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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.21 No.2 pp.151-167
DOI : https://doi.org/10.7232/iems.2022.21.2.151

A Decision-making Framework to Select a Maintenance Technology: A Case of Transmission Line

Sarayut Suriyawong, Siyeong Yun, Sungjoo Lee*
Department of Industrial Engineering, Ajou University, Republic of Korea
Department of Artificial Intelligence, Ajou University, Republic of Korea
Department of Industrial Engineering, Seoul National University, Republic of Korea
*Corresponding Author, E-mail: sungjoolee@snu.ac.kr
February 14, 2020 ; July 17, 2020 ; February 8, 2021

Abstract


The purpose of our study is to propose a decision-making framework to select a maintenance technology. The combination of interpretive structural modeling and analytic network processes with the benefits, opportunities, costs, and risk model was applied to the prioritization of alternatives. The priorities were then calculated by zero-one goal programming to suggest the most appropriate maintenance technology. The proposed framework was implemented in the case of transmission line maintenance to test its usability and receive expert feedback.



초록


    1. INTRODUCTION

    Maintenance is defined as the combination of technical and administrative actions that aim to preserve the good working condition of an item or restore an item to a state in which it can perform its required function (British Standard Glossary of Terms Used in Terotechnology, 1993). Effective maintenance can preserve a piece of equipment in proper working condition and extend its lifetime and availability (Swanson, 2001), and maintenance activities have been recognized as a potential profit generator that can increase the performance of businesses (Waeyenbergh and Pintelon, 2002).

    Maintenance approaches, such as reactive, preventive, and predictive maintenance, have been implemented to maximize the availability of equipment and provide the desired output (Pintelon and Gelders, 1992), for which decision-making tools have been proposed (e.g., Ji et al., 2019). However, to improve the efficiency of these performances, more emphasis should be placed on using maintenance technologies to enhance system availability, decrease operational cost, and provide better service to customers (Tsang, 2002;Alsyouf, 2009). Such maintenance technologies are generally applied to the assessment of an object’s degradation with age and use (Ben-Daya et al., 2016). With the advances in technologies, maintenance issues can be detected at an early stage and maintenance task planning as well as scheduling can be improved significantly (Alsyouf, 2009).

    However, decision makers have faced difficulties in selecting the most appropriate technology to apply to their organization’s maintenance activities owing to the following reasons. First, technology selection has been restricted by maintenance-related factors and constraints. Unlike existing technology evaluation, which evaluates new technologies or ideas, many factors and constraints are involved in maintenance practices because the evaluation of maintenance technology is based on existing technology. Second, maintenance is currently challenged by rapid technological change (Tsang, 2002). The emergence of various technologies and the increase in technological advancement make the selection of technology more difficult. Although many studies have examined maintenance technology (Hess et al., 2001;Mahulkar et al., 2009;Zhao et al., 2009;Veldman et al., 2011;Halász et al., 2016), they mainly focus on the management, evaluation, and application of maintenance technology, and thus few studies address maintenance technology selection.

    Therefore, to bridge this gap, we developed a decision-making framework for adopting proper maintenance technology to support decision makers, attempting to overcome the limitations of previous studies. In this framework, the first step was to identify the decision criteria and alternatives with respect to the benefits, opportunities, costs and risks (BOCR) model through a literature review and expert opinions. Second, the relationships between the decision criteria and available alternatives were investigated by means of interpretive structural modeling (ISM). As the investigated relationships between the criteria were interdependent, an analytic network process (ANP) was applied to determine the weights of alternatives. In the final step, the most proper maintenance technology was determined by zero-one goal programming (ZOGP), which was formed by the weighing the alternatives and given constraints. The proposed framework was applied to the case of selecting an aerial patrol system (APS) to test its usability for transmission line maintenance. The proposed framework is expected to help firms select the most appropriate maintenance technology, because it can evaluate alternatives from a BOCR perspective in terms of technology-related decision criteria.

    The rest of the paper is organized as follows. Section 2 provides a background on combined approaches that consist of ISM, ANP with BOCR, and ZOGP. Section 3 illustrates the proposed decision-making framework. An application of the framework in a case study of transmission line maintenance is shown in Section 4, whereas conclusions are drawn in Section 5.

    2. BACKGROUND

    2.1 MCDM Methods

    Multi-criteria decision-making (MCDM) is a process of defining goals and finding the best alternatives in complex decision-making standards (Opricovic and Tzeng, 2004). Examples of MCDM methods include the technique for order preference by similarity to an idle solution (TOPSIS), analytic hierarchy process (AHP), and ANP. TOPSIS is based on the logic that the chosen alternative should be the closest to the best alternative and the furthest away from the worst alternative (Chen, 2000). However, that the method does not take into account the relative importance of the distance between the best and worst alternatives is a drawback (Opricovic and Tzeng, 2004). AHP is also a method of grasping the importance of decision-making criteria (Pakkar, 2016), and it is actively used in the field of customer value evaluation, but has the disadvantage of not being able to grasp the interdependencies between criteria (Özcan et al., 2011). The selection of maintenance technology is based on the existing technology, and because the interdependence between criteria is high, we focus on ANP among MCDM methods and propose a methodology for selecting maintenance technology. In the application of ANP, the following techniques were applied in this study.

    First, a BOCR–ANP model was applied to obtain the weights for selection criteria. Classifying the criteria into benefits, opportunities, costs, and risks can help a decision maker easily understand the characteristics of decision-making along with those of alternative technologies.

    Second, ISM was used to analyze the relationships between criteria. The criteria by which to choose a maintenance technology are likely to be strongly related to each other. Thus, a systematic approach is required to investigate the relationships between the criteria. In other words, the interrelationship between criteria for each BOCR criterion was calculated through ISM, and this was reflected in ANP analysis to reduce computational complexity and increase decision-making efficiency.

    Finally, ZOGP was employed for final technology selection, considering the aspect that the selection is confined to the existing facilities and equipment already established in an organization, which allows for the selection of the optimal maintenance technology, taking into account various constraints. A more detailed explanation of each of the techniques is given in the following sections.

    2.2 ANP with BOCR Model

    ANP is a multi-criteria measurement that derives the relative priorities of pairwise comparisons from individual assessments or from actual measurements (Saaty, 1996) and has frequently applied to support selection-related decisions (e.g., Mulebeke and Zheng, 2006;Aragonés-Beltrán et al., 2017;Islami et al., 2018). The ANP framework was provided to deal with decisions without specifying the level of elements (Saaty, 1999) while taking interdependence and feedback into consideration (Ergu and Peng, 2014) or adopting fuzzy numbers (Razmi et al., 2009).

    BOCR is a way to analyze decisions in terms of benefit, opportunity, cost and risk (Yazgan et al., 2010). Through the BOCR concept, decision makers can assess not only benefit and cost, but also opportunity and risk aspects of problems (Lee et al., 2009). With regard to the BOCR model defined by Tornjanski et al. (2014), the benefits (B) and costs (C) refer to short-term period effects, whereas the opportunities (O) and risks (R) refer to long-term period effects. Thus, BOCR correlated with these strategies can provide appropriate decision making for decision makers.

    Because BOCR-based ANP can make decisions considering various qualitative and quantitative data and helps decision makers evaluate criteria in various aspects (Dziadosz et al., 2018), BOCR-based ANP has been used in various studies. For example, the BOCR-based ANP model was used to solve a scheduling problem in a manufacturing system (Yazgan et al., 2010) and to select a logistics center site or adopt a strategy (Azizi et al., 2005;Šimelytė et al., 2014;Hernandez et al., 2016;Peker et al., 2016;Dziadosz et al., 2018;Sarmiento et al., 2018). In addition, Wijnmalen (2007) proposed the BOCR application method according to the project purpose through verification of the BOCR-based ANP model in the project decision. To apply the ANP with the BOCR model, four steps are required as follows (Saaty, 1996):

    • Step 1: Problem structure and model. Here, the goals, decision criteria (main and sub-criteria), and alternatives related to the problem under consideration are identified, and their network is constructed.

    • Step 2: Making pairwise comparisons. Pairwise comparisons are performed in each cluster for each one of the BOCR control criteria by a panel of experts. The comparison was made by using the 9-point Saaty scale presented in Appendix 1 (Saaty, 2008a). Rank 1 indicates that two elements have equal importance, whereas rank 9 indicates the absolute importance of one element in comparison to another (Felice and Petrillo, 2010). Additionally, reciprocal values represent the respective opposite values:

    A l t 1 A l t i x 1 x 2 x n W M = A l t 1 A l t i x 1 x 2 x n [ W M 11 W M 12 W M 21 W M 22 ]

    where W is the super matrix, M denotes the main-criteria (B, O, C, and R), Alt denotes the alternative, and i is the number of alternatives. Furthermore, in M, x denotes the n sub-criteria, W M 11 is the pairwise comparison between alternatives, W M 12 is the pairwise comparison alternatives with regard to criteria, W M 21 is the pairwise comparison criteria regarding each alternative, and W M 22 is the pairwise comparison of related criteria.

    • Step 3: Formulating the supermatrix. When the pairwise comparison is completed, the results are synthesized. To obtain the results, the following supermatrices were used (Saaty, 2008b):

      • The unweighted supermatrix, a matrix containing the priories/weights obtained by the pairwise comparison of elements in accordance with the inter-dependencies between elements.

      • The weighted supermatrix, a matrix obtained by multiplying the unweighted supermatrix by the cluster priorities/weights.

      • The limit supermatrix, a matrix obtained by potentiating the weighted supermatrix.

    • Step 4: Selecting the best alternative. The priorities or weights of alternatives for each B, O, C, and R criterion from the limit matrix were synthesized to determine the final ranking of the alternatives. The calculation can be performed in two ways (Saaty, 2008b). First, the value for the multiplicative formula, BO/CR, can be calculated. The product of the benefit priority (B) and opportunity priority (O) is divided by the product of the cost priority (C) and risk priority (R). There are no negative results of final priorities in this formula. Second, the value for the additive formula, bB + oO – cC – rR, can be obtained. Here, the weights of b, o, c, and r, were gained by rating B, O, C, and R with respect to the strategic criteria, whereas the priority of B, O, C, and R was calculated in the same way as in the first approach. The results of this formula can be negative. In this study, the first formula was implemented because no strategic criteria were used in the proposed framework.

    2.3 ISM

    Proposed by Warfield (1974), ISM is used to understand complex situations and determine actions to solve a problem. To begin ISM procedures, binary matrices are calculated individually or in groups to present the relations of elements in what is called a relation matrix (Huang et al., 2005). The question “Does the feature ei inflect the feature ej?” is asked to form a relation matrix, and if the answer is “Yes,” then πij = 1; otherwise πij = 0 (Huang et al., 2005). The general form of the relation matrix is presented as follows:

    e 1 e 2 e p D = e 1 e 2 e p [ 0 π 12 π 1 n π 21 0 π 2 n π m 1 π m 2 0 ]

    where ei is the ith element in the system, πij denotes the relation between the ith row and jth column element, and D is the relation matrix.

    After the relation matrix (D) is formed, the reachability matrix is developed to check the transitivity of the contextual relation (Ravi and Shankar, 2005). In ISM, the basic assumption of the transitivity states that if variable A is related to B and B is related to C, then A is necessarily related to C (Ravi and Shankar, 2005). The reachability matrix is obtained by using Eqs. (1) and (2) (Warfield, 1974;Huang et al., 2005;Yang et al., 2008;Lee et al., 2010):

    M   =   D   +   I
    (1)

    M * =   M k =   M k + 1 k > 1
    (2)

    x 1 x 2 x n M * = x 1 x 2 x n [ π 11 * π 12 * π 1 n * π 21 * π 22 * π 2 n * π n 1 π n 2 * π n n * ] i = 1 , 2 , n ; j = 1 , 2 , , n

    where I is the unit matrix, k denotes the power, M is the initial reachability matrix, M* is the final reachability matrix, and *ij* denotes the relation between the ith row and jth column criteria.

    In addition, the reachability matrix is under Boolean multiplication and addition operators (i.e., 1 × 1 = 1, 1 + 1 = 1, 1 0 = 0 × 1, 1 + 0 = 0 + 1 = 1).

    In this study, the final reachability matrix (M*) for each benefit, opportunity, cost, and risk (main criteria) is generated through ISM to measure the degree of relationship between elements (sub-criteria).

    2.4 ZOGP

    ZOGP is a mathematical programming approach for optimizing the values of variables in situations where multiple goals and goal priorities exist (Karsak et al., 2003). ZOGP is suitable for considering resource limitations and other options to be taken into account when selecting alternatives (Yilmaz et al., 2011), and thus it has been used in studies to solve decision problems (Rabbani et al., 2006;Meethom and Koohathongsumrit, 2018). In addition, a few studies have examined ways to select the optimal alternative by integrating ZOGP and ANP models (Wei and Chang, 2008;Tu et al., 2010;Agha, 2001;Lubis and Mawengkang, 2019). The ANP weights used in the ZOGP formulation can reflect the preference of decision makers with respect to the relative importance of each goal. In this study, we used the ZOGP model proposed by Wei and Chang (2008), as shown in Eq. (3):

    Minimize Z = P k ( w j d i + , w j d i ¯ )
    (3)

    subject to

    a i j x i j + d i b i f o r i = 1 , 2 , , m j = 1 , 2 , , n
    (4)

    and

    x j + d i = 1 f o r i = m + 1 , m + 2 , m + n j = 1 , 2 , n
    (5)

    In Eqs. (3)–(5), m is the number of goals to be considered; n is the number of possible maintenance technologies to choose from; wj is the ANP weight on j = 1, 2,…, n; Pk = some k priority preemptive priority (P1>P2 >…>Pk), for i = 1, 2,…, m; d i + , d i is the ith positive and negative deviation variables for i = 1, 2,…, n; and xj is a zero-one variable, where j = 1, 2,…, n, such that

    x j { 1 : s e l e c t t h e j e l e m e n t 0 : n o t s e l e c t t h e j e l e m e n t

    where aij = the jth element usage parameter of the i resource and bi = the ith available resource or limitation factors that must be considered in the selection decision.

    3. PROPOSED FRAMEWORK

    The proposed model for selecting the optimal maintenance technology is based on ISM, ANP with the BOCR model, and ZOGP. The implemented procedure consisted of four stages, as shown in Figure 1.

    In the first stage, the decision criteria was reviewed from the existing studies and the ones selected for further analysis were assigned to one of the BOCR categories.

    The second stage was to determine the interrelationships between decision criteria under the ISM model, where a panel of five experts was asked to participate when the framework was applied to the case of transmission line maintenance. The panel consisted of three male and two female experts, 33 to 65 years old, with more than 10 years of experience in the management or operation of transmission line maintenance. The experts were involved in this project from August to October 2017.

    In the third stage, the weights of the alternatives were calculated based on the ANP model. In this stage, five experts calculated the weights of the criteria and alternatives, and when performing the pairwise comparison between the criteria in the BOCR, only the pairwise comparison between elements identified as having an interrelationship through the ISM model was performed.

    Finally, ZOGP was performed using the weights of alternatives derived from the BOCR-based ANP model. Here, we reflect various constraints related to the decision of the alternative and determine the most proper maintenance technology.

    In addition, to solve emerging problems in response to changes in the external environment, continuous review of criteria is necessary. Decision-making criteria should be continuously updated through literature reviews, and weight values should be continuously updated according to the company situation by conducting ANP.

    4. APPLICATION

    4.1 Target Industry and Technology

    The proposed framework was applied to the selection of technology for transmission line maintenance. The electrical power industry is essential to human life and the development of national economies. A power system is a core part of this industry and includes a power plant and transmission and distribution networks. The system aims to generate appropriate amounts of electrical energy from a power plant and provide consumers with quality transmission and distribution networks at low cost (Sivanagaraju, 2008). With the increase in energy consumption, development of countries, and world population (Froger et al., 2016), many companies have attempted to improve and increase their performance to meet the demand and achieve the abovementioned system goals. In a power system, transmission lines play a critical role in the transferring of electrical energy from the generating plant to the distribution networks. Therefore, the security of transmission lines has become an important feature when considering the reliability of a power system (Lin et al., 2006). To ensure the reliable delivery of power, the maintenance of transmission lines is a critical factor to consider.

    The target technology is an APS, which is an airborne inspection technology that applied to transmission line inspection. The performance of airborne inspections can enhance a utility company’s overall line inspection and maintenance program. An APS contains four different cameras (i.e., an infrared thermography camera, a daytime corona inspection camera, a video camera, and a digital frame camera. In this case, two alternatives of an APS labeled APS1 and APS2 are considered.

    4.2 Application Results

    4.2.1 Defining the Decision Criteria and Alternatives under the BOCR Model

    The proposed framework is based on the BOCR model, and each element of the model has related decision criteria obtained from the literature. Accordingly, 19 criteria were identified, which include five benefit-related, four opportunity-related, four cost-related, and six risk-related criteria. The definitions and references of all decision criteria in our framework are summarized in Appendix 2. In the selection of the APS technology, there were two possible alternative solutions: APS1 and APS2. By using the proposed framework, the APS technology selection model could be formulated as shown in Figure 2.

    4.2.2 Determining the Interrelationship among Decision Criteria by ISM

    ISM was applied to determine the relationships between the criteria in each one of the BOCR models. Five experts identified the degree of relationship between any two criteria in each BOCR model using prepared questionnaires, and the arithmetic mean was also used to calculate the mean values of all expert opinions ( A R ). The threshold value (η) was also used to decide whether the criteria were related. To show how to apply ISM, an example of the benefits model is presented in Figure 3, whereas the calculation processes for the rest of the three models are described in Appendix 3.

    To apply ISM, first, the mean values of all expert opinions ( A R ) were calculated as shown in Figure 3(a). Second, the relation matrix (D) was constructed by A R and the threshold value. In this study, a threshold value of 0.8 was provided to decide whether the criteria were related. If a mean value ( A r i i ) in A R was more than the threshold value ( r i j η ), then the criteria were evaluated to be related with each other, and in the relation matrix (D), a value of 1 was given to πij, whereas if not, then the criteria were evaluated as independent of each other and a value of 0 was given to πij. The relation matrix of the benefits model is shown in Figure 3(b). Next, the reachability matrix in Figure 3(d) was obtained by Eq. (1), after which the final reachability matrix in Figure 3(e) was produced by powering the matrix M accordingly to satisfy Eq. (2). From the final reachability matrix, the interrelationships between the criteria under the benefits model were identified. Figure 4 shows the final analysis results for the four models.

    4.2.3 Calculating the Weights of the Alternatives by ANP with the BOCR Model

    To find the weights of the alternatives, the same five experts first provided a weighted score using the 9-point Saaty scale in the questionnaires. The geometric mean of the score assigned by the experts was calculated and used for a pairwise comparison. By taking the benefits model as an example, the pairwise comparison (including consistency analysis) was then performed in three steps.

    In the first step, a pairwise comparison was performed on the dependent criteria. Figure 5, again, shows an example of pairwise comparison results in the case of the benefits model. The consistency of each comparison was expected to be no more than 0.1, which was satisfied by all the matrixes in the figure.

    In the second step, a pairwise comparison of each criterion in the BOCR model was performed with regard to each possible alternative (see Figure 6).

    Then, in the third step, a pairwise comparison of possible alternatives (APS1 and APS2) with respect to each criterion in the BOCR model was performed (see Figure 7).

    After the pairwise comparisons were completed, all weights gained from steps 1–3 were gathered to develop the unweighted, weighted, and limit supermatrices (see Figure 8).

    From Figure 8(c), the priorities of the two alternatives (APS1 = 0.326, APS2 = 0.179) in the benefits model were obtained, which means that APS1 is preferred to APS2 in terms of benefits. The same calculation was carried out for the remaining O, C, and R models to build a supermatrix for each (see Appendix 4). Finally, the weights of each alternative from the BOCR model were synthesized and calculated by a multiplicative formula (BO⁄CR) to determine the final weights of APS1 (1.305) and APS2 (1.421), as shown in Table 1. The results indicate that APS1 is superior to APS2 with respect to benefits and opportunities. However, APS1 is expected to bring higher costs and risks than APS2. Consequently, considering such high costs and risks, APS2 seems to be preferred to APS1.

    4.2.4 Determining the Most Proper Maintenance Technology under ZOGP Constraints

    Because maintenance technology is likely to be subjected to various constraints caused by the characteristics of existing facilities and financial budgets, by adopting ZOGP, these constraints and limitations could be reflected in the final decision, which could result in a practical decision. Table 2 describes the basic technological specifications for the two alternative technologies and the goals required by the company for which the five experts work. More specifically, in selecting the APS technology, its specifications and functions were considered to enhance the effectiveness of inspection for transmission lines, whereas other factors such as budget, maintenance time, and labor were also taken into account so that the limited operation time and costs were not exceeded.

    These constraints and the final BOCR–ANP results for APS1 (1.305) and APS 2 (1.421) were used to form the ZOGP formula (see Table 3). This optimization problem was solved using LINDO (version 17.0).

    Finally, the result of ZOGP indicated that APS2 should be selected (t2=1) as the most proper APS system that met the given requirements. Selecting APS2 also could save $31,000 in system costs, require one less day of maintenance time, and use labor equal to the requirement, so d 14 ¯ = 31 , d 15 ¯ = 1 , and d 16 ¯ = 0 are shown (see Table 4).

    4.3 Validity Test Results

    This study adopted Brooke’s (1996) system usability scaling (SUS) to verify the usability of the suggested decision-making framework. SUS is composed of 10 statements and a 5-point scale of agreement to measure users’ perceived usability concerning a specific product or service (Bangor et al., 2008). It was applied to assess the experts’ perceived usability of the proposed framework. Table 5 shows the SUS evaluation results from the five experts involved in this study. The proposed framework achieved a score of 60.5, which is acceptable (Bangor et al., 2008). Although the score is lower than what we expected, the experts said that this kind of systematic evaluation process could improve their decision-making process significantly, signifying the potential of the proposed framework. In addition, we indicated the top three items with high deviations among the experts’ evaluations. The statements addressed the complexity of the methodology, and therefore, it was found that the methodology’s process needs to be improved.

    5. CONCLUSION

    Our study proposed a decision-making framework for selecting a maintenance technology and assessed its usability by using the case of a transmission-line maintenance decision. We showed that the proposed framework is usable. The proposed framework can thus contribute to research on the adoption of maintenance technology as follows. First, as we highlighted, only a few studies have addressed the topic of maintenance technology adoption. Aiming to fill this gap, we proposed a decision-making framework to support decision makers in the adoption of maintenance technology in their organizations. Second, the category of decision criteria in our framework was reviewed with reference to various sources in the literature on maintenance technology across industries. Therefore, although the case study was conducted in the context of transmission line maintenance, the criteria reviewed are generalizable to other industries and may be helpful in other industries for selecting a maintenance technology. Moreover, the combination of the ANP–BOCR and ZOGP approaches can enhance decision-making. The decision criteria as well as the constraints or limitations reflected from actual working conditions, such as technology specifications, budget, labor, and other requirements, were taken into consideration. Finally, the proposed framework can support not only decision-making but also other tasks with regard to the adoption of maintenance technologies. For example, the decision criteria under the costs model could provide managers with financial information to manage their budgets with respect to the targeted maintenance technology.

    Despite such contributions, there are several limitations in this study that require future research. First, the experts who determined the criteria interrelationships and weighted alternatives belonged to the same organization. Further case studies are needed for other industries with the participation of experts from different organizations to ensure the generalizability of the research findings. Second, many criteria related to maintenance technology were considered to form this decision-making framework. The change in work conditions in the organization and the current increase in the development of technology may lead to the emergence of other criteria. Thus, the collection of decision criteria and their interrelationships identified in this study need to be updated to reflect such changing external conditions. Finally, the weight of alternative technologies that was obtained from the ANP–BOCR approach was based on the opinion of the decision makers. Hence, some subjective or individual factors may affect the result. To reduce this effect, a fuzzy triangular number approach can be carried out. Future research will address these issues.

    ACKNOWLEDGEMENT

    This study was funded by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF—2019R1F1A1063032) and Seoul National University (0661-20210042).

    Figures

    IEMS-21-2-151_F1.gif

    Proposed framework.

    IEMS-21-2-151_F2.gif

    APS technology selection.

    IEMS-21-2-151_FA1.gif

    ISM calculation in the opportunities (O) model.

    IEMS-21-2-151_FA2.gif

    ISM calculation in the costs (C) model.

    IEMS-21-2-151_FA3.gif

    ISM calculation in the risks (R) model.

    IEMS-21-2-151_F3.gif

    Example of ISM calculation in the benefits model.

    IEMS-21-2-151_F4.gif

    Interrelationships between criteria in the benefits, opportunities, costs, and risks models.

    IEMS-21-2-151_F5.gif

    Pairwise comparison of related criteria in the benefits model.

    IEMS-21-2-151_F6.gif

    Pairwise comparison criteria regarding each alternative in the benefits model.

    IEMS-21-2-151_F7.gif

    Pairwise comparison alternatives with regard to criteria in the benefits model.

    IEMS-21-2-151_F8.gif

    Unweighted, weighted, and limit supermatrices of the benefits model.

    IEMS-21-2-151_FA4.gif

    Unweighted, weighted, and limit supermatrices of the opportunities (O) model.

    IEMS-21-2-151_FA5.gif

    Unweighted, weighted, and limit supermatrices of the costs (C) model.

    IEMS-21-2-151_FA6.gif

    Unweighted, weighted, and limit supermatrices of the risks (R) model.

    Tables

    The 9-point Saaty scale

    The definitions and references of decision criteria in the BOCR model

    Final weights of APS alternatives

    Constraints for consideration in selecting the APS technology

    ZOGP formation for APS technology selection under constraints

    ZOGP results (deviations when t1 = 0, t2 = 1)

    SUS evaluation results

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