A sustainability approach for selecting maintenance strategy

Abstract

Appropriate maintenance can prolong the life of an asset and prevent costly breakdowns that may result in lost production, failed shipping schedules and a decline in customer satisfaction. The goal of this study was to present a comprehensive framework that utilises sustainability metrics based on social, environmental and economic criteria to select an appropriate maintenance strategy among a variety of maintenance strategy alternatives, such as preventive, failure-based, reliability-centred, condition-based and total productive maintenance strategies, for a manufacturing company. The sustainability-based approach may significantly influence the personnel, energy, material and the overall costs in a company. In the first step of this paper, a sustainability-based decision-making structure is proposed for the maintenance strategy selection problem applying the concept of factor analysis to determine the leading factors in each of the sustainability pillars. In the next step, a fuzzy VIKOR framework is used to select the most appropriate maintenance strategy. The provided approach is illustrated using a manufacturing industry case study.

Keywords::

• sustainability
• maintenance selection problem
• fuzzy VIKOR

Introduction

Maintenance planning may extend machine lifetime, prevent costly breakdowns, decrease operating expenses and increase profitability (Sharma, Kumar, and Kumar 2005). Maintenance costs, including spare parts, repair, material and labour costs, constitute 15–60% of the total production cost based on the type of industry (Mobley 2002).

The main contribution of this paper is to develop a comprehensive maintenance strategy selection framework in conjunction with an effective sustainability program, considering the uncertainty involved in the decision-making process. This paper is one of the first attempts to consider all sustainability pillars in the maintenance strategy selection process: in the proposed framework, not only cost and technical issues, but also social and environmental criteria are considered simultaneously to select the best maintenance strategy. The other contributions of this paper can be listed as follows: (1) this research provides a comprehensive list of sustainability criteria summarised from the literature and expert opinions, and presents a reduced decision-making tree (DMT) for the maintenance strategy selection problem (MSSP) using factor analysis (FA) to decrease the number of criteria based on uncertain collected data; (2) uncertainty in the data is modelled using fuzzy numbers to provide more flexibility for decision-makers in the decision-making process; (3) fuzzy VIKOR methodology has been used for the first time to select the best maintenance alternative; (4) the proposed framework is generic and is applicable for any other company and any set of maintenance alternatives at the same management level.

Failure of a system component may cause catastrophic failure in an entire system, higher repair cost and lower quality of the final product, and it might cause the production line to stop completely. The worldwide trend towards Just-in-Time systems motivates zero unscheduled downtimes due to the minimal level of work-in process inventory (Arunraj and Maiti 2007). Hence, an effective maintenance strategy implementation is a key concern that must be addressed for cost reduction and productivity enhancement. Furthermore, an effective maintenance strategy may decrease environmental risks and reduce greenhouse gas emissions, water pollution and soil contamination (Yan and Hua 2010).

As a machine degrades during its lifetime, energy consumption increases (Yan and Hua 2010). The implementation of an optimal maintenance strategy can result in considerable energy consumption savings (Takata et al.2004). Unscheduled stops and downtimes due to machine breakdowns require unnecessary set-ups. Energy consumption increases dramatically every time the machine turns on (Heilala et al.2008) as a result of initial start-up power requirements (Mouzon, Yildirim, and Twomey 2007), which may adversely impact machine reliability and lifetime due to the resulting shocks (Ghazi Nezami, Yildirim, and Wang 2012).

Conventional maintenance strategy selection approaches primarily focus on monetary and technical criteria as the key factors for selecting the best maintenance strategy. Public awareness and governmental rules such as Clean Air Act (1970), Resource Conservation and Recovery Act (1976) and Toxic Substances Control Act (1976) may force companies to consider some soft and non-monetary aspects such as social and environmental standards for MSSP. A sustainable manufacturing system incorporates ecological, social and economic issues during all phases of the product life cycle – from initial design to delivery of the finished product to an end-user. Sustainable management systems can provide the basis for significant savings in these areas by efficiently controlling time, personnel, energy and material (Neugebauer, Wertheim, and Harzbecker 2011).

The sustainable MSSP is a multi-criteria decision-making (MCDM) problem because it addresses a wide variety of social, environmental and economic criteria to select the best maintenance alternative. Proposing a framework to address all these criteria simultaneously seems a necessity. To the best of our knowledge, none of the papers in the literature has addressed a comprehensive framework to accommodate all the criteria of business/economic, social/ethical and environmental sustainability pillars for MSSP while considering uncertainty in decision-maker's ratings modelled as fuzzy numbers.

MSSP relies heavily on decision-makers' (DMs) judgements on various criteria. A fuzzy approach can be used to address the inherent vagueness and uncertainty in the evaluation process, especially when some of the decision criteria are conceptual and the assessment process is carried out using linguistic variables (Al-Najjar and Alsyouf 2003).

This paper proposes a two-phase framework to select a sustainable maintenance strategy: in the first step of phase 1, all the criteria in each sustainability pillar that can impact the sustainable MSSP are listed. Next, a group of sustainability experts evaluates the resulted extensive and detailed sets of criteria to determine the leading factors in each pillar using FA. In the second phase, a fuzzy VIKOR framework is proposed to select the most appropriate maintenance strategy using the leading factors. This framework is summarised as follows: (1) all feasible maintenance strategies (alternatives) at the same management level are determined for a given system; (2) using the main sustainability factors (phase 1 output), alternatives are evaluated by DMs applying linguistic variables translated into fuzzy numbers; (3) a modified fuzzy VIKOR approach, a decision-making tool, is applied to select the best maintenance strategy.

The paper is organised as follows: Section 2 presents a brief literature review of fuzzy approach of the MSSP. Section 3 provides an introduction about maintenance strategy alternatives. Section 4 gives insights into sustainability metrics and explains the FA approach (phase 1) to determine the leading factors in each sustainability pillar. Section 5 describes the fuzzy VIKOR evaluation framework (phase 2). Section 6 illustrates the proposed framework through a case study in a manufacturing company and Section 7 presents the conclusions.

Literature review

Van Horenbeek, Pintelon, and Muchiri (2010) provide a literature review on maintenance optimisation models and develop a general classification structure for maintenance selection model. In their general framework, they consider some technical criteria such as quality, reliability, cost and inventory, as well as the environmental impacts. However, they do not consider the social factors that can impact the sustainable MSSP. Mechefske and Wang (2003) develop a multi-objective model to evaluate and select the most appropriate maintenance strategy. First, they define goals, and then the capability of each strategy for satisfying the given objectives is evaluated with fuzzy expressions. However, they do not address any of the environmental concerns in their study. Al-Najjar and Alsyouf (2003) apply a fuzzy MCDM approach to rank the seven most popular maintenance strategies regarding their abilities to present the information about 13 failure causes, such as humidity, radiation, load, speed and so on. Bertolini and Bevilacqua (2006) propose an integrated analytic hierarchy process (AHP) and lexicographic goal programming approach to select the best maintenance strategy in an oil refinery company. They only consider occurrence, severity and detectability as the selection criteria. In another study, Van Horenbeek and Pintelon 2011 propose a general framework for maintenance optimization problem using analytical network process (ANP) to prioritize the criteria.

Wang, Chu, and Wu (2007) develop a fuzzy AHP approach for the MSSP. Their structure includes only four criteria of cost, safety, feasibility and added value. Jafari et al. (2008) propose a fuzzy Delphi approach to use experts' opinions in simple additive weighting method for the MSSP. They assume four tangible goals of cost, reliability, quality and inventory level, and two intangible objectives of competitiveness and acceptance by labours. Mousavi et al. (2009) present a two-step approach using FA and TOPSIS method to choose the most appropriate maintenance strategy, but they do not consider environmental impacts. Vahdani et al. (2010) propose a VIKOR-based method using interval numbers for MSSP while considering monetary and labour acceptance objectives. They did not consider the environmental criteria and the vagueness involved in the evaluation process. None of the papers above considered the simultaneous impacts of economic, social and environmental criteria on MSSP, considering the uncertainty in evaluation processes.

Maintenance strategies

Several maintenance strategy categories are proposed in the literature. Five of the most common categories are selected here as possible alternatives for the proposed decision-making process. It is also assumed that the following five alternatives are at the same management level:

• Preventive maintenance (PM): this time-based strategy utilises periodical inspection and maintenance over specific time points (age based or calendar time), regardless of the machine condition. Inappropriate inspection interval may expose unnecessary costs to the system (Al-Najjar and Alsyouf 2003).

• Failure-based maintenance: in this corrective maintenance strategy, no maintenance is performed unless a failure occurs. This strategy can be implemented in companies with large marginal profits (Wang, Chu, and Wu 2007).

• Reliability-centred maintenance (RCM): the main goal of the RCM strategy is to increase machine uptime and maintain the machine reliability level rather than restoring it to an ideal situation (Sharma, D. Kumar, and P. Kumar 2005).

• Condition-based maintenance (CBM): sensor data such as vibration, lubricant level and ultrasonic sound level are collected and analysed to determine likelihood of a potential failure. This strategy might not be affordable for all companies due to the significant investment for installing necessary sensors and monitoring technology (Sharma, Kumar, and Kumar 2005).

• Total productive maintenance (TPM) strategy: this alternative integrates the concepts of maintenance and quality via performing daily inspections by trained operators to eliminate major losses in downtimes, set-ups and yield in production. Successful implementation of this strategy requires a high level of employee involvement (Sharma, Kumar, and Kumar 2005).

In the next section, all the sustainability-based criteria that can impact MSSP are described. It is important to note that the proposed sustainability-based framework with the fuzzy decision-making methodology is applicable to evaluate any set of maintenance alternatives at the same management level and is not limited to the above maintenance strategies.

Phase 1: Sustainability and related metrics

Successful implementation of a sustainable development plan entails the incorporation of some predetermined criteria at all operational activity levels. Tables 1, 2 and 3 provide an extensive set of criteria for each sustainability pillar using the literature cited in Section 2 and also through discussions with experts in sustainability.

Table 1 Business sustainability subcriteria.

Pillar	Subcriteria
Business excellence/economic factors	1. Hardware cost	17. Mean time to repair
	2. Applied technology complexity	18. Manufacturing system type
	3. Software cost	19. Detailed production scheduling
	4. Mean time between failures	20. System design
	5. Risk level of the system	21. Repairability
	6. Research and development cost	22. Failures type severity
	7. Customer satisfaction	23. Technical feasibility
	8. Product variety	24. Flexibility
	9. Creativity	25. Return on investment
	10. Product development stage	26. Demand urgency
	11. Competitive enhancement	27. Spare machine availability
	12. Current reliability level	28. Spare parts availability
	13. Reliability improvement plans	29. Tear and wear rate
	14. Access difficulty	30. Lead time
	15. Quality of the product/service	31. Lost production cost
	16. Time efficiency	32. Personnel training cost

Table 2 Social sustainability subcriteria.

Pillar	Subcriteria
Social/human contribution factors	1. Stakeholder participation	6. Development of management and engineering expertise
	2. Employment issues	7. Personnel health
	3. Personnel safety	8. Personnel wage
	4. Personnel training	9. Government regulations
	5. Acceptance by personnel	10. Holding related to social standards

Table 3 Environmental sustainability subcriteria.

Pillar	Subcriteria
Environmental factors	1. Energy consumption	6. Waste cleaning cost
	2. Holding environmental standards	7. Waste type
	3. Environmental planning	8. Toxic emissions to air, soil and water
	4. Inside toxic emissions	9. Resource availability
	5. Raw material consumption	10. Environmental management systems

The first sustainability pillar, business/economic, includes 32 cost- and technical-related subcriteria, which have been mostly considered by other research papers about the MSSP (Table 1). These subcriteria address the concepts of cost, efficiency, quality and technical aspects of a maintenance strategy and are obtained through a comprehensive literature review [e.g. Mechefske and Wang (2003), Al-Najjar and Alsyouf (2003), Bertolini and Bevilacqua (2006), Garg and Deshmukh (2006)].

Hardware and software costs along with personnel training costs address the implementation costs of a specific maintenance strategy. The cost of lost production and return on investment are indicators of a maintenance strategy's economic impact on a production system. Spare machine and part availability, as well as repairability, may impose constraints on the level of inspections for a maintenance strategy. Rendering high-quality products within a specified lead time and satisfying customer expectations are some of the key factors for the sustainable MSSP, since maintenance strategies impact the availability time and quality of the finished products.

Meantime between failures, equipment tear and wear rate and the severity of failure type illustrate the importance of choosing an appropriate maintenance strategy because these factors can extensively impact a machine's degradation status. Once a detailed production schedule (criterion 19) is available, DMs may plan accordingly for maintenance, considering the information about machine availability times. System design is also another factor in the sustainable MSSP, because failure of one component may propagate throughout the system due to stochastic dependence among components (Nicolai and Dekker 2007).

Technical feasibility is the very initial condition of the MSSP because not all maintenance strategies are appropriate for a given machine. Difficulty in accessing machine components may lead to disassembling the machine for repair, and consequently more downtime and more production and profit losses. Also, appropriate maintenance strategies can provide the required accuracy and availability level of important resources such as laboratories and machines within a company which may flourish creativity in developing new services and products. Furthermore, proper maintenance planning may prevent unwanted breakdowns in any of the introduction, growth and maturity phases of the product life cycle which may result in significant losses in market share and profit.

Expected and current reliability levels of a system are good indicators in determining the criticality of choosing the appropriate maintenance strategy. Considering the type of manufacturing system during maintenance selection is of great importance as well. Maintenance strategies for a job shop may not be efficient in a flow shop or cellular manufacturing system. Meanwhile, system flexibility is a factor that can be achieved through an appropriate maintenance strategy implementation.

The social or ethical pillar of sustainability addresses the human or societal capital concerns affecting the MSSP (Table 2). Successful implementation of any strategy in a company needs its stakeholders' support and participation. It also requires personnel acceptance in order to guarantee the goal achievement. Employment subcriteria address whether current personnel is capable of implementing the chosen strategy or new personnel should be hired or trained to execute the strategy. Safety and health standards within the company, as well as governmental regulations, can impact MSSP.

Environmental-based subcriteria of sustainability such as toxic emissions, energy consumption, resource depletion and waste production are the factors that may impact MSSP significantly (Table 3). Companies are willing to modify their policies to minimise these negative impacts. There is no doubt that applying an appropriate maintenance strategy will reduce emissions and waste production rate, which in turn results in raw material conservation, especially because some types of waste are hazardous, unrecyclable or too expensive to be cleaned up. Moreover, implementing an appropriate maintenance strategy will decrease machine downtime and consequently decrease the energy consumed by succeeding machines running idle and the spike energy for turning the repaired machine on again (Ghazi Nezami, Yildirim, and Wang 2012).

In summary, we identified 32 economic/business, 10 social and 10 environmental subcriteria influencing the MSSP. DMs may find the evaluation process of maintenance alternatives for so many subcriteria difficult and confusing, and the results may be inaccurate and inconsistent. Exploratory FA is utilised to determine leading factors and decrease the total number of 52 subcriteria to achieve a more effective evaluation process.

Determining leading factors

FA is an efficient covariance-based statistical dimension-reduction method that can identify the latent structure affecting variables (Lattin et al.2003). The main purpose of FA is to reduce the number of integrated variables (subcriteria) to a smaller number of clusters based on the strength of the relations among variables with the least amount of data missing. Figure 1 depicts the concept of FA. Each variable (subcriteria) is affected by underlying factors; however, a given factor may influence a variable more than other factors. This influence is determined by the strength of the correlations (Fruchter 1954).

Figure 1 FA (p < t).

The FA process is summarised as follows (Lattin et al.2003):

• Data are collected for each variable.

• For a given set of variables, a correlation matrix is calculated.

• If there is significant correlation between variables, a set of factors is extracted.

• A rotation method can be applied to transform the data for ease of interpretation.

• If each subcriteria shows a significant load on one factor, STOP. Otherwise go to Step 2.

The factors extracted in the third step are based on the variance of the data that can be explained by these factors. A rotation method can be applied to obtain an easier and more reliable interpretation of factors. In this paper, Varimax, a common orthogonal rotation method, is applied (Lattin, Carroll, and Green 2003). As a result of rotation, each factor explains fewer criteria. FA is performed using the SAS software (http://www.sas.com/?gclid = CKzKhKLZh60CMFQDQAoddVOGnQ, March 2012).

To provide the data for FA (data collection step), initially 52 variables are evaluated by a group of 30 sustainability experts via questionnaires using linguistic terms. These linguistic terms, which are transformed into fuzzy numbers (Table 4), address the impact of each subcriterion to achieve the objectives of sustainability in each pillar with respect to experts' opinions. Some of the selected factors, such as personnel effect and environmental management systems, are conceptual criteria, and their impact on sustainability is difficult to express with crisp numbers. Moreover, uncertainty and vagueness are always involved in decision-making processes. These issues are solved by utilising linguistic variables transformed into fuzzy numbers. The sustainability experts' evaluations are integrated by taking the weighted average of the fuzzy numbers to calculate the final score of each subcriterion.

Table 4 Fuzzy linguistic terms in assessing the impact of each subcriterion on each sustainability pillar.

Linguistic term	Fuzzy triangular number
Very low (VL)	(0, 0, 0.1)
Low (L)	(0, 0.1, 0.3)
Medium low (ML)	(0.1, 0.3, 0.5)
Medium (M)	(0.3, 0.5, 0.7)
Medium high (MH)	(0.5, 0.7, 0.9)
High (H)	(0.7, 0.9, 1)
Very high (VH)	(0.9, 1, 1)

The first iteration of FA implementation on economic/business pillar subcriteria (Z_i, i = 1,…,32) using experts' preferences reveals that five subcriteria did not have considerable weight on the extracted factors (small correlation to all factors). These criteria are removed from the list of 32 criteria, and FA is again performed on the remaining subcriteria in the SAS software (http://www.sas.com/?gclid = CKzKhKLZh60CFQMDQAoddVOGnQ, March 2012). The results after rotation are presented in Table 5. The subcriteria showing significant load on factors are marked with star (^*). This significance is determined proportionally in comparison to the other load values in the associated factor column and are mainly assumed to be greater than 45 (almost 50% relevance).

Table 5 Business and economic FA results after rotation.

	Factor 1	Factor 2	Factor 3	Factor 4	Factor 5	Factor 6
Z1	− 18	4	91*	4	10	12
Z2	− 48*	− 4	38	13	17	− 14
Z3	− 5	− 9	65*	− 8	14	8
Z4	17	4	12	− 4	86*	9
Z5	12	35	41	− 9	0	61*
Z6	30	76*	0	− 9	2	− 32
Z8	− 13	72*	− 13	16	6	− 6
Z9	26	88*	5	− 8	− 8	− 4
Z10	8	85*	6	19	2	16
Z11	− 1	91*	− 13	9	6	1
Z14	60*	40	4	− 42	− 14	5
Z15	− 23	32	− 21	63*	14	4
Z16	33	40	− 2	31	69*	5
Z17	1	7	10	15	77*	7
Z18	− 9	− 9	24	28	17	77*
Z20	38	− 25	34	− 40	14	47*
Z21	67*	33	25	17	7	25
Z22	74*	2	13	− 16	21	2
Z23	58*	− 11	27	− 45	− 2	17
Z24	67*	19	− 17	− 6	− 30	23
Z26	9	3	34	65*	− 17	10
Z27	89*	10	3	18	9	− 16
Z28	82*	2	− 3	10	4	− 22
Z29	58*	20	2	21	25	− 13
Z30	2	4	− 27	80*	21	15
Z31	30	35	47*	− 11	1	− 7
Z32	33	− 5	71*	− 14	− 1	13

The first factor, ‘technological feasibilities and reliability’, includes a variety of subcriteria, including technology complexity; machine design specifications such as reparability, spare parts and machine availability; wear and tear rate of machine components; failure severity type and machine flexibility level. This factor reveals how the technical specifications and reliability constraints are important for the MSSP. The second factor, ‘innovation’, addresses five criteria of research and development activity costs, product variety, product development stage, creativity and competitive enhancement actions within the firm. Innovative companies require more accurate maintenance strategies in order to achieve higher levels of competitive advantages and flexibility.

Factor 3, ‘implementation cost control’, includes hardware and software costs, personnel training cost and lost production cost. This factor investigates the cost-efficiency of a strategy. Factor 4, ‘demand satisfaction’, mainly addresses customer satisfaction-based criteria, such as quality of the final product or service and lead time duration in order to satisfy the demand at the right time. Maintenance strategies influencing system downtime can greatly impact the lead time.

The time between failures, the time to repair and the time efficiency subcriteria show a higher load in factor 5. These metrics are indicators of ‘time efficiency’ of a maintenance strategy, which can provide some insights about maximum allowable machine downtime due to scheduling. The last factor, ‘systematic compatibility’, refers to system design characteristics, manufacturing system type and risk level. As explained earlier, the MSSP for a flow shop system is more critical in comparison to a job shop environment, since any interruption in a production line may cause the entire line to stop. Moreover, higher level of dependencies between system components increases the overall risk of failure. The allowed risk level of the system, indicating the impact of undesirable events on a system, is an important factor in MSSP as well.

Applying FA on the data collected via questionnaires on social pillar subcriteria (X_i; i = 1,…,10) results in three underlying factors. Regarding factor loadings after the initial rotation, it is observed that variable X₂ has nearly equal loads on factors 1 and 2. This subcriterion (employment issues) is removed considering the correlation values, and FA is performed again over the remaining variables (X₁, X₃,…,X₁₀). Results are shown in Table 6.

Table 6 Secondary social FA results after rotation.

	Factor 1	Factor 2	Factor 3
X1	56*	− 11	16
X3	9	81*	1
X4	− 19	13	80*
X5	33	− 38	55*
X6	73*	17	− 11
X7	0	74*	24
X8	31	27	56*
X9	84*	− 4	22
X10	54*	4	− 5

In Table 6, each variable has a meaningful load on one of the three extracted factors. The first factor, ‘stakeholders’ satisfaction', includes stakeholder participation, development of management and engineering expertise, government regulations and social standards. The second factor, ‘safety’, refers to the ability of the selected strategy to provide required levels of safety and minimise the negative health impacts. The third factor includes the remaining criteria such as personnel wage and required training for performing a specific type of maintenance strategy and personnel acceptance. These metrics refer to a common concept of ‘personnel competency’.

Table 7 presents the results of FA implementation after rotation for the environmental criteria (Y_i; i = 1,…,10), leading to three underlying factors. Factor 1, ‘waste emissions control’, contains toxic emissions within the manufacturing plant, waste cleaning and recycling costs, waste type, and toxic emissions to air, soil and water. The second factor, indicating environmental standards, environmental planning and management systems, is referred to as ‘environmental management system support’. The third factor, or ‘resource and energy consumption control and conservation’, includes the remaining environmental metrics and evaluates the capability of each maintenance strategy in energy and resource conservation.

Table 7 Environmental FA results after rotation.

	Factor 1	Factor 2	Factor 3
Y1	0	12	72*
Y2	− 2	57*	11
Y3	17	74*	20
Y4	53*	14	4
Y5	− 6	8	59*
Y6	46*	− 25	15
Y7	63*	− 3	4
Y8	78*	− 22	− 18
Y9	25	6	53*
Y10	34	− 62*	40

In summary, as the output of phase 1, the subcriteria affecting MSSP are decreased to 12 factors (instead of the originally proposed 52 subcriteria) as a result of FA. This approach provides a simplified decision-making tree (DMT) by decreasing the number of subcriteria in each sustainability pillar, thus resulting in a more consistent and reliable decision-making process.

It is important to note that the composition of leading factors may change if another group of sustainability experts is consulted: for a given group of experts, the proposed framework is generic and applicable to any sustainable selection problem that has alternatives at the same management level.

Phase 2: Fuzzy VIKOR evaluation framework

The output of phase 1, the reduced DMT, is an input of phase 2. In this phase, given maintenance strategy alternatives and ratings on the sustainability factors by DMs, a fuzzy VIKOR evaluation framework is utilised to determine the best maintenance strategy.

Fuzzy evaluation

Deterministic decision-making techniques cannot model the inherent uncertainty in human judgement accurately. In this case, a fuzzy approach can be utilised as a powerful method for modelling decision-making problems when subjective judgements of DMs are available (Cai 1996).

In the proposed framework, the first step involves DMs specifying the weights of the main subcriteria shown in the second level of the DMT (i.e. extracted factors, see Figure 2) to indicate the importance of each factor in satisfying sustainability objectives for the sustainable MSSP, using the linguistic variables provided in Table 4. Also, the capability of each maintenance strategy alternative (level 3 in the DMT in Figure 2) is evaluated for satisfying the objectives of each sustainability factor, using the linguistic terms shown in Table 8 (Mousavi et al.2009). These linguistic variables are transformed into fuzzy numbers. The main fuzzy mathematical relations used in this research are summarised in Appendix.

Figure 2 Reduced DMT.

Table 8 Linguistic variables for the rating alternatives.

Linguistic term	Fuzzy triangular number
Very poor (VP)	(0, 0, 1)
Poor (P)	(0, 1, 3)
Medium poor (MP)	(1, 3, 5)
Fair (F)	(3, 5, 7)
Medium good (MG)	(5, 7, 9)
Good (G)	(7, 9, 1)
Very good (VG)	(9, 1, 1)

Fuzzy VIKOR method

Once the weights of criteria and alternatives are determined, a fuzzy VIKOR method is utilised to select the best maintenance strategy. The VIKOR method is an efficient decision-making technique for complex systems with multiple conflicting objectives, which provides a compromise solution with a ranking index, based on the distance from the ideal solution (Opricovic and Tzeng 2004).

The VIKOR method has some advantages to other common MCDM alternative ranking methods such as TOPSIS and the AHP. The VIKOR method uses linear normalisation, which causes the normalised values to be independent of measurement units whereas the TOPSIS method uses the vector normalisation method in which the normalised values will be dependent on the criteria-measurement units. The most appropriate alternative in the VIKOR approach is the one closest to the ideal point; however, in the TOPSIS approach, the best alternative can be different from VIKOR's output since it is based on the ranking indexes (Opricovic and Tzeng 2004). AHP is a systematic approach that determines the best alternative by performing pair-wise comparisons among alternatives and lacks a strong normative foundation (Bertolini and Benilacqua 2006).

The applied fuzzy VIKOR method includes the following steps (Büyüközkan and Ruan 2008):

Step 1	=	Generate m feasible alternatives, define k evaluation criteria and establish a group of n DMs.
Step 2	=	Define linguistic variables and related fuzzy numbers using Tables 4 and 8. Linguistic variables are used to assess the importance of the criteria and rate the alternatives with respect to various criteria and subcriteria.
Step 3	=	Integrate DMs' preferences by aggregating the fuzzy weight of criteria and fuzzy rating of alternatives from n DMs of the same importance: where rij is the rate of alternative i with respect to criterion j

.

Step 4

=

Construct a normalised (0 < f < 1) fuzzy decision matrix: where is a triangular number defined as

Step 5

=

Determine the fuzzy best alternative, , as (1,1,1)

Step 6

=

Calculate and values for each alternative: where , the maximum group utility, is the average score of alternative Ai calculated by the sum of the distances from the fuzzy best alternative, and , the individual regret, is the worst group score of alternative Ai, defined to be the maximum distance from the best alternative

Step 7

=

Calculate the value of based on the considerations of both group utility and individual regret, using normalised values of and ( and , respectively) through the following equation: where v is the weight of the strategy ‘maximum group utility’. When v>0.5, the compromise solution is obtained with voting by the majority, while v = 0.5 yields consensus and v < 0.5 gives veto compromise solutions

Step 8

=

Defuzzify the triangular fuzzy numbers (TFNs) of , and , and sort them in increasing order. Defuzzification is performed using centroid approach (Fullér 1995)

Step 9

=

Determine the compromise solution using following conditions:

• Condition 1 [C1]: Acceptable advantage of alternative J_I, the alternative with the smallest value of Q in the sorted set (Q[1]), if:

• Condition 2 [C2]: Stability in decision-making: J₁ is a stable solution by having the same order in the sorted sets of R and/or S.If one of the above conditions is not satisfied, then a compromise solution should be proposed as follows:

• Alternatives J₁, J₂,…,J_m if [C1] is not met, and J_m is specified by Q_[m]–Q_[1] < DQ for the maximum m.

• Alternatives J₁ and J₂ if [C2] is not met.

In the next section, the framework is illustrated using a case study.

Case study

This case study presents the application of the proposed approach in a car manufacturing company with a sustainable development plan, looking to select the most appropriate maintenance strategy for their system.

Phase 1 provides a reduced DMT. As the first step of phase 2, feasible maintenance strategy alternatives are presented to three managers (n = 3) in the company. Preventive (A₁), failure-based (A₂), reliability-based (A₃), condition-based (A₄) and total productive (A₅) maintenance strategies are five alternatives (m = 5), which are evaluated using the 12 sustainability factors shown in the second level of the DMT in Figure 2. Chief executive manager (D₁), maintenance manager (D₂) and production manager (D₃) are three individuals whose speciality judgements are equally weighted in this decision-making process.

The managers are asked to weight the sustainability factors using the linguistic variables provided in Table 4. Results are shown in Table 9. These weights show the importance of each factor in level 2 for achieving sustainability objectives of the company with respect to DMs' working experience. The weights of social, economic and environmental pillars (level 1 of the DMT in Figure 2) are assumed to be equal and very high (VH), since they are the foundations of a successful sustainable development plan. Analysing the responses, one can observe that the managers have different insights. For example, the chief executive manager is mainly focused on profit, whereas the production manager is primarily concerned about time, quality and lost production cost factors. The maintenance manager's decisions address reliability and implementation barriers.

Table 9 Criteria weighting by DMs.

	S1	S2	S3	E1	E2	E3	B1	B2	B3	B4	B5	B6
DM1	VH	MH	ML	H	VH	MH	VH	MH	VH	M	H	ML
DM2	M	VH	VH	VH	MH	M	VH	H	MH	VH	MH	H
DM3	ML	VH	M	H	ML	VH	VH	MH	H	VH	VH	MH

In the next step, the DMs are asked to rate the alternatives (level three of the DMT in Figure 2) for the second-level factors using the linguistic variables presented in Table 8. Results are shown in Table 10, where S1–S3 refer to the three social criteria of stakeholder's support, safety and personnel competency, respectively. Also, E₁–E₃ address waste emission control, environmental management system support, and resource and energy consumption control criteria in the environmental pillar. B₁–B₆ include the business/economic pillar's factors shown in Figure 2. The ratings in Table 10 present the capability of each maintenance strategy, with respect to managers' perspectives, to help the company satisfy sustainability subcriteria objectives (Steps 1 and 2).

Step 3

=

Managers are then asked to repeat weighting the criteria and rating the alternatives three times in order to check the consistency of their ideas. Inconsistency could have been observed if they gave different weights to the same criterion on different occasions. In the case of any inconsistency, we would have had another interview questioning the reason for this change and asking the managers to repeat the weighting and rating procedure. At the final stage, managers' preferences are transformed into fuzzy triangular numbers and then integrated using Equation (1). Here, no inconsistency was observed. Table 10 Alternative ratings by DMs on sustainability subcriteria. S1 S2 S3 E1 E2 E3 B1 B2 B3 B4 B5 B6 DM1 A1 MG VG G VG VG VP G VG P VG MP MG A2 G MP F VP MP G G P G F G F A3 MP G MG VP VP G G VG G F G MG A4 F VG MG VG MP MP G G VG F P G A5 VG F G F MP F F VG P VG F MG DM2 A1 MP G G VG VG VP G MP MP G VP MP A2 P VP F VP VP VP VP VP VP P MP P A3 MP P G MP MP F G G F MP F VP A4 G VG G VG VG MG F VG P G VG G A5 G G F G G F G G P VG MP G DM3 A1 F G G G G P G P MP F VP F A2 G P G VP VP VP F P MP VP F F A3 G MP G P P F G F G MP F MP A4 MP F G VG VG G G VG MP VG VG F A5 VG G G VG F G G F MP G MP F

Step 4

=

A normalised fuzzy decision matrix is constructed using the linear transformation Equation (7).

Step 5

=

Fuzzy best alternative is determined as (1, 1, 1).

Step 6

=

The values of , are calculated for each alternative, given v = 0.5.

Step 7

=

is calculated using normalised values of () and () (Table 11). Table 11 S′,R′ and Q values for each alternative. S′ R′ Q A1 0.48 0.61 0.71 0.70 0.87 0.97 0.59 0.74 0.84 A2 0.69 0.88 1.00 0.62 0.82 0.99 0.66 0.85 1.00 A3 0.54 0.68 0.78 0.77 0.93 1.00 0.65 0.81 0.89 A4 0.29 0.37 0.42 0.41 0.51 0.56 0.35 0.44 0.49 A5 0.40 0.50 0.57 0.66 0.82 0.91 0.53 0.66 0.74

Step 8

=

TFN , and are defuzzified and sorted increasingly based on the values of defuzzified numbers (Table 12). Table 12 Defuzzified values of S′, R′ and Q. S′ Ranking index R′ Ranking index Q Ranking index A1 0.60 3 0.85 4 0.72 3 A2 0.86 5 0.81 3 0.83 5 A3 0.67 4 0.90 5 0.78 4 A4 0.36 1 0.49 1 0.43 1 A5 0.49 2 0.80 2 0.65 2

Step 9

=

For determining the compromise solution:

It can be seen that condition [C1], acceptable advantage of alternative J_I, is not satisfied. However, alternative A₄ is stable because it has the same ratings in the sorted sets of R′ and S′ (condition 2 is held). Since one of the conditions is not held, a compromise solution set of A₄ (CBM strategy) and A₅ (TPM) is proposed for the given v = 0.5. The compromise solution set includes the ranked solutions, having the first alternative as the first option to implement.

The weight of the strategy ‘maximum group utility’, v, is an important factor in determining the compromise solution in the VIKOR method. Table 13 provides some information about the impact of v variations on the compromise solutions. By decreasing the value of v as the weight of the average score, which entails assigning higher weight to individual regret score, the condition-based strategy will be the only selected maintenance alternative for this company. However, increasing this value to 1, showing the average distance of the alternatives from the ideal for all criteria, the solution set is expanded and includes condition-based, reliability-based and PM strategies.

Table 13 Analysis of v changes on alternative ranking.

V	Compromise solution
0	A4
0.25	A4
0.5	A4, A5
0.75	A4, A5
1	A4, A5,A1

This process relies heavily on managers' opinions. Considering different weights for the managers, factors and subcriteria may significantly impact the results. The weights of factors are defined with respect to the expectations and conditions of the company. In this section, the most important scenarios for the above case study are presented. Analysis shows that for v = 0.5, when only the social factor is considered in the decision-making process, A₅, A₄ and A₁ strategies are obtained as the compromise solution set: the total productive maintenance is the most confirmative strategy to social criteria. If only social and environmental criteria are considered as the decision-making criteria, the compromise solution set remains as before (A₄, A₅), which indicates the importance of the other criteria rather than the economic criteria, which have been mostly ignored in previous research studies for the MSSP. Ignoring the impact of social and economic factors (considering only environmental pillar) yields the same results showing the impact of the environmental factors in MSSP. Considering only the economic criteria, the model gives (A₃, A₄) as the compromise solution set. Alternative A₃ (reliability based) was not selected in any of the previous scenarios. It shows that including only the economic criteria may not be adequate for selecting a sustainability-based maintenance strategy. One can argue that the reliability-based strategy is mostly concerned about machine uptime and failure likelihood and is less sensitive to environmental and social issues, based on managers' opinions.

Companies are more sensitive to sustainability, especially to the environmental pillar, in the current competitive market. Although reducing environmental impact may increase the cost of operations, companies are investing towards a sustainable future and enforcing this standard throughout their supply chains.

Conclusion

Instead of considering a large number of subcriteria in a sustainability-based maintenance selection problem, the first phase of this study determines the leading factors in each sustainability pillar. In the second phase of this research, a fuzzy VIKOR method is utilised to rate the maintenance strategy alternatives using sustainability factors. To the best of our knowledge, the previous studies did not consider the simultaneous analysis of the social, environmental and economic factors in MSSP. Because, the VIKOR method provides a compromise ordered solution set, a company can incorporate the benefits of the selected strategies to be more efficient. The provided case study also approves the criticality of the social and environmental criteria for MSSP, which are mostly disregarded in the previous research papers.

For more analysis, this decision-making process may be repeated considering all the 52 criteria and compare the results with the outputs of this study to investigate the amount of data loss through FA. Also, the ANP method (Van Horenbeek and Pintelon 2011) can be applied to the sustainability criteria and the results of ANP can be compared with the proposed framework.

Appendix: Fuzzy numbers theory

Basic Definition: A TFN can be defined as a triplet of crisp numbers () and membership function of for the fuzzy number such that:

Suppose that and are two TFNs shown as and , respectively. The operational rules of these two TFNs are as follows (Ganoulis 2009) Figure 3:

Figure 3 Membership function of TFN.

The distance between two TFNs and is calculated (Chen 2000) as

The fuzzy maximum of and is calculated using (Ganoulis 2009):