**5. Economic criteria and cost‐benefit analysis**

Research and development in the field of electrical energy is not oriented to the production part only, but it should be achieved through management of transmission and distribution networks. Due to the volatility of renewable resources, their integration poses major stability problems in overall networks. It is important to emphasize that technological advances have certain inertia and uncertainties in the outcome. Compared to these two characteristics, it is highly useful to introduce an adequate method of cost/benefit analysis and the decision applicability following economic criteria in uncertain future.

Cost‐benefit analysis (CBA) incorporates many different aspects and interests of the involved parties in the decision of the investment strategy. In the traditional least cost planning method, the project with the lowest cost is selected. In that case, the overall cost involves operational, maintenance, and investment costs. However, this is only an economic criterion, and an energy production project might still not be able to provide satisfactory profit, as many parties are affected and during the project period the system configuration may change (e.g., increasing clean energy and decreasing fossil one, and vice versa). The proposed method will help select the project with a discounted benefit greater than its discounted cost, given as an indication of its profitability. It should be combined with the multi‐criteria analysis described earlier to provide satisfactory information for a confident solution. We propose a CBA that considers environmental, economic, and social benefits. The expression of these benefits turns around the rest of the difference between the revenues and the total costs. For economic criteria inspired from the game theory, there are a number of criteria for the analysis of game matrix and decision choice [17, 30].

In the Bayes‐Laplace criterion, a probability or a weight is associated with each scenario *i*. If the cost associated with scenario *i* for a strategy *j* is *Vij* and the probability of each scenario is *Qj* , then the selection is made as follows:

$$Z\_{BL} = \min\_{j} \sum\_{j} \mathcal{Q}\_{j} V\_{y} \tag{10}$$

In this economic criterion, each scenario is taken into account, and its importance is reflected through its probability of occurrence. The advantage of this criterion is that it leads to a risky decision.

In Laplace's criterion, the occurrence probabilities of scenarios are unknown, and the events are assumed equality probable. Laplace's criterion is processed as an optimal solution, minimizing the mathematical expectation of costs; its formulation is as follows:

**Figure 2.** An explicit hierarchy to determination of business electricity sustainability.

284 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

Research and development in the field of electrical energy is not oriented to the production part only, but it should be achieved through management of transmission and distribution networks. Due to the volatility of renewable resources, their integration poses major stability problems in overall networks. It is important to emphasize that technological advances have certain inertia and uncertainties in the outcome. Compared to these two characteristics, it is highly useful to introduce an adequate method of cost/benefit analysis and the decision

Cost‐benefit analysis (CBA) incorporates many different aspects and interests of the involved parties in the decision of the investment strategy. In the traditional least cost planning method, the project with the lowest cost is selected. In that case, the overall cost involves operational, maintenance, and investment costs. However, this is only an economic criterion, and an energy production project might still not be able to provide satisfactory profit, as many parties are affected and during the project period the system configuration may change (e.g., increasing clean energy and decreasing fossil one, and vice versa). The proposed method will help select the project with a discounted benefit greater than its discounted cost, given as an indication

**5. Economic criteria and cost‐benefit analysis**

applicability following economic criteria in uncertain future.

$$Z\_L = \min\_i \frac{1}{n} \sum\_j V\_y \tag{11}$$

The mini‐max decision rule is to seek decision makers' action, which minimize the maximum potential loss. A decision maker who uses the mini‐max criterion acts extremely conservative. He seeks the actions that achieve the best outcome under the worst scenario. The optimal solution is given as follows:

$$Z\_{mM} = \min\_{i} \max\_{j} \quad V\_{y} \tag{12}$$

The maxi‐min criterion, known as Wald one, describes a prudent attitude of a decision maker. Its objective involves the identification of a scenario leading to worse outcomes. A decision maker adopting this criterion tries to cover himself by providing the least bad possible result. This technique provides information that the evolution of the competition (scenarios) is detrimental to the company.

$$Z\_{Mm} = \max\_{i} \min\_{j} \ V\_{ij} \tag{13}$$

Adopting the Hurwitz criterion consists of the assessment for each strategy a weighted average of the worst and the best of its potential outcomes and choose the one for which the solution is the largest. According to this criterion, the solution is given as follows:

$$Z\_H = \min\_i \left[ \alpha. \max\_j (V\_{ij}) + (\mathbf{l} - \alpha). \min\_j (V\_{ij}) \right] \tag{14}$$

where 0≤*α* ≺1 is a parameter indicating planers' attitude toward risk. The value *α* =1 reduces Hurwitz' criterion to mini‐max criterion as described above and corresponds to an extremely pessimistic decision maker. The value *α* =0 corresponds to an extreme optimism.

### **6. Electricity sustainability development**

#### **6.1. Criteria and indicators**

This investigation was conducted to assist decision makers to understand the societal, economic, and environmental issues of the need for sustainable energy transition. The assumptions and models were summarized on the basis of existing data provided in the bibliographic references. They were submitted to experts to select those that meet the criteria of quality and relevance. The data used in this work are obtained from the statistical treatment and probabilistic modeling in the case where there are no archive data or a limited number available, with the help of expert judgments. Experts are energy service providers, politics oriented to research and development, specialists in the integration of renewable resources to networks, nuclear and nonrenewable energy scientists, researchers in risk analysis, and specialists in the management of energy‐related conflicts. Each expert group dealing with the issue of sustainable development can provide a range of economic, environmental, and social indicators. As noticed in the literature, economic and environmental indicators seem to be obvious and common to the overall society, but it is not the case for social ones. Certainly, the sources of conflicts and accidents in the energy field are not frequent looking to electricity, but the impact of nuclear component highlights the main concerns. They reside in the utilities dysfunction causing blackouts due to their high capacities of production and risk of contam‐ ination in the case of accidents (random or premeditated (sabotage)). As for sustainable development, electricity sustainability (ES) is based on the three known pillars such as social aspects, economic and environment criteria, and indicators noted (*Ci*) and their associated sub‐ criteria noted (*Cij*).

Environment (C1): Resources (C11; energy resources and mineral resources), Climate change (C12), Ecosystem damage (C13; impacts from normal operation and impacts from severe accidents), Waste (C14; chemical waste in underground depositories and radioactive waste in geological repositories).


#### **6.2 Case study application, simulation, and results**

Adopting the Hurwitz criterion consists of the assessment for each strategy a weighted average of the worst and the best of its potential outcomes and choose the one for which the solution

> a

ë û (14)

*<sup>H</sup>* min .max( ) (1 ).min( ) *ij ij i j <sup>j</sup> Z VV*

pessimistic decision maker. The value *α* =0 corresponds to an extreme optimism.

é ù <sup>=</sup> + - ê ú

where 0≤*α* ≺1 is a parameter indicating planers' attitude toward risk. The value *α* =1 reduces Hurwitz' criterion to mini‐max criterion as described above and corresponds to an extremely

This investigation was conducted to assist decision makers to understand the societal, economic, and environmental issues of the need for sustainable energy transition. The assumptions and models were summarized on the basis of existing data provided in the bibliographic references. They were submitted to experts to select those that meet the criteria of quality and relevance. The data used in this work are obtained from the statistical treatment and probabilistic modeling in the case where there are no archive data or a limited number available, with the help of expert judgments. Experts are energy service providers, politics oriented to research and development, specialists in the integration of renewable resources to networks, nuclear and nonrenewable energy scientists, researchers in risk analysis, and specialists in the management of energy‐related conflicts. Each expert group dealing with the issue of sustainable development can provide a range of economic, environmental, and social indicators. As noticed in the literature, economic and environmental indicators seem to be obvious and common to the overall society, but it is not the case for social ones. Certainly, the sources of conflicts and accidents in the energy field are not frequent looking to electricity, but the impact of nuclear component highlights the main concerns. They reside in the utilities dysfunction causing blackouts due to their high capacities of production and risk of contam‐ ination in the case of accidents (random or premeditated (sabotage)). As for sustainable development, electricity sustainability (ES) is based on the three known pillars such as social aspects, economic and environment criteria, and indicators noted (*Ci*) and their associated sub‐

Environment (C1): Resources (C11; energy resources and mineral resources), Climate change (C12), Ecosystem damage (C13; impacts from normal operation and impacts from severe accidents), Waste (C14; chemical waste in underground depositories and radioactive waste in

is the largest. According to this criterion, the solution is given as follows:

286 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

a

**6. Electricity sustainability development**

**6.1. Criteria and indicators**

criteria noted (*Cij*).

geological repositories).

To the hierarchy given in **Figure 1**, were associated the criteria and their sub‐criteria introduced in ‐Section 6.1 and using energy production resources as alternatives, we have determined a long‐run growth of a company in the context of electricity sustainability.

To highlight the great interest of AHP application in sustainability, particularly in the field of energy, we have applied this process with the objective to compare the obtained results with those outlined by other MCDA methods summarized by Hirschberg [3], investigating the development of sustainability assessment at PSI. The different steps of AHP applications were followed, and the pair‐wise comparison results between the indicators with respect to the goal are given in **Table 1**.


**Table 1.** Pair‐wise comparison matrix of the criteria with respect to the goal.

It appears clearly that the criteria are equally prioritized and shown in **Figure 3(a)**. In **Figure 3(b)** are given the proportions (in %) of each sub‐criterion against its main criterion (red color % represents the main criterion, black color % represents the sub‐criterion against the main criterion, and blue color % represents the sub‐criterion against the goal). Each value of a sub‐criterion can be found using the following operation: (sub‐criterion priority (in %) = the sub‐criterion priority (in %) against the goal/the main criterion priority (in %) against the goal). In this case, the advantage of the AHP method is that it is possible to change weights to have an appropriate priority. However in the case of MCDA proposed in reference [3], the results are obtained from a survey work. The results in **Table 2** show the priorities of alternatives are based on all sub‐criteria. The results have allowed us to do a synthesis in the case of equal priorities of main criteria, as given in **Table 3**. From decision makers' point of view, this consideration shows the prudent attitude. And the results show a high priority to renewable resources, followed by nuclear one, but the gap is not significant.

**Figure 3.** Syntheses of criteria and sub‐criteria priorities (case of a prudent decision maker): Main criteria with relative‐ ly equal priorities (a) and sub‐criteria weights (% in black) using AHP, to achieve the priorities (% in blue) compared to the goal (b).

Combining AHP Method with BOCR Merits to Analyze the Outcomes of Business Electricity Sustainability http://dx.doi.org/10.5772/64042 289


**Table 2.** Comparison matrices and local priorities.

**Figure 3.** Syntheses of criteria and sub‐criteria priorities (case of a prudent decision maker): Main criteria with relative‐ ly equal priorities (a) and sub‐criteria weights (% in black) using AHP, to achieve the priorities (% in blue) compared to

288 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

the goal (b).


**Table 3.** Final results using synthesis (equal importance of main criteria).

In the case where the decision maker is optimistic toward environment effects, a high priority is given to the environmental aspects as highlighted in **Table 4** and confirmed in **Figure 4**; it shows that the renewable resources won the highest priority with an important gap com‐ pared to the other alternatives.

**Figure 4.** Syntheses of criteria and sub‐criteria priorities (case of an optimistic decision maker toward environment): Main criteria with the main dominance of environment criterion (a) and sub‐criteria weights (% in black) using AHP, to achieve the priorities (% in blue) compared to the goal (b).

Combining AHP Method with BOCR Merits to Analyze the Outcomes of Business Electricity Sustainability http://dx.doi.org/10.5772/64042 291


**Table 4.** Final results using synthesis (with the dominance of environmental aspect).

**ENVIRONMENT (C1) ECONOMY (C2) SOCIETY (C3) Priorities**

*Weights* **0.343 0.343 0.314**

290 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

**Table 3.** Final results using synthesis (equal importance of main criteria).

pared to the other alternatives.

*Sub‐criteria* C11 C12 C13 C14 C21 C22 C23 C24 C31 C32 C33 C34 C35 C36 *Weights* 0.254 0.346 0.242 0.157 0.321 0.252 0.226 0.200 0.139 0.207 0.205 0.149 0.153 0.145 *Nuclear resource* 0.222 0.249 0.105 0.135 0.637 0.297 0.527 0.539 0.581 0.558 0.332 0.539 0.218 0.186 0.364 *Fossil resource* 0.112 0.097 0.256 0.235 0.258 0.539 0.332 0.163 0.309 0.319 0.527 0.297 0.151 0.126 0.266 *Renewable resources* 0.666 0.654 0.639 0.630 0.104 0.163 0.139 0.297 0.109 0.122 0.139 0.163 0.630 0.687 0.370

In the case where the decision maker is optimistic toward environment effects, a high priority is given to the environmental aspects as highlighted in **Table 4** and confirmed in **Figure 4**; it shows that the renewable resources won the highest priority with an important gap com‐

**Figure 4.** Syntheses of criteria and sub‐criteria priorities (case of an optimistic decision maker toward environment): Main criteria with the main dominance of environment criterion (a) and sub‐criteria weights (% in black) using AHP,

to achieve the priorities (% in blue) compared to the goal (b).

Based on the investigation of Doane and Mac Gillivray [4], where they have stated that the economic criterion should be of high interest compared to the other criteria, we have consid‐ ered that the decision maker is optimistic toward economy and relatively pessimistic toward social and environmental issues. The synthesis given in **Table 5** shows a high priority for nuclear resource with a nonsignificant gap compared to the other alternatives.


**Table 5.** Final results using synthesis (with the dominance of economic aspects) with a completed number of sub‐ criteria.

Through this simulation, we retain the interest of the environmental aspect in sustainable development, and the development of renewable resources is imperative. From decision makers' point of view, the AHP method allowed us to simulate attitudes of managers without difficulty.
