Evaluating Performance-Based Logistics in Manufacturing Through Polytopic Fuzzy SWARA: A Criterion Assessment Approach

Today, competition for businesses is realized through supply chain management, and PBL measurements have become very important. Supply chain management performance factors require an effective decision mechanism, thus forcing businesses to make decisions continuously in rapidly challenging and ever-changing market conditions [1]. In this context, PBL applications, a method that has been used in both civilian and military fields for nearly thirty years, come to the fore. In particular, applications, which are an approach that envisages the purchase of the required service at the performance level instead of purchasing logistics elements, offer various gains to businesses [2].

PBL is the procurement of logistics support as an integrated, cost-acceptable performance package designed to meet a system's performance objectives and ensure that the system is ready for the appropriate level of value through long-term logistics support contracts with clearly defined authorities and responsibilities. Instead of purchasing spare parts, equipment, and information (the classical approach), it is defined as purchasing a predetermined level of services to meet operational objectives [3]. In another definition, it is stated that it is a product/material support approach that ensures that systems are reliable, sustainable, and readily available when and where end users need them to ensure mission success, focusing on the performance outputs of the systems and aiming to operate and maintain these systems in a cost-effective manner in the life cycle [4]. The aim of these applications is to provide life-cycle product support where the required reliability and availability are provided at a lower cost and the use of inventory in the procurement process is maximized through PBL [5].

The PBL strategy aims to purchase performance targets rather than supply products. With the PBL approach, it is aimed at creating an environment where the requirements of the end customer are determined, performance values are purchased instead of material supply, the supplier is told what is desired, not how, a strategic link is established, risk sharing is made, a program management perspective is dominant, all partners focus on their core capabilities, and the focus is on the life cycle [6]. In fact, while increasing the availability of systems, subsystems, or components with effective applications, it also reduces the cost of services per performance unit. In addition, it has been observed that PBL provides 20–40\% performance efficiency while reducing costs by 15-20% [7].

Again, with PBL applications, the increase in the level of readiness and reliability of the systems leads to savings in total life cycle costs and shorter waiting times for the end user. It also provides reduced inventory quantities, increased consistency in meeting mission requirements, reduced risks in achieving expected performance, and early detection of errors using predictive and diagnostic analysis. In addition, thanks to the related applications, the support provider has flexibility in producing solutions without compromising the performance of the system, keeps the budget under control by establishing a performance-based cost calculation system, and contributes to allocating more share to innovation by including long-term contracts and sharing the profits obtained with the support providers [8].

On the other hand, PBL applications also enable the measurement of efficiency through performance parameters. Performance-based parameters are optimized through contract management [9]. The PBL approach also serves to create an environment where the real needs of the end-user are determined, the supplier is told what is desired, not how, performance is purchased instead of individual products, strategic relationships are established, risk sharing is made, the program management perspective is dominant, all stakeholders focus on their own capabilities, and the focus is on the life cycle [5].

In conclusion, when we look at the benefits of a PBL system, it can be said that it is a strategic approach that focuses on the procurement of reliable, maintainable, and readily available systems in line with the needs of the user and the cost-effective operation, maintenance, and sustainment of these systems [4].

Based on the above-mentioned issues, it is seen that PBL practices affect critically important issues such as efficiency, competitiveness, effectiveness, performance, and end-user satisfaction for both businesses and users. Therefore, PBL application advantages are seen as extremely important issues and are considered to be issues that need to be emphasized meticulously. Because making supply chain management flexible and agile affects not only production management but also the entire process up to the end consumer, related practices are defined as critical components. At the same time, it provides important indicators at the point of creating the motivation source of the study. Based on all these issues, the study aims to identify and rank the advantages of PBL applications by using MCDA methods in manufacturing enterprises with corporate identity in Ordu province.

A literature review on PBL and PBL practices is presented below:

• Hypko et al. [10] created a new conceptual model for PBL practices in their detailed literature review.

• Kaczmarski [11] examined the issue of funding as a barrier to achieving the strategic objectives of PBL considerations. In addition, he investigated the potential impact of contractor-funded procurement on system readiness and cost.

• Guajardo et al. [12] empirically investigated how product reliability is affected by the use of two different aftermarket maintenance support contracts (traditional, i.e., time and materials contracts, and performance-based contracts) using a real data set provided by a major aircraft engine manufacturer.

• Ahmad [13] a quantitative investigation for investigating the effectiveness of performance-based logistics. It also investigated the relationships between performance-based logistics facilitators and performance-based logistics effectiveness.

• Micklich and Lasch [14] designed a contract by proposing a morphological box for performance-based contracts.

• Kim et al. [15] compared traditional support strategies and PBL strategies using the game theory.

• Dirican [7], a mathematical model was developed to determine the contract terms in the PBL application and was run for scenarios varying in terms of contract duration, number of supported systems, incentive amount, and order response time for a helicopter engine in the inventory.

• Ivan et al. [16] performance-based logistics theory and explores the potential of applying the service model under the theory to Taiwan's heavy-duty truck supply chains. A multiple case study approach is used to explore this research question.

• Hur et al. [17] addressed the problem of inventory control of aircraft spare parts at the end of their life cycle and developed an algorithm that calculates the final order quantity.

• Wang et al. [18] presented a new optimal maintenance policy under performance-based contracting that improves system readiness while maximizing suppliers' profits.

• Glas [19] presented case studies of PBL in the military as a lesson.

• Zhu et al. [20] presented a framework for integrating prognostics and health management into PBL.

• Agdas and Gencer [21] proposed a dynamic performance evaluation model to support the material availability of the public organization and select the most appropriate service provider within PBL.

• Stiller [22] conducted a qualitative study investigating the interest of non-governmental organizations in participating in PBL.

In the detailed literature review given above, PBL applications have been investigated in different ways. It is thought that the proposed study will contribute to the literature both in terms of the method used in the application and the province where the application is made.

Uncertainties arise from the variety of elements involved in decision-making problems. In order to process the uncertainties in the problems and reach feasible solutions, many fuzzy sets have been developed. Bet et al.'s Polytopic Fuzzy Sets (PtFSs) are one of them [23]. PTFSs are considered a generalization of picture fuzzy sets (PFSs), and q-rung orthopair fuzzy sets (q-ROFSs). In particular, it has been stated that PtFSs can be used as an effective tool to solve decision-making problems where SFSs, PFSs, and q-ROFSs cannot be applied [23].

The decision-making problem in this study will be solved using the SWARA technique as defined under PtFS. SWARA makes it possible to effectively obtain problem-related evaluations from evaluators who are unfamiliar with MCDA methods. SWARA has a simple-to-understand and easy-to-apply structure. PtFS-SWARA, proposed in this study, enables the modeling of uncertainties in addition to the mentioned features.

The basic PtFS operations will be presented first in this section. Following that, the PtFS-SWARA processing steps will be explained.

Assuming that $X$ is a universe of discourse, then a PtFS $H$ of $X$ can be stated as $H=$ $\left\{\left\langle x,\alpha_H(x), \eta_H(x), \beta_H(x)\right\rangle: x \in X\right\}$, where $0 \leq \alpha_H(x)^q+\eta_H(x)^q+\beta_H(x)^q \leq 1$. Also, $\alpha_H: X \rightarrow[ 0,1]$ is the positive membership degree, $\eta_H: X \rightarrow[ 0,1]$ is the neutral membership degree, and $\beta_H: X \rightarrow[ 0,1]$ is the negative membership degree of $x \in X$ to PtFS $H$. The triplet $\langle\alpha, \eta, \beta\rangle$ is called a PTF number (PtFN) for the simplicity. The basic operations for PtFNs are presented below, where $h=\langle\alpha, \eta, \beta\rangle, h_1=\left\langle\alpha_1, \eta_1, \beta_1\right\rangle, h_2=\left\langle\alpha_2, \eta_2, \beta_2\right\rangle$ are three PtFNs [23].

The score function $(\mathcal{S}(h))$ and accuracy function $(\mathcal{A}(h))$ are calculated using Eqs. (6)-(7), respectively [23].

The PtF weighted aggregation operator (PtFWA) is calculated using Eq. (8), where $h_i$ for $i=1, \ldots, m$ are PtFNs [23].

In Eq. (8), $k$ is the weight vector, where $k=1, \ldots, r$.

The PtF-SWARA implementation steps are presented below [24].

Step 1. The decision-making problem is defined. The criteria to be considered in solving the problem and the experts to be consulted for their evaluations are determined. In this context, $C_1, \ldots, C_n$ represent criteria, and $U_1, \ldots, U_r$ represent decision-makers or experts.

Step 2. Experts use the linguistic terms in Table 1 to express the criteria's levels of importance [24]. As a result, $\iota_{j k}=\left\langle\alpha_{j k}, \eta_{j k}, \beta_{j k}\right\rangle$ shows the importance of the $j$-th criterion determined by the $k$-th expert.

Step 3. The experiences, occupations, and positions of experts may influence how they are evaluated. This might require giving expert assessments different weight values. In this case, Table 1's linguistic terms are used to estimate the importance of expert evaluations. Expert weight values are then computed using Eq. (9), where $\iota_k$ is the PtF importance value of k-th expert, and $\mathcal{S}\left(\iota_k\right)$ depicts the score function of $\iota_k$.

Step 4. Expert judgments regarding the importance of the criteria are merged using Eq. (10). As a result, the integrated PTF importance values are obtained, where $k=1, \ldots, r$ and $j=1, \ldots, n$.

Step 5. The score function value of each criterion is computed using Eq. (6). Here, $\mathcal{S}\left(\iota_j\right)$ shows the score function value of the $j$-th criterion.

Step 6. The ranking order of criteria is created based on $\mathcal{S}\left(\iota_j\right)$ values. Thus, $\theta_j$ shows the ranking place of.

Step 7. The comparative significance of criteria $\left(\theta_j\right)$ is calculated using the $\mathcal{S}\left(\iota_j\right)$ values. The $\theta_j$ value for the firstranked criterion is 0 . The $\theta_j$ value of the second-ranked criterion is calculated by subtracting its $\mathcal{S}\left(\iota_j\right)$ value from that of the first-ranked criterion. A similar procedure is followed for the two consecutive criteria in the ranking.

Step 8. The revised comparative value of each criterion $\left(\zeta_j\right)$ is obtained using Eq. (11).

Step 9. The comparative importance value of each criterion $\left(\lambda_j\right)$ is calculated using Eq. (12). $\lambda_{j-1}$ is the comparative importance value of the criterion that is one position ahead of criterion $j$ in the ranking.

Step 10. The weight coefficient of each criterion $\left(\iota_j\right)$ is computed by applying Eq. (13), where $\sum_{j=1}^n w_j=1$, and $0 \leq$ $w_j \leq 1$.

The studied problem includes ten criteria, denoted as C1-C10. Three logistics managers were invited to provide their opinions on the problem. Table 2 shows these judgments and the clear names of the criteria.

Equal weights were assigned to experts in this study due to their similar characteristics. Table 3 shows the results obtained after following the PtF-SWARA application steps. Besides, Table 3 lists the criteria in ranking order of weight values.

According to the results, the most important criterion is C6 (Providing more effective management). The second most important criterion is $\mathrm{C} 2$ (Concentrating on essential tasks and improving core capabilities). Moreover, the importance ranking order of criteria is obtained as $\mathrm{C} 6\succ\mathrm{C} 2\succ\mathrm{C} 1 \succ \mathrm{C} 3\succ\mathrm{C} 7\succ\mathrm{C} 4\succ\mathrm{C} 9\succ\mathrm{C} 5>\mathrm{C} 8\succ\mathrm{C} 10$.

In recent years, the increase in globalization and the determinants of customer satisfaction have brought sustainable production practices to the forefront. As in every sector, in the manufacturing sector, reducing energy consumption, minimizing waste, increasing efficiency in production processes, and ensuring competitiveness have turned PBL applications into vital components. Therefore, PBL applications are seen as indispensable components for manufacturing enterprises. As such, PBL application advantages have played a critical role for manufacturing enterprises.

In this context, the advantages of PBL applications were determined and ranked by using MCDA methods in manufacturing enterprises with corporate identities in Ordu province. The most important PBL application advantages in manufacturing enterprises are "Providing more effective management,” “Concentrating on essential tasks and improving core capabilities," and "Improving performance and quality while keeping costs low." When the results of the study are evaluated, effective management and senior management practices come to the forefront and should be supported by ownership of essential tasks and capability development in providing flexibility to businesses. One way to ensure effective PBL practices is to increase performance and quality by reducing costs and utilizing economies of scale with the support of senior management by prioritizing core competencies. This is also an important indicator of waste reduction and efficiency.

In conclusion, there are many theoretical and practical contributions of PBL implementation benefits to manufacturing enterprises. The adoption of PBL implementation benefits enables business managers to improve important components such as productivity, efficiency, effectiveness, customer satisfaction, flexibility, and generally contributes to increasing operational efficiency. Therefore, adopting PBL execution benefits will enable businesses to gain a competitive advantage, optimize production management operations, and achieve overall success in today's market conditions.

Finally, the study includes the usage of PtFSs in a decision-making problem and the PtF-SWARA technique, a novel SWARA extension. With these features, it can be stated that the study will be a guide for future studies on PtFSs, SWARA, and different MCDA methods.

This study is a revised and expanded version of the study titled “An analysis of PBL advantages using a polytopic fuzzy subjective weighting approach: A case study of manufacturing firms in Ordu province,” which was presented as a full-text oral presentation at the 9th International Conference on Transport and Logistics (til 2023).