emergency requirements.

Maximum coverage model is an extension and expansion of set covering model. This model can be used to consider the maximization of demand site value coverage (population or other indicators). Maximum coverage model was originally presented by Church and ReVelle, where *d*i refers to the demand of node *i*, p refers to the available emergency resources. Binary variables yi can be used to present whether the demand site is overwritten or not, when the demand site is overwritten, *y*i = 1, otherwise *y*i = 0.

resource base stations set up should be able to cover all sites requiring service. And it is one of the common goals of optimal planning of emergency logistics base station to cover all

Set covering model is simple, but highly practical. It can be used to determine the most efficient number the emergency resource base stations covering all demand sites. Since the investment in emergency resource base stations can be quite expensive, so decision-makers need to keep a minimum number of base stations at the same time of taking providing services of necessary level to each demand site into account, therefore, they need to determine the reasonable number of emergency logistics base station under the limitation of

The binary decision variable *x*j is set as follows: When the candidate site *j* is selected, *x*j = 1; otherwise *x*j= 0. if the set of candidate sites which can cover all the demand sites *i* is *N*i = {*j*| *d*ij ≤ *S*} (or *N*i = {*j*| *t*ij ≤ *R*}), the minimum number of the necessary facilities which can cover

In which the objective function can minimize the number of base stations, the constraint 1 can ensure that each demand site is covered by at least one emergency resource base station, and it is one of the basic objectives of optimal planning of emergency resource base station.

0 1

1

*x jJ*

*j*

*j J*

*z x*

*j*

*st x i I*

Set covering model is of integer linear programming model, mathematically, it is a typical NP-hard model. Generally, its solution can be obtained through relaxing integer limiting requirement against *x*j, using the procedure of general linear programming, and in most

After the first phase of finding model solution, the number of emergency resources base stations providing services to all the demand sites in the whole region can be determined. Being clear about the number of base stations, the goal of the second stage is to optimize the spatial layout of these emergency resource base stations, to enable them to meet emergency

Maximum coverage model is an extension and expansion of set covering model. This model can be used to consider the maximization of demand site value coverage (population or other indicators). Maximum coverage model was originally presented by Church and ReVelle, where *d*i refers to the demand of node *i*, p refers to the available emergency resources. Binary variables yi can be used to present whether the demand site is overwritten

The constraint 2 limits the decision variables *x*j as integer variables between (0, 1).

 **( , )**  *i*

*j*

*j N*

cases, integer solution of general problems can be directly obtained.

or not, when the demand site is overwritten, *y*i = 1, otherwise *y*i = 0.

b. Space layout optimization - maximum coverage model

requirements.

(10)

demand sites with the minimum number of emergency logistics base stations.

covering distance or covering time.

all the demand sites may be decided by set covering model:

**min** 

**. .** 

$$\begin{aligned} \text{Maximize } & \sum\_{i \in V} d\_i \mathbf{y}\_i \\ \text{subject to } & \\ & \sum\_{j \in W\_i} \mathbf{x}\_j \ge \mathbf{y}\_i \quad (i \in V) \\ & \sum\_{j \in W} \mathbf{x}\_j = p \\ & \mathbf{x}\_j \in \{0, 1\} \quad (j \in W) \\ & \mathbf{y}\_i \in \{0, 1\} \quad (i \in V) \end{aligned} \tag{11}$$

Maximum coverage model can be used to seek the best possible using method of available resources, but does not guarantee to cover all demand sites. Therefore, maximum coverage model can be used to determine the optimal solution of maximum coverage on the base of the optimal solution of set coverage.

#### **3.3 Appropriate allocation of emergency resources**

#### **3.3.1 Research background**

At present, our country is in an important opportunity period for economic and social development, which is also the crucial period to implement the third-step strategic deployment of the modernization construction; therefore, the important task of our country is to maintain the long-term harmonious and stable social environment and stable and united situation. As the most important link in emergency handling, the contingency plan strengthens the research in respect of optimized resource allocation, which has very important significance for promoting the technological level of dealing with unexpected accidents and emergency management capacity of our country, guaranteeing public safety in our country and establishing reasonable and efficient contingency plans for national public safety.

The emergency resource management process of unexpected public events is in fact a set of decisions and decision implementation processes under a series of goal constraint conditions. These series of decisions and decision implementation processes mean "when and which resources at which place to allocate, and what to do". It is necessary to invest in enhancing urban comprehensive emergency capability, which proposes the problems of optimized allocation and dispatch of limited emergency resources, and the problem solving relates to whether the limited resources can exert the greatest effect, whether the emergency rescue system can achieve the desired goal and so on. At present, the researches related to emergency resource allocation practically aim at single resource optimization, such as the emergency service vehicle dispatch or vehicle relocation problems. When the emergency service vehicle system receives the service demand, it dispatches its emergency response unit (such as police car, fire engine, ambulance and so on) to the service demand zone. After

Theories and Methods for the Emergency Rescue System 135

11 1 (, ) *kk k uxw*

*k* 1

*<sup>k</sup>* <sup>2</sup> *x*

( ) *Dk k x*

11 1 (,, ) *Lx u w kk k*

k1 k k k x f(x ,u ,w )(k 0,1,2, ,N 1) (12)

p(x ) (u (x ),u (x ), ,u (x )) k 11 22 NN (13)

J J(x(0),x(1), ,x(N);u(0),u(1), ,u(N)) (14)

(x(0),x(1), ,x(N);u(0),u(1), ,u(N)) (15)

J J(x(0),u(0),u(1), ,u(N)) (16)

*wk wk* <sup>1</sup> *wk n*,

Fig. 3. The relation of proximate emergency stages based on dynamic programming.

The decision function sequence composed of the decision u (x )(k 1,2, ,N) k k at each stage is called the whole process strategy, strategy for short. Strategy refers to the set of all emergency resource allocation decisions established at any emergency stage, which is only

An appropriate *u* value (namely, appropriate decision sequence) is selected, so as to minimize *J* (or use other evaluation standards of *J*, such as the maximization of *J*), and

The decision-making process at the *N*th stage is determined using the following factors.

k1 k k k x f(x ,u ,w )(k 0,1, ,N 1 2, ) , and *x*(0) is the known initial state, suppose that all x(k)(k 1 N ,2, , ) can be expressed as *x*(0) and u(k)(k 0, , 1, N 1) , so the criterion

*x(0)* is the given initial state, decision u(k)(k 0 N ,1, , ) is free variables, so the

Where, *N* is the number of emergency zones in the emergency process.

related to the stage and state in that stage process, and is expressed as p(x ) <sup>k</sup>

optimize the objective function. Function *J* is called the criterion function.

**3.3.2.2 Establishment of an optimized resource allocation model** 

function

simultaneous nonlinear equation

For the objective function *J* with given state and decisions, it can be expressed as

(, ) *kk k uxw*

(,, ) *Lx u w kk k*

For the ( k 1 )*th* stage, the dynamic system has

*k <sup>k</sup> x <sup>k</sup>* <sup>1</sup> *x*

an emergency service vehicle is dispatched for service, it is necessary to study the vehicle relocation problems to guarantee the defence demand in remaining zones. Studies on the emergency resource allocation beyond service vehicles are still at the initial stage. In China, Liu Chunlin et al (1999) studied the minimized transportation time problems of emergency resource allocation in continuous consumption system and one-off consumption system [41]; Liu Chunlin et al (2000) studied the emergency problems when the required time from the depot to emergency zone is a fuzzy number. In overseas countries, Fiorucci et al (2005) studied the emergency resource allocation and scheduling problems before and after the fire through building a dynamic model; Fiedrich et al (2000) studied the problems of simultaneous resource allocation for different disaster relief tasks and so on through building a dynamic programming model [42]. At the present stage, there are fewer studies on optimized allocation of many resources under unexpected accident disasters, moreover the majority of studies only take shortest emergency time as the optimized objective of the system, and the optimized method is too simple, and lacks consideration of the complexity of the emergency process; in addition, static models are more widely used in the studies, which lack emergency resource allocation parameters reflecting the accident disaster development status.

The present research aims at enhancing the urban emergency management capacity, establishes the emergency resource allocation model in view of many accident disasters, so as to effectively integrate various emergency resources, and reduce the investment cost of emergency resource management.

#### **3.3.2 Optimized resource allocation model**

#### **3.3.2.1 Decision model based on dynamic programming**

The emergency resource allocation process is divided into *N* corresponding stages in view of the accident disaster emergency management characteristics, using the dynamic programming method, and according to the number of emergency zones (the number is supposed as *N*), based on which, a mathematical model is built, so as to optimize the emergency resource allocation. In the emergency process, a certain amount of resources are allocated to meet the emergency demand, and various parameter variables are expressed as follows.

*k* is the emergency stage (k 1,2, ,N) ; k x is the state variable in the dynamic programming model, representing the gross amount of allocated emergency resources at the *kth* stage; uk is the decision variable in the model, representing the alternative decision scheme; wk represents the emergency resource demand at the *kth* stage with given probability distribution. Dk is the set of all decision variables from 1st stage to the *kth* stage.

Suppose that w ,w , ,w 12 N are independent random variables depending on the disaster situation at emergency zones. The relationship between allocatable resource <sup>k</sup> x , emergency resource demand wk and emergency decision variables uk in the emergency process is shown in Figure 3.

an emergency service vehicle is dispatched for service, it is necessary to study the vehicle relocation problems to guarantee the defence demand in remaining zones. Studies on the emergency resource allocation beyond service vehicles are still at the initial stage. In China, Liu Chunlin et al (1999) studied the minimized transportation time problems of emergency resource allocation in continuous consumption system and one-off consumption system [41]; Liu Chunlin et al (2000) studied the emergency problems when the required time from the depot to emergency zone is a fuzzy number. In overseas countries, Fiorucci et al (2005) studied the emergency resource allocation and scheduling problems before and after the fire through building a dynamic model; Fiedrich et al (2000) studied the problems of simultaneous resource allocation for different disaster relief tasks and so on through building a dynamic programming model [42]. At the present stage, there are fewer studies on optimized allocation of many resources under unexpected accident disasters, moreover the majority of studies only take shortest emergency time as the optimized objective of the system, and the optimized method is too simple, and lacks consideration of the complexity of the emergency process; in addition, static models are more widely used in the studies, which lack emergency resource allocation parameters reflecting the accident disaster

The present research aims at enhancing the urban emergency management capacity, establishes the emergency resource allocation model in view of many accident disasters, so as to effectively integrate various emergency resources, and reduce the investment cost of

The emergency resource allocation process is divided into *N* corresponding stages in view of the accident disaster emergency management characteristics, using the dynamic programming method, and according to the number of emergency zones (the number is supposed as *N*), based on which, a mathematical model is built, so as to optimize the emergency resource allocation. In the emergency process, a certain amount of resources are allocated to meet the emergency demand, and various parameter variables are expressed as

*k* is the emergency stage (k 1,2, ,N) ; k x is the state variable in the dynamic programming model, representing the gross amount of allocated emergency resources at the *kth* stage; uk is the decision variable in the model, representing the alternative decision scheme; wk represents the emergency resource demand at the *kth* stage with given probability distribution. Dk is the set of all decision variables from 1st stage to the

Suppose that w ,w , ,w 12 N are independent random variables depending on the disaster situation at emergency zones. The relationship between allocatable resource <sup>k</sup> x , emergency resource demand wk and emergency decision variables uk in the emergency process is

development status.

follows.

*kth* stage.

shown in Figure 3.

emergency resource management.

**3.3.2 Optimized resource allocation model** 

**3.3.2.1 Decision model based on dynamic programming** 

Fig. 3. The relation of proximate emergency stages based on dynamic programming.

For the ( k 1 )*th* stage, the dynamic system has

$$\mathbf{x}\_{\mathbf{k}+1} = \mathbf{f}(\mathbf{x}\_{\mathbf{k}'} \mathbf{u}\_{\mathbf{k}'} \mathbf{w}\_{\mathbf{k}}) (\mathbf{k} = 0, 1, 2, \cdots, \mathbf{N} - 1) \tag{12}$$

Where, *N* is the number of emergency zones in the emergency process.

The decision function sequence composed of the decision u (x )(k 1,2, ,N) k k at each stage is called the whole process strategy, strategy for short. Strategy refers to the set of all emergency resource allocation decisions established at any emergency stage, which is only related to the stage and state in that stage process, and is expressed as p(x ) <sup>k</sup>

$$\mathbf{p(x\_k) = (u\_1(x\_1), u\_2(x\_2), \dots, u\_N(x\_N))}\tag{13}$$

For the objective function *J* with given state and decisions, it can be expressed as

$$\mathbf{J} = \mathbf{J}(\mathbf{x}(0), \mathbf{x}(1), \dots, \mathbf{x}(N); \mathbf{u}(0), \mathbf{u}(1), \dots, \mathbf{u}(N)) \tag{14}$$

An appropriate *u* value (namely, appropriate decision sequence) is selected, so as to minimize *J* (or use other evaluation standards of *J*, such as the maximization of *J*), and optimize the objective function. Function *J* is called the criterion function.

#### **3.3.2.2 Establishment of an optimized resource allocation model**

The decision-making process at the *N*th stage is determined using the following factors.

$$(\mathbf{x}(0), \mathbf{x}(1), \dots, \mathbf{x}(N); \mathbf{u}(0), \mathbf{u}(1), \dots, \mathbf{u}(N)) \tag{15}$$

k1 k k k x f(x ,u ,w )(k 0,1, ,N 1 2, ) , and *x*(0) is the known initial state, suppose that all x(k)(k 1 N ,2, , ) can be expressed as *x*(0) and u(k)(k 0, , 1, N 1) , so the criterion function

$$\mathbf{J} = \mathbf{J}(\mathbf{x}(0), \mathbf{u}(0), \mathbf{u}(1), \dots, \mathbf{u}(N)) \tag{16}$$

*x(0)* is the given initial state, decision u(k)(k 0 N ,1, , ) is free variables, so the simultaneous nonlinear equation

Theories and Methods for the Emergency Rescue System 137

emergency decision-makers to determine future resource scheduling according to the emergency resource demand situation at the present stage, and multi-stage emergency resource scheduling with the event development and changes and according to the emergency effect at the last stage and present situation. Therefore, the emergency resource scheduling is a dynamic process. Under the situation that the emergency resource site layout and allocation is known, emergency managers are concerned about the problems of how to formulate optimized scheduling scheme, guarantee the timeliness of emergency resource scheduling, and minimize the resource arrival time [43-44]. As a result, it is necessary to formulate beforehand the optimized scheme of emergency resource scheduling in the light of the specific scene of sudden public events, so as to start the emergency resource scheduling scheme as early as possible and guarantee the timeliness of emergency

The Markov decision process can select an action from the available action set to make a decision according to the observed state at each moment. Meanwhile, the decision makers can make another new decision according to the newly observed state, and repeat such process [45]. Therefore, this section plans to study the dynamic optimization of emergency resource scheduling of sudden public events using the Markov decision process, so as to provide a basis for optimized emergency resource scheduling under sudden public events

Due to a series of characteristics of sudden public events, such as nonrepeatedness, uniqueness, gradual evolution and so on, the decision-making problems for emergency resource scheduling have three main characteristics: sudden public event is dynamically changing; information about the event development is from fuzziness to clearness and from incompleteness to completeness, namely the future state is uncertain; the scheme formulated under incomplete information can be easily adjusted in time under complete information. The optimized emergency resource scheduling can be more scientifically and reasonably realized by referring to the Markov decision analysis method, but sudden public events are not evolved and developed according to the pre-established direction. Therefore, emergency measures can be only taken according to previous experience, emergency plan and real-time information at the scene of accident (usually incomplete), and be adjusted according to

The application of Markov decision analysis method in the optimized emergency resource scheduling process of sudden public events is shown in Figure 4. The whole decisionmaking process is how to select a scheme to cope with the uncertainty development state of

Basic thought of the Markov process is to infer the future state distribution according to the probability distribution of current state, and make judgment and decisions accordingly.

X(t) is used to express the system state, the state sequence {X(t);t T} is a stochastic process, <sup>m</sup> U(i) is the decision set of the state i at the *n*th stage. Suppose that Pij is the one-step state transition probability, n n f (i, ) represents the expected total reward when the system state shifts from X(n) i at the *n*th stage to the process end; ij r represents the

the sudden public event, until the sudden public event is completely under control.

**3.4.2 Dynamic Markov decision of emergency resource scheduling** 

unceasing improvement of the information in the emergency process.

rescue action.

$$\frac{\partial \mathbf{j}}{\partial \mathbf{u}(\mathbf{k})} = 0, (\mathbf{k} = 0, 1, \cdots, \mathbf{N}) \tag{17}$$

To solve practical problems, it is necessary to analyze and calculate the form of limit criterion function *J* in multistage decision process. In the present model

$$\mathbf{u}(\mathbf{k}) = \mathbf{u}(\mathbf{x}(\mathbf{k}), \mathbf{w}(\mathbf{k}), \mathbf{k}) \tag{18}$$

i.e., the existing decision is only the function of existing state and stochastic disturbance.

The criterion function of emergency resource allocation has Markov properties, i.e., the objective function has the following attributes

$$\mathbf{J} = \sum\_{\mathbf{k}=0}^{N} \mathbf{L}(\mathbf{x}(\mathbf{k}), \mathbf{u}(\mathbf{k}), \mathbf{w}(\mathbf{k})) \tag{19}$$

Where, L(x(k),u(k),w(k)) is the objective function at each stage of the emergency process. In this model, *L* is a nonnegative function depending on the state and sum of decision items at a single stage. *J* is the objective function of the whole emergency process, equivalent to the sum of objective functions at all stages.

In general, it is known that a group of states x(k) X , and *X* is available emergency resources, then a new group of states x(k 1) can be obtained according to x(k) with the computing formula as

$$\mathbf{x}(\mathbf{k}+1) = \mathbf{f}(\mathbf{x}(\mathbf{k}), \mathbf{u}(\mathbf{k}), \mathbf{w}(\mathbf{k})) \tag{20}$$

At the same time, J(x(k 1),k 1) can also be calculated

$$\mathbf{J}(\mathbf{x}(\mathbf{k}+1), \mathbf{k}+1) = \mathbf{L}(\mathbf{x}(\mathbf{k}+1), \mathbf{u}(\mathbf{k}+1), \mathbf{w}(\mathbf{k}+1) + \mathbf{J}(\mathbf{x}(\mathbf{k}), \mathbf{k}) \tag{21}$$

So the total cost function of the emergency process of any systematic sample can be expressed as

$$\begin{cases} \mathbf{J}\_{\mathbf{k}+1}(\mathbf{x}\_{\mathbf{k}+1}) = \min \sum\_{\mathbf{k}=1}^{N-1} \mathbf{L}\_{\mathbf{k}} = \min(\mathbf{L}\_{\mathbf{k}+1}(\mathbf{x}\_{\mathbf{k}+1}, \mathbf{u}\_{\mathbf{k}+1}, \mathbf{w}\_{\mathbf{k}+1}) + \mathbf{J}\_{\mathbf{k}}(\mathbf{x}\_{\mathbf{k}})) \\ \text{s.t. } \mathbf{u}\_{\mathbf{k}} \in \mathbf{p}\_{\mathbf{k}}(\mathbf{x}\_{\mathbf{k}}) \\ \mathbf{L}\_{0}(\mathbf{x}\_{1}) = 0 \\ \frac{\partial \mathbf{J}}{\partial \mathbf{u}(\mathbf{k})} = 0 \end{cases} \tag{22}$$

#### **3.4 Optimal dispatching of emergency resources**

#### **3.4.1 Research background**

It is necessary for the emergency command department to make the emergency resource scheduling decisions after the occurrence of sudden public events. It is necessary for

<sup>J</sup> 0,(k 0,1, ,N) u(k)

To solve practical problems, it is necessary to analyze and calculate the form of limit

i.e., the existing decision is only the function of existing state and stochastic disturbance.

The criterion function of emergency resource allocation has Markov properties, i.e., the

J L(x(k),u(k),w(k))

Where, L(x(k),u(k),w(k)) is the objective function at each stage of the emergency process. In this model, *L* is a nonnegative function depending on the state and sum of decision items at a single stage. *J* is the objective function of the whole emergency process, equivalent to the

In general, it is known that a group of states x(k) X , and *X* is available emergency resources, then a new group of states x(k 1) can be obtained according to x(k) with the

So the total cost function of the emergency process of any systematic sample can be

k1 k1 k k1 k1 k1 k1 k k

It is necessary for the emergency command department to make the emergency resource scheduling decisions after the occurrence of sudden public events. It is necessary for

J (x ) min L min(L (x ,u ,w ) J (x ))

criterion function *J* in multistage decision process. In the present model

N

k 0

objective function has the following attributes

sum of objective functions at all stages.

At the same time, J(x(k 1),k 1) can also be calculated

k kk

**3.4 Optimal dispatching of emergency resources** 

s.t. u p (x ) L (x ) 0 <sup>J</sup> <sup>0</sup> u(k)

0 1

**3.4.1 Research background** 

N 1

k 1

computing formula as

expressed as

(17)

u(k) u(x(k),w(k ) ),k (18)

(19)

x(k 1 ) ) f(x(k),u(k),w ) (k (20)

(22)

J(x(k 1),k 1) L(x(k 1),u(k 1),w(k 1) J(x(k),k) (21)

emergency decision-makers to determine future resource scheduling according to the emergency resource demand situation at the present stage, and multi-stage emergency resource scheduling with the event development and changes and according to the emergency effect at the last stage and present situation. Therefore, the emergency resource scheduling is a dynamic process. Under the situation that the emergency resource site layout and allocation is known, emergency managers are concerned about the problems of how to formulate optimized scheduling scheme, guarantee the timeliness of emergency resource scheduling, and minimize the resource arrival time [43-44]. As a result, it is necessary to formulate beforehand the optimized scheme of emergency resource scheduling in the light of the specific scene of sudden public events, so as to start the emergency resource scheduling scheme as early as possible and guarantee the timeliness of emergency rescue action.

The Markov decision process can select an action from the available action set to make a decision according to the observed state at each moment. Meanwhile, the decision makers can make another new decision according to the newly observed state, and repeat such process [45]. Therefore, this section plans to study the dynamic optimization of emergency resource scheduling of sudden public events using the Markov decision process, so as to provide a basis for optimized emergency resource scheduling under sudden public events

#### **3.4.2 Dynamic Markov decision of emergency resource scheduling**

Due to a series of characteristics of sudden public events, such as nonrepeatedness, uniqueness, gradual evolution and so on, the decision-making problems for emergency resource scheduling have three main characteristics: sudden public event is dynamically changing; information about the event development is from fuzziness to clearness and from incompleteness to completeness, namely the future state is uncertain; the scheme formulated under incomplete information can be easily adjusted in time under complete information.

The optimized emergency resource scheduling can be more scientifically and reasonably realized by referring to the Markov decision analysis method, but sudden public events are not evolved and developed according to the pre-established direction. Therefore, emergency measures can be only taken according to previous experience, emergency plan and real-time information at the scene of accident (usually incomplete), and be adjusted according to unceasing improvement of the information in the emergency process.

The application of Markov decision analysis method in the optimized emergency resource scheduling process of sudden public events is shown in Figure 4. The whole decisionmaking process is how to select a scheme to cope with the uncertainty development state of the sudden public event, until the sudden public event is completely under control.

Basic thought of the Markov process is to infer the future state distribution according to the probability distribution of current state, and make judgment and decisions accordingly.

X(t) is used to express the system state, the state sequence {X(t);t T} is a stochastic process, <sup>m</sup> U(i) is the decision set of the state i at the *n*th stage. Suppose that Pij is the one-step state transition probability, n n f (i, ) represents the expected total reward when the system state shifts from X(n) i at the *n*th stage to the process end; ij r represents the

Theories and Methods for the Emergency Rescue System 139

To research the transient state behavior the ergodic Markov chain, it is necessary to obtain its basic equations set using z transform analysis method. z transform can transform the difference equation to corresponding generalized equation. There is one-to-one correspondence between the function and its z transform, and meanwhile the primary function can be mutually converted with its z transform. Therefore, the following formulae

nv f q p [(n 1)v f ]i 1,2, ,m

This is the basic equations set for Markov decision problems, which can be obtained through

a. An initial strategy n is selected, a decision regulation n is selected for each state

b. For the known strategy <sup>n</sup> , let (n) f 0 <sup>m</sup> , the corresponding strategy profit (n) v and corresponding value (n) f (i 1,2, ,m ;n 0,1,2, ) can be obtained through solving

c. A new strategy regulation n 1 is sought using the (n) fm obtained from the last strategy,

d. If the obtained strategy πn+1 is completely equal to the strategy πn obtained through the last iteration, namely πn+1=πn, then the iteration is stopped, and the optimized strategy

The prediction process above can be applied not only in the prediction on emergency resource demand for the public emergencies that have not yet happen, but also in the

<sup>n</sup> (n) i ij j i j 1 q pff 

(26)

(i) (i) n 1 n 1

achieves its maximal value, and a new strategy n 1 is obtained accordingly;

**4.1 Case study – Emergency resources demand prediction using case-based** 

prediction on emergency resource demand for occurred public emergencies.

m i i ij j j 1 n i i ij i j 1

i(i 1,2, ,m ) , so that its decision <sup>k</sup> u (i) (i) n , and let n 0 ;

the basic equations set for Markov decision problems;

is obtained. Otherwise, return to step 2 and let n = n+1.

nv f q p f i 1,2, ,m

(24)

(25)

f (i, ) p r p f (i, ),i 1,2, ,m;n 1,2,

n n n n ij ij ij n 1 n 1 j1 j1

This formula is the basic equation for Markov decision problems.

can be obtained through z transform

the following algorithms.

so that for each state i ,

**4. Case study** 

**reasoning** 

corresponding reward when the state shifts from X(n) i to the next state X(n 1) j , then there is

$$\mathbf{f}\_{\mathbf{n}}(\mathbf{i}, \boldsymbol{\pi}\_{\mathbf{n}}) = \mathbf{q}(\mathbf{i}) + \sum\_{\mathbf{j}=1}^{n} \mathbf{p}\_{\vec{\mathbf{j}}} \mathbf{f}\_{\mathbf{n}+1}(\mathbf{i}, \boldsymbol{\pi}\_{\mathbf{n}+1}), \mathbf{i} = 1, 2, \cdots, \mathbf{m}; \mathbf{n} = 1, 2, \cdots \tag{23}$$

Fig. 4. Diagram of Markov decision processes in the emergency resources scheduling of the sudden public events.

n represents the sequence n n1 { , ,} , n n n1 (, ) of the decision regulation from the *n*th stage to the process end, where n is the decision regulation at the *n*th stage.

If n ij ij j 1 q(i) p r ,i 1,2, ,m , q(i) represents the expected reward when the state i shifts

once, namely the real-time expected reward of the state, then the above formula can be rewritten as

corresponding reward when the state shifts from X(n) i to the next state X(n 1) j , then

f (i, ) q(i) p f (i, ),i 1,2, ,m;n 1,2,

Fig. 4. Diagram of Markov decision processes in the emergency resources scheduling of the

Space for emergency resource scheduling scheme

n represents the sequence n n1 { , ,} , n n n1 (, ) of the decision regulation from

once, namely the real-time expected reward of the state, then the above formula can be

, q(i) represents the expected reward when the state i shifts

the *n*th stage to the process end, where n is the decision regulation at the *n*th stage.

(23)

Emergency objectives

Duration

Emergency resource

n n n ij n 1 n 1 j 1

Risks of sudden public events

Possible state and evolution trend of sudden public events

> Optimized scheme

Markov decision

there is

sudden public events.

n

rewritten as

ij ij j 1

q(i) p r ,i 1,2, ,m

If

$$\mathbf{f}\_{\mathbf{n}}(\mathbf{i}, \pi\_{\mathbf{n}}) = \sum\_{\mathbf{j}=1}^{\mathbf{n}} \mathbf{p}\_{\mathbf{i}\mathbf{j}} \mathbf{r}\_{\mathbf{i}\mathbf{j}} + \sum\_{\mathbf{j}=1}^{\mathbf{n}} \mathbf{p}\_{\mathbf{i}\mathbf{j}} \mathbf{f}\_{\mathbf{n}+1}(\mathbf{i}, \pi\_{\mathbf{n}+1}), \mathbf{i} = \mathbf{1}, \mathbf{2}, \cdots, \mathbf{m}; \mathbf{n} = \mathbf{1}, \mathbf{2}, \cdots \tag{24}$$

This formula is the basic equation for Markov decision problems.

To research the transient state behavior the ergodic Markov chain, it is necessary to obtain its basic equations set using z transform analysis method. z transform can transform the difference equation to corresponding generalized equation. There is one-to-one correspondence between the function and its z transform, and meanwhile the primary function can be mutually converted with its z transform. Therefore, the following formulae can be obtained through z transform

$$\begin{aligned} \mathbf{n} \mathbf{v} + \mathbf{f}\_{\mathbf{i}} &= \mathbf{q}\_{\mathbf{i}} + \sum\_{\mathbf{j}=1}^{\mathbf{m}} \mathbf{p}\_{\mathbf{ij}} [(\mathbf{n} - \mathbf{1})\mathbf{v} + \mathbf{f}\_{\mathbf{j}}] \mathbf{i} = \mathbf{1}, \mathbf{2}, \cdots, \mathbf{m} \\ \mathbf{n} \mathbf{v} + \mathbf{f}\_{\mathbf{i}} &= \mathbf{q}\_{\mathbf{i}} + \sum\_{\mathbf{j}=1}^{\mathbf{n}} \mathbf{p}\_{\mathbf{ij}} \mathbf{f}\_{\mathbf{i}} \qquad \mathbf{i} = \mathbf{1}, \mathbf{2}, \cdots, \mathbf{m} \end{aligned} \tag{25}$$

This is the basic equations set for Markov decision problems, which can be obtained through the following algorithms.


$$\mathbf{q}\_{\mathbf{i}}^{\delta\_{n+1^{(i)}}} + \sum\_{\mathbf{j}=1}^{n} \mathbf{p}\_{\mathbf{i}\mathbf{j}}^{\delta\_{n+1^{(i)}}} \mathbf{f}\_{\mathbf{j}}^{\mathbf{(n)}} - \mathbf{f}\_{\mathbf{i}} \tag{26}$$

achieves its maximal value, and a new strategy n 1 is obtained accordingly;

d. If the obtained strategy πn+1 is completely equal to the strategy πn obtained through the last iteration, namely πn+1=πn, then the iteration is stopped, and the optimized strategy is obtained. Otherwise, return to step 2 and let n = n+1.

#### **4. Case study**

#### **4.1 Case study – Emergency resources demand prediction using case-based reasoning**

The prediction process above can be applied not only in the prediction on emergency resource demand for the public emergencies that have not yet happen, but also in the prediction on emergency resource demand for occurred public emergencies.

Theories and Methods for the Emergency Rescue System 141

..... ( )

**05 07 07 08 06** *n b <sup>T</sup> bbbbb*

**12345**

*b* ( )**<sup>2</sup>**

( ) *n b***<sup>1</sup>** ( ) *n b***<sup>2</sup>** ( ) *n b***<sup>3</sup>** ( ) *n b***<sup>4</sup>** ( ) *n b***<sup>5</sup>**

*b* ( )**<sup>3</sup>**

Therefore, the weight value of each characteristic factor can be calculated as follows: *w*1=0.35, *w*2=0.15, *w*3=0.32, *w*4=0.09 and *w*5=0.09. According to the similarity calculation method, the similarity of each case is calculated as follows: *sim*(*T*, *C*1)=0.36, *sim*(*T*, *C*2)=0.66, *sim*(*T*,*C*3)=0.86 and *sim*(*T*, *C*4)=0.66. All above are shown in Table 2, and the similarity of

 *sim*(*T*, *C*1)<*sim*(*T*, *C*2) =*sim*(*T*, *C*4) <*sim*(*T*, *C*3) (29) It can be seen from the calculations above that this Emergency response is similar to the case *C*3 in the case library, so that the emergency resource demand prediction results of this Emergency response are similar to that of the case *C*3. Consequently, the conclusions of prediction on this emergency resource demand can be drawn by correcting and adjusting

(10,000 peoples) 0.15 0.8 0.5 0.4 0.6

(10,000 yuan) 0.32 100 11 10.6 9 Stricken area (km2) 0.09 5 3 2 2

(day) 0.09 10 6 6 5 Similarity with current case 0.36 0.66 0.86 0.66

**4.2 Case study – Application of multi-stage location planning model in optimizing** 

In this section, the author makes an optimization of location planning of emergency resource base stations in City T according to the specific circumstances of City T. City T has jurisdiction over 15districts including Heping, Hedong, Nankai, Hexi, Hebei, Hongqiao, Tanggu, Hangu, Dagang, Dongli, Xiqing, Jinnan, Beichen, Wuqing, Baodi, and 3 counties such as Jinghai, Ninghe and Jixian.. The distribution of major districts and counties (the six districts including Heping, Hedong, Nankai, Hexi, Hebei, Hongqiao are called as a unified

**each attribute Case 1 Case 2 Case 3 Case 4** 

large Large Large Large

the emergency resource demand analysis results of the case *C*3.

Disaster intensity 0.35 Extra

Table 3. Characteristic Factor Information of each Case.

**location of emergency resource base stations** 

**Attribute No. Weight of** 

It can be calculated that =0.68, =0.68, =0.7, =0.65 and =0.65, further it can be obtained that =0.192, =0.083, =0.173,

( )**<sup>1</sup>** 

=0.05 and =0.05.

( )**<sup>5</sup>** *b*

each case is ordered as follows:

Disaster-affected population

Direct economic losses

Duration time of disaster

urban) is shown in Figure 5.

(28)

*b* ( )**<sup>4</sup>**

*b*

Given that the city T plans to conduct a prediction on the demand of emergency resource when the earthquake occurs, and there are four cases for this type of Emergency response in the case library, expressing as *C*=(*C*1, *C*2, *C*3, *C*4), and each case includes the demand information of quantity, quality and type of corresponding emergency resource, as shown in Table 2.


Table 2. Simplified Instance of Case Information Library.

Given that the emergency rescue plans for this type of Emergency response are the same. Through the risk analysis, five characteristic factors reflecting the characteristics of Emergency response are selected, meaning that the characteristic factor set B is composed of hazard intensity, disaster-affected population, direct economic losses, stricken area and duration time of disaster, and the membership function of four cases to five characteristic factors is as follows respectively:

$$\begin{aligned} n\_{C\_1}(b) &= \frac{0.8}{b\_1} + \frac{0.7}{b\_2} + \frac{0.4}{b\_3} + \frac{0.3}{b\_4} + \frac{0.6}{b\_5} \\ n\_{C\_2}(b) &= \frac{0.6}{b\_1} + \frac{0.6}{b\_2} + \frac{0.8}{b\_3} + \frac{0.9}{b\_4} + \frac{0.7}{b\_5} \\ n\_{C\_3}(b) &= \frac{0.4}{b\_1} + \frac{0.6}{b\_2} + \frac{0.8}{b\_3} + \frac{0.8}{b\_4} + \frac{0.6}{b\_5} \\ n\_{C\_4}(b) &= \frac{0.9}{b\_1} + \frac{0.8}{b\_2} + \frac{0.8}{b\_3} + \frac{0.8}{b\_4} + \frac{0.7}{b\_5} \end{aligned} \tag{27}$$

Given that an Emergency response occurs now, and it needs to conduct a prediction on its emergency resource demands. Given that the emergency resource demand prediction plan for this Emergency response expressed as T, and its membership function can expressed as the formula below:

Given that the city T plans to conduct a prediction on the demand of emergency resource when the earthquake occurs, and there are four cases for this type of Emergency response in the case library, expressing as *C*=(*C*1, *C*2, *C*3, *C*4), and each case includes the demand information of quantity, quality and type of corresponding emergency resource, as shown in

**quantity** 

Instant noodle 140,000 Excellent Quilt 100,000 Excellent Cotton dress 100,000 Excellent

Stretcher 5000 Excellent Tent 150,000 Excellent Food 200,000 kg Excellent

Cloth 120,000 Excellent Drinking water 200,000 kg Excellent Fresh vegetables 150,000 kg Excellent

Given that the emergency rescue plans for this type of Emergency response are the same. Through the risk analysis, five characteristic factors reflecting the characteristics of Emergency response are selected, meaning that the characteristic factor set B is composed of hazard intensity, disaster-affected population, direct economic losses, stricken area and duration time of disaster, and the membership function of four cases to five characteristic

..... ( )

**12345**

*bbbbb*

**06 06 08 09 07**

**08 07 04 03 06**

**12345**

*bbbbb*

**04 06 08 08 06**

**12345**

*bbbbb*

**09 08 08 08 07**

**12345**

*bbbbb*

..... ( )

..... ( )

..... ( )

Given that an Emergency response occurs now, and it needs to conduct a prediction on its emergency resource demands. Given that the emergency resource demand prediction plan for this Emergency response expressed as T, and its membership function can expressed as

Tent 100,000 Excellent Clean water 150,000kg Excellent Blood plasma 2000 ml Excellent

**Emergency resource quality** 

(27)

**Case Emergency resource type Emergency resource** 

Table 2. Simplified Instance of Case Information Library.

**1**

*n b*

*C*

**2**

*n b*

*C*

**3**

*n b*

*C*

**4**

*n b*

*C*

factors is as follows respectively:

the formula below:

Table 2.

*C*1

*C*2

*C*3

*C*4

$$m\_{\tau}(b) = \frac{\mathbf{0.5}}{b\_1} + \frac{\mathbf{0.7}}{b\_2} + \frac{\mathbf{0.7}}{b\_3} + \frac{\mathbf{0.8}}{b\_4} + \frac{\mathbf{0.6}}{b\_5} \tag{28}$$

It can be calculated that =0.68, =0.68, =0.7, =0.65 and =0.65, further it can be obtained that =0.192, =0.083, =0.173, =0.05 and =0.05. ( ) *n b***<sup>1</sup>** ( ) *n b***<sup>2</sup>** ( ) *n b***<sup>3</sup>** ( ) *n b***<sup>4</sup>** ( ) *n b***<sup>5</sup>** ( )**<sup>1</sup>** *b* ( )**<sup>2</sup>** *b* ( )**<sup>3</sup>** *b* ( )**<sup>4</sup>** *b* ( )**<sup>5</sup>** *b*

Therefore, the weight value of each characteristic factor can be calculated as follows: *w*1=0.35, *w*2=0.15, *w*3=0.32, *w*4=0.09 and *w*5=0.09. According to the similarity calculation method, the similarity of each case is calculated as follows: *sim*(*T*, *C*1)=0.36, *sim*(*T*, *C*2)=0.66, *sim*(*T*,*C*3)=0.86 and *sim*(*T*, *C*4)=0.66. All above are shown in Table 2, and the similarity of each case is ordered as follows:

$$
\sim \text{sim}(T, \text{C}\_1) < \sim \text{sim}(T, \text{C}\_2) = \text{sim}(T, \text{C}\_4) < \sim \text{sim}(T, \text{C}\_5) \tag{29}
$$

It can be seen from the calculations above that this Emergency response is similar to the case *C*3 in the case library, so that the emergency resource demand prediction results of this Emergency response are similar to that of the case *C*3. Consequently, the conclusions of prediction on this emergency resource demand can be drawn by correcting and adjusting the emergency resource demand analysis results of the case *C*3.


Table 3. Characteristic Factor Information of each Case.

#### **4.2 Case study – Application of multi-stage location planning model in optimizing location of emergency resource base stations**

In this section, the author makes an optimization of location planning of emergency resource base stations in City T according to the specific circumstances of City T. City T has jurisdiction over 15districts including Heping, Hedong, Nankai, Hexi, Hebei, Hongqiao, Tanggu, Hangu, Dagang, Dongli, Xiqing, Jinnan, Beichen, Wuqing, Baodi, and 3 counties such as Jinghai, Ninghe and Jixian.. The distribution of major districts and counties (the six districts including Heping, Hedong, Nankai, Hexi, Hebei, Hongqiao are called as a unified urban) is shown in Figure 5.

Theories and Methods for the Emergency Rescue System 143

The 15 administrative districts are respectively defined in Table 5. To divide the distances by

district Tanggu Hangu Dagang Dongli Xiqing Jinnan Beichen Wuqing Baodi Jixian Ninghe Jinghai A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13

(min) Urban Tanggu Hangu Dagang Dongli Xiqing Jinnan Beichen Wuqing Baodi Jixian Ninghe Jinghai Urban 0 29.48 39.75 27.23 7.28 12.98 15.23 9.98 24.23 50.25 78.23 42.75 23.78 Tanggu 29.48 0 20.78 19.50 22.50 42.53 17.48 36.98 48.98 61.28 86.48 27.00 47.48 Hangu 39.75 20.78 0 45.53 38.03 51.98 34.28 43.50 50.48 45.75 71.25 6.53 62.48 Dagang 27.23 19.50 45.53 0 21.53 36.98 12.98 36.98 51.23 72.53 99.53 45.98 35.03 Dongli 7.28 22.50 34.50 21.53 0 20.03 9.00 16.28 30.00 52.50 80.03 38.03 27.98 Xiqing 12.98 42.53 51.98 36.98 20.03 0 27.00 9.98 20.03 51.53 79.50 54.00 18.00 Jinnan 15.23 17.48 34.28 12.98 9.00 27.00 0 24.53 38.78 60.00 87.53 39.00 30.00 Beichen 9.98 36.98 43.50 36.98 16.28 9.98 24.53 0 14.48 40.50 71.03 45.00 27.00 Wuqing 24.23 48.98 50.48 51.23 30.00 20.03 38.78 14.48 0 33.00 60.00 50.03 37.50 Baodi 50.25 61.28 50.48 72.53 52.50 51.53 60.00 40.50 33.00 0 27.98 45.75 69.53 Jixian 78.23 86.48 71.25 99.53 80.03 79.50 87.53 71.03 60.00 27.98 0 65.48 97.50 Ninghe 42.75 27.00 6.53 45.98 38.03 54.00 39.00 45.00 50.03 45.75 65.48 0 66.00 Jinghai 23.78 47.48 62.48 35.03 27.98 18.00 30.00 27.00 37.50 69.53 97.50 66.00 0

Table 7-9 show the minimum numbers of emergency resource base stations covering all the administrative districts and specific sites, in the case of that emergency response time

Table 6. The travel times between centers of various administrative districts.

the speed of 80km / h, the travel times are listed in Table 6.

Table 5. Signs of various administrative districts.

standards are 30min, 45min and 60min respectively.

District Districts within a 30-min drive A1 A2,A4,A5,A6,A7,A8,A9,A13 A2 A1,A3,A4,A5,A7,A12

A5 A1,A2,A4,A6,A7,A8,A9,A13 A6 A1,A5,A7,A8,A9,A13 A7 A1,A2,A4,A5,A6,A8,A13 A8 A1,A5,A6,A7,A9,A13 A9 A1,A5,A6,A8,

A3 A2,A12 A4 A1,A2,A5,A7

A10 A11 A11 A10 A12 A2,A3

1. When the emergency response time standard is set as 30min

Table 7. The coverage for different administrative districts in T=30min.

Using WinQSB to find the solution of set covering model, the optimal solution of z = 4 is obtained, that is, to cover all demand sites, four emergency resource base stations are

Urban

Time

Fig. 5. Administrative Map of City T.

For the sake of computational convenience, and the visual presentation method, in this paper, distances between these administrative districts are presented with straight-line distances, and the central areas of these administrative districts with high concentration of population are determined as the ends of distance calculations, Table 4 shows the straight-line distances between these districts and the population distribution of various administrative districts.


Table 4. The straight-line distances between centers of various administrative districts.

For the sake of computational convenience, and the visual presentation method, in this paper, distances between these administrative districts are presented with straight-line distances, and the central areas of these administrative districts with high concentration of population are determined as the ends of distance calculations, Table 4 shows the straight-line distances between these districts and the population distribution of various administrative districts.

district 0 39.3 53 36.3 9.7 17.3 20.3 13.3 32.3 67 104.3 57 31.7 Tanggu 39.3 0 27.7 26 30 56.7 23.3 49.3 65.3 81.7 115.3 36 63.3 Hangu 53 27.7 0 60.7 50.7 69.3 45.7 58 67.3 61 95 8.7 83.3 Dagang 36.3 26 60.7 0 28.7 49.3 17.3 49.3 68.3 96.7 132.7 61.3 46.7 Dongli 9.7 30 46 28.7 0 26.7 12 21.7 40 70 106.7 50.7 37.3 Xiqing 17.3 56.7 69.3 49.3 26.7 0 36 13.3 26.7 68.7 106 72 24 Jinnan 20.3 23.3 45.7 17.3 12 36 0 32.7 51.7 80 116.7 52 40 Beichen 13.3 49.3 58 49.3 21.7 13.3 32.7 0 19.3 54 94.7 60 36 Wuqing 32.3 65.3 67.3 68.3 40 26.7 51.7 19.3 0 44 80 66.7 50 Baodi 67 81.7 67.3 96.7 70 68.7 80 54 44 0 37.3 61 92.7 Jixian 104.3 115.3 95 132.7 106.7 106 116.7 94.7 80 37.3 0 87.3 130 Ninghe 57 36 8.7 61.3 50.7 72 52 60 66.7 61 87.3 0 88 Jinghai 31.7 63.3 83.3 46.7 37.3 24 40 36 50 92.7 130 88 0

(10000) 389 45 17 32 30.4 31 42 34 82 65 78 36 50

Table 4. The straight-line distances between centers of various administrative districts.

district Tanggu Hangu Dagang Dongli Xiqing Jinnan Beichen Wuqing Baodi Jixian Ninghe Jinghai

Fig. 5. Administrative Map of City T.

Distance (km)

Urban

Population

Urban

The 15 administrative districts are respectively defined in Table 5. To divide the distances by the speed of 80km / h, the travel times are listed in Table 6.


Table 5. Signs of various administrative districts.


Table 6. The travel times between centers of various administrative districts.

Table 7-9 show the minimum numbers of emergency resource base stations covering all the administrative districts and specific sites, in the case of that emergency response time standards are 30min, 45min and 60min respectively.


1. When the emergency response time standard is set as 30min

Table 7. The coverage for different administrative districts in T=30min.

Using WinQSB to find the solution of set covering model, the optimal solution of z = 4 is obtained, that is, to cover all demand sites, four emergency resource base stations are

Theories and Methods for the Emergency Rescue System 145

When p = 1, the solution is A8 = 1, Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y9 = Y10 = Y12 = Y13 = 1, z = 819.4, it means that if a emergency resource base station is build in Beichen, it can cover the urban district, Tanggu, Hangu and Dagang, Dongli, Xiqing, Jinnan, Wuqing, Baodi, Ninghe and Jinghai within 45min, the total number of the population in these

When p = 2, the solution is A8 = A10 = 1, Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = Y9 = Y10 = Y11 = Y12 = Y13 = 1, z = 931.4, it means that if two emergency resource base stations are built in Beichen and Baodi respectively, they can cover all the administrative regions in 45-

min, the total number of the population in these districts is 9.314 million.

**District Districts within a 60-min drive** 

A10 A1,A3,A5,A6,A7,A8,A9,A11,A12

A12 A1,A2,A3,A4,A5,A6,A7,A8,A9,A10

Through the same calculation process as above, the optimal solution of z = 2 is obtained, that is, to cover all demand sites, two emergency resource base stations are necessary. Then using MCLP model and having the p-value increase continuously from 1 to 2, using

When p = 1, the solution is A9 = 1, Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = Y10 = Y11 = Y12 = Y13 = 1, z = 849.4, it means that if a emergency resource base station is build in Wuqing, it can cover the urban district, Tanggu, Hangu, Dagang, Dongli, Xiqing, Jinnan, Beichen, Baodi, Jixian County, Ninghe and Jinghai within 60min, the total number of the population

When p = 2, the solution is A2 = A9 = 1, Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = Y9 = Y10 = Y11 = Y12 = Y13 = 1, z = 931.4, it means that if two emergency resource base stations are built in Tanggu and Wuqing respectively, they can cover all the administrative regions in 60

A11 A9,A10

WinQSB, solution of the model can be obtained as follows:

in these districts is 8.494 million.

Table 9. The coverage for different administrative districts in T=60min.

min, the total number of the population in these districts is 9.314 million.

A1 A2,A3,A4,A5,A6,A7,A8,A9,A10,A12,A13 A2 A1,A3,A4,A5,A6,A7,A8,A9,A12,A13 A3 A1,A2,A4,A5,A6,A7,A8,A9,A10,A12 A4 A1,A2,A3,A5,A6,A7,A8,A9,A12,A13 A5 A1,A2,A3,A4,A6,A7,A8,A9,A10,A12,A13 A6 A1,A2,A3,A4,A5,A7,A8,A9,A10,A12,A13 A7 A1,A2,A3,A4,A5,A6,A8,A9,A10,A12,A13 A8 A1,A2,A3,A4,A5,A6,A7,A9,A10,A12,A13 A9 A1,A2,A3,A4,A5,A6,A7,A8,A10,A11,A12,A13

3. When the emergency response time standard is set as 60 min

districts is 8.194 million.

necessary. Then using MCLP model, and having the p-value increase continuously from 1 to 4, using WinQSB, solution of the model can be obtained as follows:

When p = 1, the solution is: A5 = 1, Y1 = Y2 = Y4 = Y6 = Y7 = Y8 = Y9 = Y13 = 1, z = 705, it means that if an emergency resource base station is built in the Dongli District, it can cover the urban district, Tanggu, Dagang, Xiqing, Jinnan, Beichen, Wuqing and Jinghai in 30 minutes, the total number of the population in these districts is 7.05 million.

When p = 2, the solution is: A1 = A2 = 1, Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = Y9 = Y12 = Y13 = 1, z = 788.4, it means that if two emergency resource base stations are built in the urban district and Tanggu respectively, they can cover the urban district, Tanggu, Hangu, Dagang,Dongli, Xiqing, Jinnan, Beichen, Wuqing, Ninghe and Jinghai in 30 minutes, the total number of the population in these districts is 7.884 million.

When p = 3, the solution is A1 = A2 = A10 = 1, Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = Y9 = Y11 = Y12 = Y13 = 1, z = 866.4, it means that if two emergency resource base stations are built in the urban district, Tanggu and Baidi respectively, they can cover the urban district, Tanggu, Hangu, Dagang, Dongli, Xiqing, Jinnan, Beichen, Wuqing, Jixian County, Ninghe and Jinghai in 30 minutes, the total number of the population in these districts is 8.664 million.

When p = 4, the solution is A2 = A5 = A10 = A11 = 1, Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = Y9 = Y10 = Y11 = Y12 = Y13 = 1, z = 931.4, it means that if four emergency resource base stations are built in Tanggu,Dongli, Baidi and Jixian County respectively, they can cover all administrative districts in 30min, the total number of the population in these districts is 9.314 million.


2. When the emergency response time standard is set as 45min

Table 8. The coverage for different administrative districts in T=45min.

Through the same calculation process as above, the optimal solution of z = 2 is obtained, that is, to cover all demand sites, two emergency resource base stations are necessary. Then using MCLP model and having the p-value increase continuously from 1 to 2, using WinQSB, solution of the model can be obtained as follows:

necessary. Then using MCLP model, and having the p-value increase continuously from 1 to

When p = 1, the solution is: A5 = 1, Y1 = Y2 = Y4 = Y6 = Y7 = Y8 = Y9 = Y13 = 1, z = 705, it means that if an emergency resource base station is built in the Dongli District, it can cover the urban district, Tanggu, Dagang, Xiqing, Jinnan, Beichen, Wuqing and Jinghai in 30

When p = 2, the solution is: A1 = A2 = 1, Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = Y9 = Y12 = Y13 = 1, z = 788.4, it means that if two emergency resource base stations are built in the urban district and Tanggu respectively, they can cover the urban district, Tanggu, Hangu, Dagang,Dongli, Xiqing, Jinnan, Beichen, Wuqing, Ninghe and Jinghai in 30 minutes, the

When p = 3, the solution is A1 = A2 = A10 = 1, Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = Y9 = Y11 = Y12 = Y13 = 1, z = 866.4, it means that if two emergency resource base stations are built in the urban district, Tanggu and Baidi respectively, they can cover the urban district, Tanggu, Hangu, Dagang, Dongli, Xiqing, Jinnan, Beichen, Wuqing, Jixian County, Ninghe and Jinghai in 30 minutes, the total number of the population in these districts is 8.664

When p = 4, the solution is A2 = A5 = A10 = A11 = 1, Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = Y9 = Y10 = Y11 = Y12 = Y13 = 1, z = 931.4, it means that if four emergency resource base stations are built in Tanggu,Dongli, Baidi and Jixian County respectively, they can cover all administrative districts in 30min, the total number of the population in these districts is

4, using WinQSB, solution of the model can be obtained as follows:

total number of the population in these districts is 7.884 million.

2. When the emergency response time standard is set as 45min

District Districts within a 45-min drive A1 A2,A3,A4,A5,A6,A7,A8,A9,A12,A13 A2 A1,A3,A4,A5,A6,A7,A8,A12 A3 A1,A2,A5,A7,A8,A12 A4 A1,A2,A5,A6,A7,A8,A13 A5 A1,A2,A3,A4,A6,A7,A8,A9,A12,A13 A6 A1,A2,A4,A5,A7,A8,A9,A13 A7 A1,A2,A3,A4,A5,A6,A8,A9,A12,A13 A8 A1,A2,A3,A4,A5,A6,A7,A9,A10,A12,A13 A9 A1,A5,A6,A7,A8,A10,A13 A10 A8,A9,A11,A13 A11 A10

A12 A1,A2,A3,A5,A7,A8 Table 8. The coverage for different administrative districts in T=45min.

WinQSB, solution of the model can be obtained as follows:

Through the same calculation process as above, the optimal solution of z = 2 is obtained, that is, to cover all demand sites, two emergency resource base stations are necessary. Then using MCLP model and having the p-value increase continuously from 1 to 2, using

million.

9.314 million.

minutes, the total number of the population in these districts is 7.05 million.

When p = 1, the solution is A8 = 1, Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y9 = Y10 = Y12 = Y13 = 1, z = 819.4, it means that if a emergency resource base station is build in Beichen, it can cover the urban district, Tanggu, Hangu and Dagang, Dongli, Xiqing, Jinnan, Wuqing, Baodi, Ninghe and Jinghai within 45min, the total number of the population in these districts is 8.194 million.

When p = 2, the solution is A8 = A10 = 1, Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = Y9 = Y10 = Y11 = Y12 = Y13 = 1, z = 931.4, it means that if two emergency resource base stations are built in Beichen and Baodi respectively, they can cover all the administrative regions in 45 min, the total number of the population in these districts is 9.314 million.


3. When the emergency response time standard is set as 60 min

Table 9. The coverage for different administrative districts in T=60min.

Through the same calculation process as above, the optimal solution of z = 2 is obtained, that is, to cover all demand sites, two emergency resource base stations are necessary. Then using MCLP model and having the p-value increase continuously from 1 to 2, using WinQSB, solution of the model can be obtained as follows:

When p = 1, the solution is A9 = 1, Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = Y10 = Y11 = Y12 = Y13 = 1, z = 849.4, it means that if a emergency resource base station is build in Wuqing, it can cover the urban district, Tanggu, Hangu, Dagang, Dongli, Xiqing, Jinnan, Beichen, Baodi, Jixian County, Ninghe and Jinghai within 60min, the total number of the population in these districts is 8.494 million.

When p = 2, the solution is A2 = A9 = 1, Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = Y9 = Y10 = Y11 = Y12 = Y13 = 1, z = 931.4, it means that if two emergency resource base stations are built in Tanggu and Wuqing respectively, they can cover all the administrative regions in 60 min, the total number of the population in these districts is 9.314 million.

Theories and Methods for the Emergency Rescue System 147

1. Suppose that the emergency response process can be divided into 4 stages, namely 4

2. The emergency resource allocation objective at each stage is Lk , and the total emergency objective is expressed as formula (7) when the emergency stage reaches

4. Suppose that in the available allocation scheme, the emergency resource amount

provided for each emergency zone changes from 2 to 4, namely k 2u 4 ; 5. In that case, formula x(k 1) f(x(k),u(k),w(k)) can be written as k1 k k x ux ;

N 1

k

k1 k1 <sup>k</sup> 2u 4 k 1

J (x ) min L

k

Emergency resource amount Risk value of zones

N

x(k) 12

;

k 1

2 20 31 27 38 3 16 26 25 35 4 11 21 23 33

k1 k1 k1 k1 k k 2u 4

The optimized emergency resource allocation is calculated under the supposed scene of accidents with the mathematical mode of optimized emergency resource allocation, so as to

For the risk zone A, alternative resource allocation decision is 2-4, corresponding total risk value is from 20 to 11, so risks can be minimized to 11 with the decision 4 in the risk zone A (Table 11). The optimized decision scheme of zones B, C and D can be obtained with the same method (Table 12-14). Under 4 dangerous scenes, optimized allocation of limited resources is 4 in zone A, 4 in zone B, 2 in zone C and 2 in zone D, thus the total risk value is reduced to 97.

Corresponding risk value of zone A at the first stage of the

23 4 2 20+0 - - 20 3 20+0 16+0 - 16 4 20+0 16+0 11+0 11 Note: *x1* is the corresponding amount of resource demand under each resource allocation decision at the first stage; min∑*L1* is the minimum risk value corresponding to different decisions at the first stage. Table 11. Resource allocation strategies and corresponding risk value of zone A (the first

min (L (x ,u ,w ) J (x ))

resource allocation strategy u1 min∑L1

A B C D

emergency zones, i.e. k 1,2,3,4 ;

3. There is only one state variable x(k) in the example, and

Table 10. Emergency resource amount and the risk value of zones.

6. Parameters are substituted into formula (8) to obtain

0 1

 

 

obtain the optimized allocation result.

x1

stage).

J (x ) 0

k 1 ;

#### 4. Analysis of the result

Fig. 6. Results Map of City T.

Comparing the above results under the three emergency response time standards, we can find that:


#### **4.3 Case study – Appropriate allocation of emergency resources**

It is supposed that there are 4 dangerous emergency zones in the emergency process, namely N 4 ; total available amount of emergency resources is 12, namely X 12 , and X represents the total amount of available resources. Risk value when each scene is allocated with different amounts of emergency resources is listed in Table 10.

Emergency resources are dispatched according to the emergency resource allocation model, so as to achieve the optimization objective of minimizing the sum of risk values at various emergency zones in the following processing steps:

30min 45min 60min

Comparing the above results under the three emergency response time standards, we can

1. Though the solutions of set covering model and maximum coverage model, it is found that within the area of a 30-min drive(response time standard), four emergency resource base stations are the most reasonable and can meet the demand, and when the number of base stations is less than 4, the emergency demand can not be met, and when the number is more than 4, unnecessary waste and redundant coverage will be made, and through MCLP model, the construction site of the four base stations can be

2. When the emergency response time standards are set as 45min and 60min, the result shows a maximum of two emergency resources is enough to cover all administrative regions of City T, but for different time standards, the base stations should be built in different districts, when the time standard is 45min, they should be built in Beichen and Baodi, and when the time standard is 60min, they should be built in Tanggu and Wuqing. 3. Because this result is obtained through simplifying the actual problems appropriately, can provide a reference for the actual decision-making, but there may be some errors, so

the research of planning method more precise and close to the actual is required.

It is supposed that there are 4 dangerous emergency zones in the emergency process, namely N 4 ; total available amount of emergency resources is 12, namely X 12 , and X represents the total amount of available resources. Risk value when each scene is allocated

Emergency resources are dispatched according to the emergency resource allocation model, so as to achieve the optimization objective of minimizing the sum of risk values at various

**4.3 Case study – Appropriate allocation of emergency resources** 

with different amounts of emergency resources is listed in Table 10.

emergency zones in the following processing steps:

4. Analysis of the result

Fig. 6. Results Map of City T.

find that:

determined as Tanggu, Dongli, Baodi and Jixian.



Table 10. Emergency resource amount and the risk value of zones.


$$\begin{cases} \mathbf{J}\_{\mathbf{k}+1}(\mathbf{x}\_{\mathbf{k}+1}) = \min\_{2 \le \mathbf{u}\_{\mathbf{k}} \le 4} \sum\_{\mathbf{k}=1}^{N-1} \mathbf{L}\_{\mathbf{k}} = \\ \min\_{2 \le \mathbf{u}\_{\mathbf{k}} \le 4} \left( \mathbf{L}\_{\mathbf{k}+1}(\mathbf{x}\_{\mathbf{k}+1}, \mathbf{u}\_{\mathbf{k}+1}, \mathbf{w}\_{\mathbf{k}+1}) + \mathbf{J}\_{\mathbf{k}}(\mathbf{x}\_{\mathbf{k}}) \right) \\ \mathbf{J}\_{0}(\mathbf{x}\_{1}) = 0 \end{cases}$$

The optimized emergency resource allocation is calculated under the supposed scene of accidents with the mathematical mode of optimized emergency resource allocation, so as to obtain the optimized allocation result.

For the risk zone A, alternative resource allocation decision is 2-4, corresponding total risk value is from 20 to 11, so risks can be minimized to 11 with the decision 4 in the risk zone A (Table 11). The optimized decision scheme of zones B, C and D can be obtained with the same method (Table 12-14). Under 4 dangerous scenes, optimized allocation of limited resources is 4 in zone A, 4 in zone B, 2 in zone C and 2 in zone D, thus the total risk value is reduced to 97.


Note: *x1* is the corresponding amount of resource demand under each resource allocation decision at the first stage; min∑*L1* is the minimum risk value corresponding to different decisions at the first stage.

Table 11. Resource allocation strategies and corresponding risk value of zone A (the first stage).

Theories and Methods for the Emergency Rescue System 149

In order to validate the dynamic optimization process of emergency resource scheduling of sudden public events with the Markov decision process, here the rationality and practicability of dynamic optimization method of emergency resource scheduling based on the Markov decision process is proved through analysis and explanation by examples.

Now it is supposed that an earthquake disaster takes place in a city, which is likely to cause two secondary disasters *S1* and *S2*, namely the state space of this earthquake disaster is S {S ,S } 1 2 . where, *S1* and *S2* represent the initial event *S*, namely secondary accidents are

Then it is supposed that only one emergency resource *R* is required in emergency of this sudden public event, and the emergency time standard *T* is 2 time units. So long as enough amounts of emergency resources is transported to sudden public event sites within the standard time under the state of an event, then the sudden public event can be under control. If the amount of resource *R* transported to the scene of accident is insufficient, then the sudden public event can only be partially controlled (expressed as the availability of the emergency resources *a*), and the range of values of *a* is 0%~100%. It is also supposed that the relationship between the demand and the availability of the emergency resource *R* is shown

State *S* Demand of the emergency resource *R* Availability *a*/%

Table 15. Relationship between the demand and the availability of the resources under

It is supposed that 4 emergency resource sites around the sudden public events can cover this event site in 2 time units, as shown in Figure 7. As can be seen from the Figure 7, only the site A is in 1 time unit, while the site B is in the space of 1.5 time units, and both the site C and site D are in 2 time units. The amount of stored emergency resources at each site is

Now it is stipulated that the emergency satisfaction is defined as the emergency success. Under the circumstances, the emergency resource site A is closest to the scene of accident *X*, therefore it is necessary to choose the site A, so as to satisfy the shortest emergency time. When the accident is under the state of *S1*, 80 units of emergency resource *R* are transported from the emergency resource site A to the event site *X*, so the availability of the resources is only 80% under the state of *S1*, which is unable to completely satisfy the emergency demand. Under the circumstances, it is necessary to be supported by the sites B, C and D. When the sudden public event is under the state of *S1*, 40 units of emergency resources can be transported from the emergency resource sites B, C and D to the site *X*, so that the total

120 100 80 80

200 100 120 80 80 40

**4.4 Case study – Optimal dispatching of emergency resources** 

likely to be obtained from evolution of the earthquake disasters.

in Table 15.

*S1*

*S2*

different states of *S.*

also shown in the Figure 7.


Note: *x2* is the corresponding amount of resource demand under each resource allocation decision at the second stage; min∑*L2* is the minimum risk value corresponding to different decisions at the second stage.

Table 12. Resource allocation strategies and corresponding risk value of zone B (the second stage).


Note: *x3* is the corresponding amount of resource demand under each resource allocation decision at the third stage; min∑*L3* is the minimum risk value corresponding to different decisions at the third stage. Table 13. Resource allocation strategies and corresponding risk value of zone C (the third stage).


Note: *x*4 is the corresponding amount of resource demand under each resource allocation decision at the fourth stage; min∑*L*4 is the minimum risk value corresponding to different decisions at the fourth stage.

Table 14. Resource allocation strategies and corresponding risk value of zone D (the fourth stage).

allocation strategy u2 min∑L2

allocation strategy u3 min∑L3

allocation strategy u4 min∑L4

Corresponding risk value of zone B at the second stage of the resource

2 3 4

4 31+20 - - 51

5 31+16 26 + 20 - 46

6 31+11 26 + 16 21+20 42

7 31+11 26 + 11 21+16 37

8 31+11 26+ 11 21+11 32

Note: *x2* is the corresponding amount of resource demand under each resource allocation decision at the second stage; min∑*L2* is the minimum risk value corresponding to different decisions at the second

Table 12. Resource allocation strategies and corresponding risk value of zone B (the second

Corresponding risk value of zone C at the third stage of the resource

2 3 4

8 27 + 42 25 + 46 23 + 51 69

9 27 + 37 25 + 42 23+46 64

10 27 + 32 25 + 37 23+42 59

Corresponding risk value of zone D at the fourth stage of the resource

2 3 4

12 38 + 59 35 + 64 33 + 69 97

Note: *x*4 is the corresponding amount of resource demand under each resource allocation decision at the fourth stage; min∑*L*4 is the minimum risk value corresponding to different decisions at the fourth stage. Table 14. Resource allocation strategies and corresponding risk value of zone D (the fourth

Note: *x3* is the corresponding amount of resource demand under each resource allocation decision at the third stage; min∑*L3* is the minimum risk value corresponding to different decisions at the third stage. Table 13. Resource allocation strategies and corresponding risk value of zone C (the third

x2

stage.

stage).

x3

stage).

x4

stage).

#### **4.4 Case study – Optimal dispatching of emergency resources**

In order to validate the dynamic optimization process of emergency resource scheduling of sudden public events with the Markov decision process, here the rationality and practicability of dynamic optimization method of emergency resource scheduling based on the Markov decision process is proved through analysis and explanation by examples.

Now it is supposed that an earthquake disaster takes place in a city, which is likely to cause two secondary disasters *S1* and *S2*, namely the state space of this earthquake disaster is S {S ,S } 1 2 . where, *S1* and *S2* represent the initial event *S*, namely secondary accidents are likely to be obtained from evolution of the earthquake disasters.

Then it is supposed that only one emergency resource *R* is required in emergency of this sudden public event, and the emergency time standard *T* is 2 time units. So long as enough amounts of emergency resources is transported to sudden public event sites within the standard time under the state of an event, then the sudden public event can be under control. If the amount of resource *R* transported to the scene of accident is insufficient, then the sudden public event can only be partially controlled (expressed as the availability of the emergency resources *a*), and the range of values of *a* is 0%~100%. It is also supposed that the relationship between the demand and the availability of the emergency resource *R* is shown in Table 15.


Table 15. Relationship between the demand and the availability of the resources under different states of *S.*

It is supposed that 4 emergency resource sites around the sudden public events can cover this event site in 2 time units, as shown in Figure 7. As can be seen from the Figure 7, only the site A is in 1 time unit, while the site B is in the space of 1.5 time units, and both the site C and site D are in 2 time units. The amount of stored emergency resources at each site is also shown in the Figure 7.

Now it is stipulated that the emergency satisfaction is defined as the emergency success. Under the circumstances, the emergency resource site A is closest to the scene of accident *X*, therefore it is necessary to choose the site A, so as to satisfy the shortest emergency time. When the accident is under the state of *S1*, 80 units of emergency resource *R* are transported from the emergency resource site A to the event site *X*, so the availability of the resources is only 80% under the state of *S1*, which is unable to completely satisfy the emergency demand. Under the circumstances, it is necessary to be supported by the sites B, C and D. When the sudden public event is under the state of *S1*, 40 units of emergency resources can be transported from the emergency resource sites B, C and D to the site *X*, so that the total

Theories and Methods for the Emergency Rescue System 151

The state transition probability of sudden public events can be obtained using the Domino effect analysis method, as shown in Table 17. This process is complex, so it is unnecessary to

(i) pi2

*Scheme I* 0.3 0.7 -10 -3 -5.1

*Scheme II* 0.8 0.2 -12 -11 -11.8

*Scheme III* 0.6 0.4 -9 -8 -8.6

*Scheme IV* 0.5 0.5 -4 -5 -4.5

There are two states in this case, and two decisions under each state, namely the scheduling schemes. <sup>1</sup> u(1) represents selecting the scheduling scheme I when the event is under the state

<sup>2</sup> u(1) represents selecting the scheduling scheme II when the event is under the state of

<sup>1</sup> u(2) represents selecting the scheduling scheme III when the event is under the state of

<sup>2</sup> u(2) represents selecting the scheduling scheme IV when the event is under the state of

q p r 0.3 ( 10) 0.7 ( 3) 5.1

scheduling scheme I under the state of *S1*, and select the scheduling scheme II under the

 1 12 2 12 v f 5.1 0.3f 0.7f v f 8.6 0.6f 0.4f ,

The third step is the strategy improvement program, in which the improvement strategy <sup>1</sup>

 .

In the second step, calculate the fixed value, and estimate the initial strategy

, likewise

0 (1) (1) u , <sup>1</sup>

2f 0 is obtained through solving the equations set.

Note: The reward uses emergency consumption time, and is negative as a consequence.

<sup>m</sup> <sup>1</sup> 1 ij ij j 1

In the first step, select the initial strategy <sup>0</sup> ; let <sup>1</sup>

f 2.69 , (0)

state of *S2*, then there is 0.3 0.7 <sup>P</sup> 0.6 0.4 , 5.1 <sup>Q</sup> 8.6

1

Decision Transition probability Reward Expected timely

 (i) i1 r

 (i) i2 r

reward

<sup>2</sup> q 11.8 <sup>1</sup> ,

0 (2) (2) u , that is, select the

(i) qi

go into details in this section.

<sup>K</sup> V (i) (i) (i) pi1

Table 17. The transition probability and reward.

The solution process is as follows:

Expected timely reward:

let 2f 0 , (0) v 6.99 , (0)

<sup>2</sup> q 4.5 <sup>2</sup> .

State *i*

*S1*

*S2*

of *S1*;

*S2*;

*S2*;

*S2*.

<sup>1</sup> q 8.6 <sup>2</sup> ,

is obtained.

accumulated amount achieves 120 units, and the amount of resources achieves the availability of 100%; but it is necessary to transport 120 units of resources from the sites B, C and D to the site *X* under the state of *S2*, so that the total accumulated amount achieves 200 units, and the availability achieves 100%.

Fig. 7. Distribution map of the emergency resources sites.

Therefore, the state space in this example is S {S ,S } 1 2 , the decision space can be expressed as the scheduling scheme, and the reward can be expressed as the cost or scheduling duration, as shown in Table 16.


Table 16. Statistical table of the transportation quantity and cost.

accumulated amount achieves 120 units, and the amount of resources achieves the availability of 100%; but it is necessary to transport 120 units of resources from the sites B, C and D to the site *X* under the state of *S2*, so that the total accumulated amount achieves 200

Therefore, the state space in this example is S {S ,S } 1 2 , the decision space can be expressed as the scheduling scheme, and the reward can be expressed as the cost or scheduling

each site 80 30 50 90 250

Transportation quantity 80 30 20 70 200

Cost 10 30 0 30 70

Cost 10 30 20 0 60

Cost 10 30 40 150 230

Transportation quantity 80 30 50 40 200 100% Cost 10 30 80 100 220

Scheme I Transportation quantity 80 30 0 10 120

Scheme II Transportation quantity 80 30 10 0 120

Site A Site B Site C Site D Total Availability

100%

100%

100%

units, and the availability achieves 100%.

Fig. 7. Distribution map of the emergency resources sites.

Table 16. Statistical table of the transportation quantity and cost.

duration, as shown in Table 16.

State *S1*

State *S2*

Scheme III

Scheme IV

Amount of stored emergency resources at



Note: The reward uses emergency consumption time, and is negative as a consequence.

Table 17. The transition probability and reward.

The solution process is as follows:

There are two states in this case, and two decisions under each state, namely the scheduling schemes. <sup>1</sup> u(1) represents selecting the scheduling scheme I when the event is under the state of *S1*; <sup>2</sup> u(1) represents selecting the scheduling scheme II when the event is under the state of *S2*; <sup>1</sup> u(2) represents selecting the scheduling scheme III when the event is under the state of *S2*; <sup>2</sup> u(2) represents selecting the scheduling scheme IV when the event is under the state of *S2*.

Expected timely reward: <sup>m</sup> <sup>1</sup> 1 ij ij j 1 q p r 0.3 ( 10) 0.7 ( 3) 5.1 , likewise <sup>2</sup> q 11.8 <sup>1</sup> , <sup>1</sup> q 8.6 <sup>2</sup> , <sup>2</sup> q 4.5 <sup>2</sup> .

In the first step, select the initial strategy <sup>0</sup> ; let <sup>1</sup> 0 (1) (1) u , <sup>1</sup> 0 (2) (2) u , that is, select the scheduling scheme I under the state of *S1*, and select the scheduling scheme II under the state of *S2*, then there is 0.3 0.7 <sup>P</sup> 0.6 0.4 , 5.1 <sup>Q</sup> 8.6 .

In the second step, calculate the fixed value, and estimate the initial strategy

$$\begin{cases} \mathbf{v} + \mathbf{f}\_1 = -5.1 + 0.3 \mathbf{f}\_1 + 0.7 \mathbf{f}\_2\\ \mathbf{v} + \mathbf{f}\_2 = -8.6 + 0.6 \mathbf{f}\_1 + 0.4 \mathbf{f}\_2 \end{cases}\_{\mathbf{v}}$$

let 2f 0 , (0) v 6.99 , (0) 1 f 2.69 , (0) 2f 0 is obtained through solving the equations set.

The third step is the strategy improvement program, in which the improvement strategy <sup>1</sup> is obtained.

Theories and Methods for the Emergency Rescue System 153

When we design an emergency rescue system, we need to coordinate the manpower with the financial, material resources. It is a complicated process to optimally allocate various elements within a system. It involves a wide range of contents. Repeated researches should be made on several theories and methods. Designing of an emergency rescue system covers the following four aspects which have been cross-linked each other essentially, that are 1) Demand Forecasting of Emergency Resources;2) Optimal Site Selection for the Base Station of Emergency Resources;3) Appropriate Allocation of Emergency Resources;4) Optimal Dispatching of Emergency Resources. Here, it proposed the overall and detailed methods to

In the future it is necessary to develop a computer system, so that these methods can adapt to the dynamic optimization process of emergency resource scheduling scheme under complex conditions such as many times of derivation and many kinds of resources etc., and

The authors appreciate the support of No.47 China's Postdoc Foundation(NO:20100470305)

[2] Bachant, J., & McDermott, J., (1984). R1 Revisited: Four years in the Trenches. *The AI* 

[3] Coenen, F. & Bench-Capon, T.J.M. (1992). Maintenance and Maintainability in Regulation Based Systems. *ICL Technical Journal*, May 1992, pp.76-84. [4] Watson, I.D., Basden, A. & Brandon, P.S. (1992a). The Client Centered Approach: Expert

[5] Watson, I.D., Basden, A. & Brandon, P.S. (1992b). The Client Centered Approach: Expert

[6] Watson, I.D., & Abdullah, S. (1994). Developing Case-Based Reasoning Systems: A Case

[8] Schank, R. (1982). *Dynamic memory: a theory of reminding and learning in computers and* 

[9] Kolodner, J. L. (1983a). Maintaining Organization in a Dynamic Long-Term Memory.

[10] Kolodner, J. L. (1983b). Reconstructive Memory: A Computer Model. *Cognitive Science*,

*Reasoning: Prospects for Applications*, Digest No: 1994/057, pp.1/1-1/3. [7] Schank, R.C. & Abelson, R.P. (1977). *Scripts, Plans, Goals and Understanding*. Erlbaum,

Study in Diagnosing Building Defects. In, Proc. *IEE Colloquium on Case-Based* 

[1] Clancey, W.J., (1985). Heuristic Classification. *Artificial Intelligence,* 27: pp289-350.

**5. Conclusion and future researches** 

it can more greatly satisfy the actual need.

and the national science foundation for the youth (NO:41105099).

System Development. *Expert Systems* 9(iv): pp.181-88.

System Maintenance. *Expert Systems* 9(iv): pp189-96..

*people*. Cambridge University Press, Cambridge, UK.

[11] Kolodner, J. L. (1993). *Case-Based Reasoning*. Morgan Kaufmann.

fulfill these four aspects.

**6. Acknowledgments** 

*Magazine,* 5(iii).

Hillsdale, New Jersey, US.

7(iv): pp.281-28.

*Cognitive Science*, 7(iv): pp.243-80.

**7. References** 

For the state *S1*, select a strategy (k) u1 , so as to maximize kk k (0) (0) q pf Pf 1 11 12 1 1 , that is

 5.1 0.3 2.69 0.7 0 2.69 6.99 11.8 0.8 2.69 0.2 0 2.69 12.388 

Select the strategy <sup>1</sup> u(1) . Scheme I is used for emergency resource scheduling under the state of *S1*.

For the state *S2*, select a strategy (k) u2 , so as to maximize kk k (0) (0) q pf pf 2 21 22 1 2 , that is 8.6 0.6 2.69 0.4 0 0 6.99 

Select the strategy <sup>2</sup> u(2) . Scheme IV is used for emergency resource scheduling under the state of *S2*.

4.5 0.5 2.69 0.5 0 3.15

The improvement strategy is obtained as <sup>1</sup> 1 (1) (1) u , <sup>2</sup> 1 (2) (2) u from the above computing results. The strategy 1 is different from <sup>0</sup> , so no optimized strategy is obtained and it is necessary to go on iteration.

The fourth step is fixed value operation for the purpose of obtaining (1) v , (1) 1f , (1) 2f

$$\begin{cases} \mathbf{v}^{(1)} + \mathbf{f}\_1^{(1)} = -\mathbf{5}.\mathbf{1} + \mathbf{0}.\mathbf{3}\mathbf{f}\_1^{(1)} + \mathbf{0}.\mathbf{7}\mathbf{f}\_2^{(1)}\\ \mathbf{v}^{(1)} + \mathbf{f}\_2^{(1)} = -\mathbf{4}.\mathbf{5} + \mathbf{0}.\mathbf{5}\mathbf{f}\_1^{(1)} + \mathbf{0}.\mathbf{5}\mathbf{f}\_2^{(1)} \end{cases}$$

Let (1) 2f 0 , then (1) v 4.75 , (1) 1 f 0.5 , (1) 2f 0 is obtained through solving the equations set.

In the fifth step, seek the improvement strategy <sup>2</sup> .

For the state *S1*, there is

$$\begin{cases} -5.1 + 0.3 \times (-0.5) + 0.7 \times 0 + 0.5 = -4.75\\ -11.8 + 0.8 \times (-0.5) + 0.2 \times 0 + 0.5 = -11.7 \end{cases}$$

So the strategy <sup>1</sup> u(1) is still taken.

For the state *S2*, there is

$$\begin{cases} -8.6 + 0.6 \times (-0.5) + 0.4 \times 0 - 0 = -8.9 \\ -4.5 + 0.5 \times (-0.5) + 0.5 \times 0 - 0 = -4.75 \end{cases}$$

So the strategy <sup>2</sup> u(2) is still taken.

As a result, <sup>1</sup> 1 (1) (1) u , <sup>2</sup> 1 (2) (2) u is obtained, which is exactly the same as the previous iteration results, so the optimized strategy is obtained as <sup>1</sup> . That is, take the scheduling scheme I when the sudden event is under the state of *S1*, and take the scheduling scheme IV when the sudden event is under the state of *S2*.
