Production Sustainability via Supermarket Location Optimization in Assembly Lines

: Manufacturers worldwide are nowadays in pursuit of sustainability. In the Industry 4.0 era, it is a common practice to implement decentralized logistics areas, known as supermarkets, to achieve production sustainability via Just-in-Time material delivery at assembly lines. In this environment, manufacturers are commonly struggling with the Supermarket Location Problem (SLP), striving to e ﬃ ciently decide on the number and location of supermarkets to minimize the logistics cost. To address this prevalent issue, this paper proposed a Simulated Annealing (SA) algorithm for minimizing the supermarket cost, via optimally locating supermarkets in assembly lines. The e ﬃ ciency of the SA algorithm was tested by solving a set of test problems. In doing so, a holistic performance index, namely the total cost of supermarkets, was developed that included both shipment cost and the installation cost across the assembly line. The e ﬀ ect of workload balancing on the supermarket cost was also investigated in this study. For this purpose, the SLP was solved both before and after balancing the workload. The results of the comparison revealed that workload balancing could signiﬁcantly reduce the total supermarket cost and contribute to the overall production and economic sustainability. It was also observed that the optimization of material shipment cost across the assembly line is the most inﬂuencing factor in reducing the total supermarket cost.


Introduction
Manufacturers nowadays are realizing the significant economic benefits of sustainable production practices [1,2]. Production sustainability denotes the application of economically-efficient manufacturing and management processes that reduce manufacturing costs and wastes while pursuing operational efficiency [3,4]. In their quest for achieving production sustainability, modern manufacturers need to materialize the concept of the sustainable production line [5,6]. Nowadays, assembly lines are widely used in different industries due to their advantages in effectively dealing with high volume production [7]. The efficiency of an assembly line, to a great extent, depends on its configuration and design. Thus, many managers are eager to find a suitable solution method to deal with the long-term decision problem of assembly line design from the sustainable workload distribution and material supply point of view [8].
The task of workload distribution at assembly lines is known as the assembly line balancing problem (ALBP) [9]. The ALBP concerns the proper allocation of work tasks to a set of stations so that

Literature Review
Review of the literature shows that although ALBP has been studied for decades, and a rich literature exists on this topic, there are less than a handful of studies addressing the SLP while pursuing production sustainability. It is worth mentioning that there are also some similarities between the SLP addressed in this study and the studies related to the location selection problem and inventory management. However, this review is limited to only the most related studies where the SLP was addressed. The researchers interested may refer to Chen et al. [20] and Zeng et al. [21] for further reading about the two related topics mentioned above. Moreover, the studies by Li et al. [22] and Eghtesadifard et al. [23] provide a comprehensive review of recent trends and advances on ALBP.
To provide an insight into the SLP literature, a review of the most relevant studies is provided below.
Battini et al. [24] proposed a step-by-step decision support procedure to address the SLP while taking the transportation and inventory costs of supermarkets into consideration. Based on the procedure proposed for different part components, the best feeding strategy ranging from the complete centralized, supermarket, or complete decentralized areas was found. In this study, it is assumed that each supermarket feeds several assembly lines, while in practice, many real-world manufacturers employ more than one supermarket to feed each assembly line. Emde and Boysen [16] applied the Dynamic Programming (DP) approach to cope with the SLP while minimizing the supermarket installation and the tow train transportation costs. The results of the study showed that the proposed DP could optimally solve the industrial-size SLP within polynomial computational time. Through comprehensive simulation experiments, the quality of the solutions has been validated from operational and economic aspects while compared to the centralized warehouse area. The proposed DP in this study is applicable when supermarkets could be placed anywhere on the factory layout, which might not be feasible due to space limitations on the shop floor. Alnahhal and Noche [18] addressed the SLP by applying a Genetic Algorithm (GA) to optimize the total transportation and installation costs while tow trains were used for milk-run material delivery. The performance of the proposed GA was tested by solving a set of problems and comparison against the optimal solutions found by a mathematical optimization model. Despite the results obtained being motivating, no discussions or insights in terms of transportation and installation costs were provided in this study.
Nourmohammadi and Eskandari [25] developed a hierarchical approach based on mathematical models to optimize the assembly line design in terms of workload balancing and SLP. The models proposed were validated by solving a set of standard test problems using GAMS/CPLEX solver. The results obtained showed the efficiency of the models in solving problems up to a certain size. Despite the complexity of the SLP, no meta-heuristic algorithm was proposed in this study to address large-size problems. Nourmohammadi et al. [26] investigated the effect of the stations' demand variations on the SLP solutions. To this attempt, the authors developed a mathematical model for the stochastic SLP by assuming the station demands to follow a normal distribution where supermarkets had to keep safety stocks to respond to the demand variations. The results of the study showed that the mathematical optimization approach proposed could optimally solve SLP while minimizing the shipment, inventory, and installation costs. Considering the complexity of SLP, the optimization approach proposed only tested on problems of limited-size, and no huristic/met-heuristic approach was developed to tackle large size problems. Nourmohammadi et al. [27] addressed the ALBP and SLP using a hierarchical stochastic mathematical model while assuming that the task times and demands follow the normal distribution. The proposed model was validated by solving a set of test problems and computational analysis. Despite the satisfying performance of the model on solving small size problems, due to the stochastic and complex nature of the SLP, there is no guarantee that large-size problems could efficiently be solved using the same model. Thus, the lack of an efficient approximation method/algorithm is felt in this study.
Zhou and Tan [28] addressed the SLP by considering the limited capacity and the utilization rate of supermarkets. The authors proposed an algorithm based on Differential Evolution (DE) to optimize the installation/operation cost of the supermarket as well as the transportation cost. The results of the study showed that the proposed DE is capable of finding good solutions for the considered problems. The performance of the DE was tested through comparison with an existing GA approach. However, no comparison with exact methods (i.e., mathematical model) was performed to evaluate the quality of the solutions obtained and making a reliable judgment about the efficiency of the DE developed. Recently, Nourmohammadi et al. [17] addressed the joint supermarket location and transport vehicle selection problem by assuming different transportation modes for parts feeding. The authors proposed a mixed-integer programming model and a Hybrid Genetic Algorithm (HGA) with a variable neighborhood search to address large-sized problems with the objectives of minimizing the procurement and shipment costs of vehicles as well as the installation cost of supermarkets. To test the efficiency of the proposed HGA, a set of standard test problems was solved by the algorithm, the mathematical model, and another heuristic algorithm. The computational results showed that the HGA could provide quality solutions in a reasonable time. This study was merely concentrated on SLP and did not investigate the effect of the ALBP on the solutions.
The current study proposes an efficient SA algorithm customized for solving the SLP problem. In contrast with the previous studies, it is assumed that several supermarkets can be used to feed a single assembly line, and only specific places in the lineside can be chosen for establishing supermarkets. The effect of the workload balancing was also investigated on the supermarket cost, which was considered to be the sum of both the installation cost and the transportation cost. To this aim, SLP was solved twice (i.e., before and after addressing the ALBP) and the supermarket costs are compared for a reliable conclusion on the effect of line balancing on the supermarket cost.

Problem Description
A general description of the SLP, its assumptions and mathematical formulation are presented in this section.

Description of SLP
Assuming a straight assembly line where supermarkets supply stations w = 1, . . . , W (W = number of stations) with d w bins of parts, stations across the assembly line are designated by (x w , y w ). Alternatively, the locations for supermarkets are demonstrated by (X s , Y s ); s = 1, . . . , PSP where PSP denotes the possible number of places for establishing supermarkets. To determine the distance traveled by tow trains for supplying bins of parts to various stations, the three variables of (1) distance between supermarkets to stations, (2) distance from the station to station, and (3) the distance from the station back to the supermarket are calculated. In other words, dist svw that indicates the collective distance train travels from supermarket s to station v, then from station v to w and back from station w to supermarket s is calculated via the following equation.
Considering the above description, the SLP strives to discover the optimal number of supermarkets from a possible number of locations. More importantly, SLP attempts to identify the stations that should be supplied via each supermarket, considering certain assumptions. Figure 1 shows a layout of an assembly line where two supermarkets are established for material delivery to stations by tow trains.

The SLP Assumptions
According to the literature (e.g., [16,28]), the main assumptions of SLP can be summarized as

The SLP Assumptions
According to the literature (e.g., [16,28]), the main assumptions of SLP can be summarized as follows.

•
The order (sequence) through which each supermarket visits stations is consecutive. This means, for example, a particular supermarket is not allowed to serve stations 1, 2, and 5 if stations 3 and 4 are served by other supermarkets.

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The optimal number and location of supermarkets should be selected from the candidate supermarket places. Supermarket capacity, when it comes to serving the stations, is assumed to be limited. Thus, additional supermarket positions have to open when the capacity limitation of a particular supermarket is reached.

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The bins holding parts are identical and standardized in size.

•
The arrangement of stations follows a straight-line pattern. Therefore, and considering the shop floor space limitation, supermarkets are assumed to be located as close to the stations as possible.
Consistently, it is assumed that the supermarket locations smoothly scatter next to the shooter racks of workstations.

Problem Formulation
The SLP problem considered in this study is similar to the one addressed in Alnahhal and Noche [18] in terms of assumptions and constraints. To better understand the problem, the mathematical programming model of the considered SLP in this study is presented below. The notations used in the model are given in Table 1.

Notations Description
Indices: w, v station index s supermarket index Parameters W number of stations PSP possible supermarket places SIC supermarket installation cost dem w demand for station k per shift x w ,y w x and y coordinates of station w X s ,Y s x and y coordinates of supermarket s Tdem vw total demands of all stations from v to w dist svw distance AGV/tow train travels from supermarket s to feed all stations from v to w; the shipment unit cost that occurs by moving one bin for one unit of distance DSD vw demand standard deviation for all stations from v to w CAP supermarket capacity in terms of the number of bins SL service level for the probability of not exceeding the supermarket capacity Decision variables Z svw ∈ (0, 1) 1 if supermarket s feeds all stations from v to w; otherwise 0 NS ∈ Integer number of supermarkets installed According to the above notations, the Mixed Integer Programming (MIP) formulation of SLP is given as follows.
Sustainability 2020, 12, 4728 NS ≥ 1 In this model, the objective function aims to minimize the total cost (TC) of supermarkets, which includes the shipment cost (SC) and the installation cost (IC) as calculated by the first and the second terms in Equation (2), respectively. Equation (3) determines the number of supermarkets established for parts supply to stations. Equation (4) ensures that the established supermarkets feed each group of stations known as cells. Equation (5) guarantees that each group of stations/cells is supplied by only one supermarket. The capacity limitation of the established supermarkets is satisfied by Equation (6). This inequality ensures that the average demands of a group of stations assigned to each supermarket, considering a certain safety level and demand fluctuation at stations, does not exceed the supermarket capacity. Finally, Equation (7) ensures that at least one supermarket is established for material supply to stations.

The Proposed Solution Approach
In this study, a SA algorithm is proposed to address the SLP. To better clarify the solution procedure, the general structure for solving the SLP is proposed in Figure 2.

Simulated Annealing for SLP
SA is a generic probabilistic metaheuristic algorithm that was first introduced by Kirkpatrick et al. [29]. This algorithm is capable of producing near-optimum solutions with the polynomial cost for NP-hard problems. In SA, the search process is similar to the local search method in the sense that it starts with an initial solution in the search space and iteratively investigates the neighbors of each state and accepts a better solution until it has achieved a near-optimal solution. However, SA can skip local traps by accepting worse solutions with a certain probability. As suggested in the literature (e.g., [30][31][32]), the acceptance probability in this study is calculated according to the Equation presented below.
where T is the annealing temperature that imitates the reducing temperature, which is applied in the metal annealing process, and f (IS) and f (IS ) are the fitness function values of the current and the candidate neighbor solutions, respectively. This probability function is reduced as T is updated by a cooling schedule. To accept the worse solution, a number between 0 and 1 is randomly generated. The worse solution is accepted if and only if the generated number is smaller than or equal to P; otherwise, it is rejected.

Initial Temperature and Cooling Rate
The SA algorithm starts with an initial randomly generated vector of integer numbers. The initial temperature is crucial, given its sheer impact on the identification of good solutions. The selection of the starting temperature is based on the nature of the problem and the related literature. Based on some pilot studies, we have set the value of the starting temperature equal to 1000 to keep the intensification property of the SA algorithm as precise and gentle as possible. In addition, the cooling schedule is calculated using the Equation presented below. where T γ is the temperature in the iteration γ.

Solution Representation
Two representations types, namely "Prüfer number representation" and "cell boundary", exist in the SLP literature, see Alnahhal and Noche [18]. In this study, the second type of representation is used to enhance the algorithm's search efficiency. This representation, which is also called "rightmost station", constitutes a string of integer numbers representing a series of stations to be served by each supermarket. The number in each cell represents the last station to which each supermarket will serve. Figure 3 shows the cell boundary representation for a ten-supermarket instance. According to this figure, for instance, supermarket 4 will serve stations 6 to 9 where 6 and 9 are the leftmost and the rightmost stations/boundaries of supermarket 4, respectively.

Solution Representation
Two representations types, namely "Prüfer number representation" and "cell boundary", exist in the SLP literature, see Alnahhal and Noche [18]. In this study, the second type of representation is used to enhance the algorithm's search efficiency. This representation, which is also called "rightmost station", constitutes a string of integer numbers representing a series of stations to be served by each supermarket. The number in each cell represents the last station to which each supermarket will serve. Figure 3 shows the cell boundary representation for a ten-supermarket instance. According to this figure, for instance, supermarket 4 will serve stations 6 to 9 where 6 and 9 are the leftmost and the rightmost stations/boundaries of supermarket 4, respectively.

The Neighborhood Search Operator
To search the neighborhood of each solution, the mutation operator is applied. To this aim, a randomly selected cell boundary is chosen. Based on the position of this selected cell, the cell boundary is randomly changed without exceeding its right and left most boundaries (see cell boundary representation depicted in Figure 3). In this study, after some experiments and pilot tests, the mutation rate is set to 0.3. The pseudocode of the mutation operator is provided in Table 2.

The Neighborhood Search Operator
To search the neighborhood of each solution, the mutation operator is applied. To this aim, a randomly selected cell boundary is chosen. Based on the position of this selected cell, the cell boundary is randomly changed without exceeding its right and left most boundaries (see cell boundary representation depicted in Figure 3). In this study, after some experiments and pilot tests, the mutation rate is set to 0.3. The pseudocode of the mutation operator is provided in Table 2.  Generate a random number r within intervals p lb and p rb calculated above; 5 Replace the current value in position p with r; 6 Return the resulting solution as a new neighborhood solution IS ; Figure 4 provides a visual overview of the mutation operator used for the neighborhood search. In this figure, for instance, the 4th cell boundary can be altered to be any value from 6 to 8 and from 10 to 12 as the left and rightmost boundaries, respectively.

. The Evaluation Function and Termination Condition
In addressing the SLP, we aim to minimize the total logistics cost, including (1) the cost of the weighted distance traveled by tow trains and (2) the installation cost of supermarkets. The weighted distance cost is calculated through multiplying the total distance traveled from a particular supermarket for supplying a station group (cell), by the entire demand of this cell, i.e., Q svw = Tdem vw × dist svw . Thus, the objective function of the SLP known as total cost (TC) of the supermarket, which is composed of the supermarkets' transportation and installation costs, is calculated using the equation presented below.
where USC, SIC and NS are the unit shipment cost, the supermarket installation cost, and the number of supermarkets, respectively. The SA algorithm continues until a stopping condition is met. In this study, the algorithm is terminated when the maximum number of iterations is reached.

Pseudocode of the Proposed Algorithm
To better understand the proposed SA algorithm, the pseudocode of the algorithm is provided in Table 3. If Then s = s ; /*Accept the neighbor*/ 10 Else accept IS with the acceptance probability presented in Equation (8) and set IS = IS 11 Best solution = IS 12 T γ+1 = T γ − 1; /*Temperature update according to the cooling schedule*/ 13 Until the maximum number of iterations is reached. 14 Return the best solution

Computational Results
To assess the efficiency of the proposed SA algorithm, several test problems with differentiae characteristics are solved. It is worth mentioning that the test problems are taken from the "Assembly Line Balancing Data Sets & Research Topics" (see the data sets here, https://assemblyline-balancing.de/) and adapted to this study by adding the information about the material demand. The problems are divided into small, medium, and large size based on the number of assembly tasks. All the problems are solved for two scenarios in terms of possible supermarket locations in the assembly lines (i.e., PSP = 4 and 5). To further analyze and assess the effect of the installation cost on the solution, two different values are considered for the supermarket installation cost (i.e., SIC = 500 and 1000). It is also assumed that the demand for tasks is known in advance in terms of the number of bins. The demand for each task in bins is generated using uniform distribution U(1, 10). Assuming that the capacity of supermarkets is limited, the maximum capacity of each supermarket was chosen as equal to 150 bins. The shipment unit cost (SUC) is considered to be 10 units of cost.
To make a reliable comparison, considering the defined assumptions, all the problems were solved by both CPLEX and the SA algorithm proposed. No time limit was given for CPLEX and therefore, all the problems were solved to optimality. The stopping condition of the SA was set as when the final temperature of zero is reached using the relating cooling schedule. The SA algorithm was coded in Matlab R2018a and run on a computer with 2.4 GHz Core i7 CPU. Table 4 represents the comparison of the best solutions obtained by the SA with the optimal solutions obtained by CPLEX in terms of the total cost (TC). The gap between the obtained solution by SA and the optimum solution is also reported for each problem solved. All the problems were solved for two possible supermarket places (i.e., PSP = 4 and 5) and two different supermarket installation costs (i.e., SIC = 500 and 1000 unit cost). To view the stochastic treatment of the algorithm, the results are obtained after running the SA on the considered test problems 10 times, and the best-found solutions are reported. To investigate the effect and influence of the workload balancing on the solution of SLP, all the test problems are solved before and after balancing the workload (i.e., considering the feasible and the optimum solution for ALBP). Tables 5 and 6 m  IC  SC  TC  m  IC  SC  TC  m  IC  SC  TC  m  IC  SC  TC   1  Jackson  7  9  3000  6200  9200  8  3000  5960  8960  9  3000  6440  9440  8  3000  5960  8960  2  9  7  3000  5700  8700  6  2000  6300  8300  7  2000  6872  8872  6  2000  6300  8300  3  Mitchell  14  10  4000 Arcus1  3786  22  4000  81,520 85,520  21  4000  78,620 82,620  22  5000  73,454 78,454  21  5000  69,940 74,940  14  4454  21  4000  79,740 83,740  18  4000  72,300 76,300  21  5000  72,640 77,640  18  5000  64,900 69,900  15  Tonge  160  26  4000  87,750 91,750  23  4000  79,680 83,680  26  5000  75,280 80,280  23  5000  70,560 75,560  16  168  24  4000  82,920 86,920  22  4000  78,440 82,440  24  5000  73,502 78,502  22  5000 69,360 74,360

Analysis of Results and Discussion
This section provides a detailed analysis of the results presented in Tables 4-6. Moreover, the results are discussed in terms of the contribution to the literature.
Analyzing the results presented in Table 4 shows that the SA algorithm has been successful in achieving the optimal solutions in most of the test problems except for a few problems. In some cases where the optimal solution could not be found, the gap was negligible, which could be justified by the complexity of the problem. According to this table, for SIC = 500, the SA has been capable of finding the optimal TC for all the problems considering the PSP = 4. For PSP = 5, the optimal solution was found for 13 out of 16 problems (81% of the problems). Similarly, for SIC = 1000, considering PSP = 4, the SA algorithm was capable of finding the optimum solution for all the problems. For PSP = 5, the optimum solution was obtained in 9 out of 16 problems. For the other seven problems or which the optimal solution could not be found, the gaps are less than 2.7%. According to these results, it can be concluded that the performance of the SA algorithm proposed, in terms of finding the (near) optimal solutions, is promising, particularly by taking into account its minimal computational time, which ranged between 1 and 5 s for small and large size problems, respectively.
By analyzing the results reported in Tables 5 and 6, it can be seen that both SC and TC are reduced when the SLP was solved after balancing the workload at stations. These results can verify the argument that optimal workload balancing can positively affect the resolution of SLP. Moreover, the comparison of results obtained for SLP after balancing the workload and before balancing indicates that for SIC = 500 the TC has improved by 5.2% and 5.5% for PSP = 4 and PSP = 5, respectively. For SIC = 1000, TC has been enhanced by 5.2% and 4.6% for PSP = 4 and PSP = 5, respectively. Additionally, comparison of SLP solutions after and before balancing the workload for both SIC = 500 and SIC = 1000, show that the improvement in TC has been mainly caused by an improvement in SC rather than IC (i.e., equal IC while SC has almost improved in the majority of the test problems solved). Additionally, for SIC = 500, the comparison of SLP solutions after balancing the workload for PSP = 4 and PSP = 5, shows that the increase of the potential number of supermarkets has resulted in 81% (13 out of 16 problems) decrease in TC. The same effect can be seen for SIC = 1000 where a similar comparison shows 56% (9 out of 16) reduction in TC. This improvement can be justified to be the direct result of more freedom in choosing the location for establishing supermarkets, which leads to lesser transportation.
To provide a more detailed synthesis of results obtained, a comparison measure, known as the Relative Percent Deviation (RPD), is defined and presented as Equation (11). Using this measure, the relative percent deviation of different cost terms, namely installation cost (IC), shipment cost (SC), and total costs (TC) for comparing two scenarios (i.e., Feasible ALBP + SLP with Optimal ALBP + SLP) can be calculated. According to Figure 5, for PSP = 4 the amount of improvement in RPD TC is mainly caused by improvement in RPD SC . For PSP= 5, again RPD SC improvement has brought about the improvement in RPD TC . It is worth noting that for PSP = 5, despite negative RPD IC in problem 3 the positive RPD SC has led to positive RPD TC (i.e., +6.7%) in total. Figure 6 also shows the same pattern that the improvement of RPD SC led to an improvement in RPD TC with only one exception for PSP = 4, problem 2, where the positive RPD IC dominated the negative RPD SC resulting in positive RPD TC (i.e., +4.6).  According to Figure 5, for = 4 the amount of improvement in is mainly caused by improvement in . For = 5, again improvement has brought about the improvement in . It is worth noting that for = 5, despite negative in problem 3 the positive has led to positive (i.e., +6.7%) in total. Figure 6 also shows the same pattern that the improvement of led to an improvement in with only one exception for = 4, problem 2, where the positive dominated the negative resulting in positive (i.e., +4.6). Overall, the findings of this study show that balancing the workload can decrease the logistics costs by reducing the total supermarket installation cost and, more specifically, the material shipment cost. Moreover, and concerning the existing body of literature, the satisfying performance of the algorithm proposed in this study could present it as a suitable alternative to the available exact solution methods to deal with real-world large size problems. The proposed algorithm can also serve practitioners, decision-makers, and managers with more effectively designing production lines and deciding on the best location and number of the required supermarkets for efficient material delivery. The benefits offered by the SA algorithm proposed, collectively, will allow manufacturers to establish  According to Figure 5, for = 4 the amount of improvement in is mainly caused by improvement in . For = 5, again improvement has brought about the improvement in . It is worth noting that for = 5, despite negative in problem 3 the positive has led to positive (i.e., +6.7%) in total. Figure 6 also shows the same pattern that the improvement of led to an improvement in with only one exception for = 4, problem 2, where the positive dominated the negative resulting in positive (i.e., +4.6). Overall, the findings of this study show that balancing the workload can decrease the logistics costs by reducing the total supermarket installation cost and, more specifically, the material shipment cost. Moreover, and concerning the existing body of literature, the satisfying performance of the algorithm proposed in this study could present it as a suitable alternative to the available exact solution methods to deal with real-world large size problems. The proposed algorithm can also serve practitioners, decision-makers, and managers with more effectively designing production lines and deciding on the best location and number of the required supermarkets for efficient material delivery. The benefits offered by the SA algorithm proposed, collectively, will allow manufacturers to establish

Conclusions
To promote sustainability in the daily production processes, managers look for the best methods when dealing with the long-term decision problem of the assembly line design, specifically in terms of locating supermarkets. Additionally, the supermarket-concept has been recently adopted by many manufacturers to allow flexible and reliable Just-in-Time material delivery to assembly lines. Thus, this study aimed to optimize the configuration of assembly lines by considering the supermarket location problem known as SLP. For this purpose, the SA algorithm was developed to address SLP. The computational results on known test problems over the two possible supermarket places and two installation costs combinations verified that the proposed algorithm could optimize the configuration of the assembly lines from SLP considerations in terms of supermarket transportation and installation costs in a variety of test problems. Moreover, the effect of workload balancing on the solution of SLP was also investigated. The results revealed that the workload balancing reduces the total supermarket cost significantly and contributes to the overall environmental sustainability and economic sustainability of manufacturers by promoting production sustainability.

Limitation and Future Directions
The study might be considered limited in the sense that it benefited from the SA algorithm to address SLP. As future research directions, other meta-heuristic algorithms can be applied to solve the same problem and benchmarked against the SA algorithm developed in this study. Moreover, the present study and the algorithm developed could not, conceivably, incorporate the complete stochastic nature of production processes and activities within the manufacturing industry. Consistently, the stochastic nature of the production and material demand can also be taken into consideration in future studies. Additionally, the present study was developed based on the assumption of unique bin size and supermarket capacity, while future research can relax this particular assumption by considering bins with different sizes and supermarkets with different capacities. More importantly, and to address any limitations that the present study might have regarding the scope of production-related problems, investigating the effect of SLP on other operational decision problems such as routing, scheduling, and loading problems and their impacts on various dimensions of sustainability can also be an interesting research area for the future research.