**3. Application of AHP in two organisational settings**

First, in an empirical case study for selecting the most appropriate maintenance policy AHP was utilised aiming to evaluate and select the most appropriate maintenance approach. The case study was conducted at a Slovenian paper mill company.

Secondly, an expert opinion study was conducted in the context of UAE organisations using suggestion systems to formalise the importance levels for sustainability of employee sugges‐ tion system factors. The illustration of AHP for these two case instances is discussed in the next sections.

#### **3.1. Case study 1: an AHP-based framework for maintenance policy selection**

The method proposed for selecting the most appropriate maintenance approach is based on a hierarchical model composed of a set of criterion and sub-criterion. AHP method is demon‐ strated by the following case study from the paper industry. One of the Slovenian paper mill companies is the subject of the case study in this research. It could be argued that maintenance is highly crucial for this company, since production process in this company is running 24/7. Equipment life, equipment availability and equipment condition is very important in order to ensure smooth running of a paper machine, and provide on-time delivery at low prices. As such, the objective of this case study is to identify the most appropriate maintenance policy concerning the above mentioned objectives.

**Figure 1.** Steps for conducting an AHP study.

In order to select the most appropriate maintenance policy for the paper machine, this research paper uses the AHP methodology. Based on the guidelines proposed by Saaty [8], an AHP framework was developed for facilitating the study. In this regard, Saaty [8] proposed four steps to make a decision in an organised way:

1. define the problem and determine the kind of knowledge sought,

2. structure the decision hierarchy from the top with the goal of the decision, then the objectives from a broad perspective, through the intermediate levels (criteria on which subsequent elements depend) to the lowest level (which usually is a set of the alternatives),

3. construct a set of pairwise comparison matrices. Each element in an upper level is used to compare the elements in the level immediately below with respect to it,

4. use the priorities obtained from the comparisons to weigh the priorities in the level imme‐ diately below. Do this for every element. Then for each element in the level below add its weighed values and obtain its overall or global priority and

5. continue this process of weighing and adding until the final priorities of the alternatives in the bottom most level are obtained.

Using these guidelines, an AHP framework was established for facilitating the study. **Figure 1** shows a flow chart involving various steps to conduct the AHP study.

#### **Step 1:** *Define the objective or goal*

is highly crucial for this company, since production process in this company is running 24/7. Equipment life, equipment availability and equipment condition is very important in order to ensure smooth running of a paper machine, and provide on-time delivery at low prices. As such, the objective of this case study is to identify the most appropriate maintenance policy

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

concerning the above mentioned objectives.

**Figure 1.** Steps for conducting an AHP study.

The objective or goal of this study is to assess and select the most appropriate maintenance approach/policy for a paper machine.

#### **Step 2***: Identify criteria and sub-criteria for maintenance policy selection*

In this step, the objective or goal of maintenance policy selection was decomposed into three criteria (equipment- and process-related measures, financial measures and health, safety and environment measures) and 12 maintenance indicators (sub-criteria) were identified from the literature so as to form a hierarchical abstraction of the problem. A literature search was conducted using the databases such as Emerald, ABI/Inform and ScienceDirect. The search was done in different combinations of keywords such as maintenance performance, mainte‐ nance indicators, maintenance costs, maintenance savings and maintenance measurement. Results of the search show different works that have dealt with topics related to these keywords [40–42]. Maintenance indicators are vital for effective support of decision making [42]. Performance measurement provides the required information to the management for effective decision making. As such, management of maintenance performance is critical for long-term economic viability of business and industry [42]. As a result of this literature search, various maintenance performance measures were identified.

#### **Step 3:** *Determine the alternative maintenance approaches*

Different maintenance approaches, i.e. strategies and concepts, methodology or philosophy, were used in this study. Briefly, they are the following:

1. failure-based maintenance,


A more detailed description of these approaches was presented in the literature review section.

**Figure 2.** A hierarchy model for maintenance policy evaluation/selection.

#### **Step 4**: *Construct a hierarchy framework for analysis*

After the goal of this study had been established, relevant criteria and sub-criteria of mainte‐ nance performance measurement were identified via steps 1 and 2. These criteria and subcriteria were then structured into a hierarchy descending from the overall objective or goal to the various stages and related sub-criteria in successive levels. The top level of the hierarchy represents the defined objective, while the second level of the hierarchy consists of three main maintenance criteria, followed by various sub-criteria (see **Figure 2**). Finally, the fourth level of the hierarchy characterises the alternative maintenance approaches/policies.

#### **Step 5**: *Collection of empirical information and data*

2. preventive maintenance,

3. total productive maintenance,

5. reliability-centred maintenance.

4. total quality maintenance (using VBM) and

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

**Figure 2.** A hierarchy model for maintenance policy evaluation/selection.

**Step 4**: *Construct a hierarchy framework for analysis*

A more detailed description of these approaches was presented in the literature review section.

After the goal of this study had been established, relevant criteria and sub-criteria of mainte‐ nance performance measurement were identified via steps 1 and 2. These criteria and subcriteria were then structured into a hierarchy descending from the overall objective or goal to the various stages and related sub-criteria in successive levels. The top level of the hierarchy represents the defined objective, while the second level of the hierarchy consists of three main maintenance criteria, followed by various sub-criteria (see **Figure 2**). Finally, the fourth level

of the hierarchy characterises the alternative maintenance approaches/policies.

This step is concerned with the collection of empirical information and data through the combined judgements of the individual evaluators from industry and academia. For this purpose, a group of three evaluators were chosen for evaluating the selected criteria and subcriteria. Two evaluators were chosen from academia having experience in the field of main‐ tenance, and one from industry also experienced in the field of maintenance. They had sufficient knowledge, expertise and understanding of the maintenance approached used in this study.

#### **Step 6***: Perform pairwise comparisons for each level of criteria and sub-criteria*

Once the evaluators were identified and relevant empirical information and data were collected, the next step was to determine the relative importance among the criteria and subcriteria. Before conducting the pairwise comparison, all team members were given the instruction on how to complete the comparison. Invited evaluators were asked to carefully compare criteria of each hierarchy level by assigning relative scales in a pairwise fashion with respect to the goal of this study. Evaluators' judgements were then combined using the geometric mean approach at each hierarchy level to attain the corresponding consensus. A relational scale of real numbers from 1 to 9 was used in the ranking process (**Table 1**). The purpose of this scale is to determine how many times a more important or dominant element is prioritised over another element with respect to the criterion or property with respect to which they are compared [8].


**Table 1.** Scale of relative preference for pairwise comparison.

#### **Step 7:** *Perform the consistency test*

In this step consistency test was performed. A measure of inconsistency is useful in identifying possible errors in expressing judgements as well as actual inconsistencies in the judgements themselves [2]. AHP provides a method called the consistency ratio (CR) which is used to gauge whether a criterion can be used for decision making. In the AHP the pairwise compar‐ isons in a judgment matrix are considered to be consistent if the CR is less than 10% [1]. On the contrary if CR is bigger than 10%, possible cause should be examined. However, the standard consistency test has been critiqued by a number of authors [43–45]. For these reasons, we adopted a quality control approach for the consistency test, proposed by Karapetrovic and Rosenbloom [43]. Authors recommended that quality control of consistency can be performed using the simple Shewhart Xbar-R chart or exponentially weighted moving average (EWMA) chart. In this study, EWMA chart was used. This chart is suitable due to its possibility to identify small shifts in the consistency index (CI). CI can be calculated using the following equation: CI = *λ* max – *n*/*n* – 1, where '*n*' is the number of criteria or sub-criteria of each level and *λ* max is the biggest eigenvector in the matrix. In place of dividing each CI by the 'random index', we used an approach to plot the average values for CI (taking into consideration all decision makers) into EWMA chart (**Figure 3**). For this purpose, a free software environment for statistical computing and graphics *R* was applied using the QCC (an *R* package for quality control charting and statistical process control) package. We used a default value of smoothing parameter (*λ*), which was set at 0.2 in the aforementioned *R* package. **Figure 3** shows that all EWMA values were within the defined control limits. This means that decision makers were consistent.

**Figure 3.** EWMA control chart—average CIs.


**Table 2.** The local and global weights.

we adopted a quality control approach for the consistency test, proposed by Karapetrovic and Rosenbloom [43]. Authors recommended that quality control of consistency can be performed using the simple Shewhart Xbar-R chart or exponentially weighted moving average (EWMA) chart. In this study, EWMA chart was used. This chart is suitable due to its possibility to identify small shifts in the consistency index (CI). CI can be calculated using the following equation: CI = *λ* max – *n*/*n* – 1, where '*n*' is the number of criteria or sub-criteria of each level and *λ* max is the biggest eigenvector in the matrix. In place of dividing each CI by the 'random index', we used an approach to plot the average values for CI (taking into consideration all decision makers) into EWMA chart (**Figure 3**). For this purpose, a free software environment for statistical computing and graphics *R* was applied using the QCC (an *R* package for quality control charting and statistical process control) package. We used a default value of smoothing parameter (*λ*), which was set at 0.2 in the aforementioned *R* package. **Figure 3** shows that all EWMA values were within the defined control limits. This means that decision makers were

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

consistent.

**Figure 3.** EWMA control chart—average CIs.

#### **Step 8**: *Calculate the global weights of each criteria and sub-criteria*

The next step comprises a calculation of local and global weights. While local weights refer to the preceding hierarchical level, the global weights take into account the highest hierarchical level [2]. The local and global weights as well as the corresponding ranks are presented in **Table 2**.

#### **Step 9**: *Synthesising the results*

In order to obtain final results, all alternatives were multiplied by the global weight of the single decision criteria. The results are presented in **Table 3**.

In **Table 3**, the global priorities are calculated for each of the alternatives. The highest value (0.498) corresponds to the TQMain, followed by TPM (0.207) and RCM (0.162). As expected the lowest value refers to the FBM.


**Table 3.** The summarised matrix.

#### **Step 10:** *Sensitivity analysis*

In this step, a sensitivity analysis is held to show the effect of altering different parameters of the model on the choice of the maintenance policy selection. First, the current values of the model are presented. **Figure 4** demonstrates the current importance of each alternative considering all criteria used in this model. As one can see from **Figure 4**, the highest value corresponds to TQMain (49.8%). Additionally, **Figure 4** also shows the values of the weights of all three main criteria from level 2 (*C*1—equipment-/process-related measures, *C*2 financial measures and *C*3—health, safety and environment measures).

Furthermore, a series of sensitivity analysis were performed to investigate the impact of changing the priority of the criteria on the alternatives' ranking. Dynamic sensitivity of expert choice was accomplished to analyse the change in outcome caused by a change in each of the main criterion. The aim of sensitivity analysis is to explore how these changes affect the priorities of the selected alternatives. In the following three scenarios are presented. We investigated the impact of changing the priority of three main criteria on overall results. First, the criterion 'equipment-/process-related measures' was increased for approximately 25% (from 53 to 66.2). The results are presented in **Figure 5**. This figure consists of two parts. The results presented on the left side of **Figure 5** are criteria and their corresponding weights, while the right side of the figure illustrates the ranking of the alternative as expressed by importance (in percentage). The results of the sensitivity analysis showed that change (an increase of 25%) in the first criterion has no significant influence on the final ranking of the alternatives. As such, the overall rank of the final outcome remained unchanged.

**Figure 4.** Sensitivity graph—the initial results with respect to the main goal.

Secondly, the criterion 'financial measures' was increased by approximately 25% (from 27 to 33.8) (**Figure 6**). Similarly as in the first case, the change in this criterion also appears to have no substantial impact on the final ranking. As can be seen from **Figure 6**, TQMain remains the best alternative.

**Figure 5.** Scenario 1.

**Table 3.** The summarised matrix.

**Step 10:** *Sensitivity analysis*

In this step, a sensitivity analysis is held to show the effect of altering different parameters of the model on the choice of the maintenance policy selection. First, the current values of the model are presented. **Figure 4** demonstrates the current importance of each alternative considering all criteria used in this model. As one can see from **Figure 4**, the highest value corresponds to TQMain (49.8%). Additionally, **Figure 4** also shows the values of the weights of all three main criteria from level 2 (*C*1—equipment-/process-related measures, *C*2—

Furthermore, a series of sensitivity analysis were performed to investigate the impact of changing the priority of the criteria on the alternatives' ranking. Dynamic sensitivity of expert choice was accomplished to analyse the change in outcome caused by a change in each of the main criterion. The aim of sensitivity analysis is to explore how these changes affect the

financial measures and *C*3—health, safety and environment measures).

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

Finally, the last criterion 'health, safety and environment measures' was also increased by 25% (from 19.9 to 25.1), and the model was tested for the change of the final ranking. The results show (**Figure 7**) that the criterion 'health, safety and environment measures' has no major impact on the final outcome as well, and therefore TQMain remains the best alternative.

Overall, the results of the sensitivity analysis revealed that the ranks of the alternatives remained stable in all cases. Additionally, a sensitivity analysis was carried out in which main criteria were decreased by 10%. The results displayed that the model is stable also when weights are decreased. This indicates that the proposed model is stable and robust and thus appropriate for decision-making process.

**Figure 6.** Scenario 2.

**Figure 7.** Scenario 3.

### **Step 11:** *Final ranking of proposed alternatives*

Taking into account the results of the 9th step and the results of the sensitivity analysis, the final solution of the AHP method can be determined. Therefore, with respect to the main objective of the proposed model, TQMain was selected as the most appropriate maintenance approach (**Table 4**).


**Table 4.** Global importance of maintenance approaches.

Finally, the last criterion 'health, safety and environment measures' was also increased by 25% (from 19.9 to 25.1), and the model was tested for the change of the final ranking. The results show (**Figure 7**) that the criterion 'health, safety and environment measures' has no major impact on the final outcome as well, and therefore TQMain remains the best alternative.

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

Overall, the results of the sensitivity analysis revealed that the ranks of the alternatives remained stable in all cases. Additionally, a sensitivity analysis was carried out in which main criteria were decreased by 10%. The results displayed that the model is stable also when weights are decreased. This indicates that the proposed model is stable and robust and thus

Taking into account the results of the 9th step and the results of the sensitivity analysis, the final solution of the AHP method can be determined. Therefore, with respect to the main objective of the proposed model, TQMain was selected as the most appropriate maintenance approach

appropriate for decision-making process.

**Figure 6.** Scenario 2.

**Figure 7.** Scenario 3.

(**Table 4**).

**Step 11:** *Final ranking of proposed alternatives*

#### **3.2. Case study 2: prioritisation of factors for sustainability of employee suggestion schemes**

Employee suggestion system (ESS) is a tool widely used by the corporations to elicit employ‐ ees' creative ideas. It should elicit suggestions from employees, classify them and dispatch them to the 'experts' for evaluation. After this, the suggestion might be adopted, in which case the suggestion may well be rewarded. `Experts' are dedicated committees who evaluate the suggestions and propose them for its implementations.


Employee suggestion systems create win-win situation for employers and employees alike. However, despite the many benefits of the suggestion systems, sustaining them is still a challenge for organisations. Organisations need to assess their suggestion schemes to deter‐ mine their sustainability and to examine if the right conditions exist for the suggestion schemes to flourish. After all, suggestion systems can contribute to build organisations innovative capability.

The variables identified in the literature review were first subjected to a factor analysis. This enabled the emergence of five factors, namely—Leadership and Work Environment, System Effectiveness, System Capability, Organisational Encouragement and System Barriers. These five factors were considered in an AHP analysis to determine the importance levels. Expert opinion study was conducted to formalise the importance levels for the importance of factors of sustainability of employee suggestion schemes. Once the importance was identified, the initial framework was created to place the indicators in the order of their importance. An AHP expert opinion questionnaire following Saaty's [8] rating scale as reference for the expert to decide the importance of the indicators in the numerical range 1–9 or their reciprocals, i.e. 1/2– 1/9 was used.

The steps for conducting the AHP analysis were briefed in the following steps:

The data were collected from three suggestion system implementers. These implementers were contacted through an email requesting their participation in this research study. The imple‐ menters had varied experience using suggestion systems, for example, 10–15 years and were active members of IdeasArabia Group. IdeasArabia Group conducts an annual conference on suggestion systems and awards the organisation and individuals for best suggestions. The data were collected in the form of semi-structured interview and after explaining the objective of the study and the application of the AHP method, from two participations. The third participant was then shown the data collected from two participants for the final judgment as to which two users opinion about the importance level of factor indicators was more appro‐ priate for adjusting the importance level of factor indicators for pairwise comparisons or that both opinions were incorrect as per the knowledge of the third practitioner. The third user expressed satisfaction over factor importance level established by the first user and suggested that the same should be adopted in this study.

The steps for conducting the AHP analysis have been briefed in the following steps:

Reciprocal matrix: the first step is to construct a set of pairwise comparison matrices. Each element in an upper level is used to compare the elements in the level immediately below with respect to it [8]. Pairwise comparisons were carried out for all factors to be considered, usually not more than seven and the matrix is completed [46].

Eigenvector: the next step is the calculation of a list of the relative weights, importance or value of the factors, which are relevant to the problem in question and this list is called an eigenvector. Eigenvector is calculated by multiplying together the entries in each row of the matrix and then taking the *n*th root of that product gives a very good approximation to the correct answer [46].

Consistency index: the consistency index for a matrix is calculated from (*λ* max − *n*)/*n* − 1.


**Table 5.** Saaty table for calculation of consistency ratio (CR).

Consistency ratio: the final step is to calculate the consistency ratio for this set of judgments using the CI for the corresponding value from large sample of matrices of purely random judgments using **Table 5**, derived from Saaty's book, in which the upper row is the order of the random matrix and the lower is the corresponding index of consistency for random judgments [46]. CR should be less than 0.1 and if the CR is much in excess of 0.1 the judgments are untrustworthy because they are too close for comfort and to randomness and the exercise is valueless or must be repeated [46].


**Table 6.** Reciprocal matrix—overall factors.

initial framework was created to place the indicators in the order of their importance. An AHP expert opinion questionnaire following Saaty's [8] rating scale as reference for the expert to decide the importance of the indicators in the numerical range 1–9 or their reciprocals, i.e. 1/2–

The data were collected from three suggestion system implementers. These implementers were contacted through an email requesting their participation in this research study. The imple‐ menters had varied experience using suggestion systems, for example, 10–15 years and were active members of IdeasArabia Group. IdeasArabia Group conducts an annual conference on suggestion systems and awards the organisation and individuals for best suggestions. The data were collected in the form of semi-structured interview and after explaining the objective of the study and the application of the AHP method, from two participations. The third participant was then shown the data collected from two participants for the final judgment as to which two users opinion about the importance level of factor indicators was more appro‐ priate for adjusting the importance level of factor indicators for pairwise comparisons or that both opinions were incorrect as per the knowledge of the third practitioner. The third user expressed satisfaction over factor importance level established by the first user and suggested

The steps for conducting the AHP analysis were briefed in the following steps:

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

The steps for conducting the AHP analysis have been briefed in the following steps:

Reciprocal matrix: the first step is to construct a set of pairwise comparison matrices. Each element in an upper level is used to compare the elements in the level immediately below with respect to it [8]. Pairwise comparisons were carried out for all factors to be considered, usually

Eigenvector: the next step is the calculation of a list of the relative weights, importance or value of the factors, which are relevant to the problem in question and this list is called an eigenvector. Eigenvector is calculated by multiplying together the entries in each row of the matrix and then taking the *n*th root of that product gives a very good approximation to the correct answer

Consistency index: the consistency index for a matrix is calculated from (*λ* max − *n*)/*n* − 1.

**1 2 3 4 5 6 7 8 9 10 11 12 13 14 15** 0.00 0.00 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.51 1.48 1.56 1.57 1.59

Consistency ratio: the final step is to calculate the consistency ratio for this set of judgments using the CI for the corresponding value from large sample of matrices of purely random judgments using **Table 5**, derived from Saaty's book, in which the upper row is the order of the random matrix and the lower is the corresponding index of consistency for random judgments [46]. CR should be less than 0.1 and if the CR is much in excess of 0.1 the judgments

that the same should be adopted in this study.

not more than seven and the matrix is completed [46].

**Table 5.** Saaty table for calculation of consistency ratio (CR).

1/9 was used.

[46].


**Table 7.** AHP calculation for all sustainability factors.


**Table 8.** Importance rank for sustainability factors.

The reciprocal matrices created for the AHP data collected through expert opinion study have been shown in **Table 6**. The calculations of the eigenvector, consistency index and consistency ratio are shown in **Table 7**. Importance ranks for factor indicators and for overall sustainability factors are depicted in **Table 8**.

As the consistency ratio resulted in < 0.1, the judgement for overall sustainability factors are perfectly consistent.
