Shrimp closed-loop supply chain network design

Mostly, food can be divided into two main categories: perishable food (e.g. fruits, vegetables, fishery, aquaculture products, meats, etc.) and non-perishable (e.g. canned, pickled, dehydrate, dried products). Recently, several studies investigated perishable food supply chain for fresh fruits (Cheraghalipour et al. 2018; Soto-Silva et al. 2016), agricultural (Borodin et al. 2016), and dairy (Sel et al. 2015) come along with different components of the supply chain such as inventory, resources location-allocation, planning and scheduling, production, and distribution (Musavi and Bozorgi-Amiri 2017; Govindan et al. 2014; Attanasio et al. 2007; Kaasgari et al. 2017; Dai et al. 2018; Triki 2016; Wu et al. 2018).

One of the first studies on perishable food supply chain was conducted by Stoecker et al. (1985). They used linear integer programming for maximizing the profit and for planning the farm’s crop, livestock, and labor decisions. Miller et al. (1997) provided a simple and a fuzzified linear programs to produce scheduling of fresh tomato packinghouse, then, they compared the costs obtained by each model. Ten Bergeet al. (2000) proposed an explorative model at the whole farm level that effectively integrates component knowledge at a crop or animal level. Then, case studies in dairy farming, flower bulb industry, and arable farming were provided. A mathematical model was presented by Caixeta-Filho (2006) who developed a linear optimization model with chemical, biologic, and logistic constraints for quality of harvested Brazilian’s oranges. Ferrer et al. (2008) recommended a mixed-integer linear programming model containing harvest scheduling, labor allocation, and routing decisions on wine grape harvesting operations by considering both operational costs and grape quality. Arnaout and Maatouk (2010) focused on a vineyard harvesting problem in developing countries to improve wine quality and reduce the operational costs. Additionally, they utilized heuristics for better assigning of harvesting days to different grape blocks and validated the proposed model by solving several numerical examples. Their results showed that their model is prominently able to reduce harvesting costs.

With the aim of maximizing revenues under production and distribution decisions, an operational model was suggested by Ahumada and Villalobos (2011). Tan and Çömden (2012) proposed a planning model to handle the random supply of annual fruits and vegetables from farms and random demands of the retailers, which are results of the uncertainty of harvest time, and uncertainty of weekly demand, respectively. A simulation model for perishable fruit and vegetables supply chain was presented by Teimoury et al. (2013) to investigate behaviors and relationships of supply chain and supply, demand and price interactions. Agustina et al. (2014) studied a mixed-integer linear model of vehicle scheduling and routing at a cross-docking center for perishable food supply chains to minimize earliness, tardiness, inventory holding, and transportation cost. A planning model for apples orchards was proposed by González-Araya et al. (2015) to minimize labor costs, equipment use, loss of fruit quality, and also satisfying packing plants demand. The implementation of this model on three orchards in Chile showed a 16% decrease in the labor costs and loss of income.

Rocco and Morabito (2016) suggested a production and logistics planning linear model for the Brazilian tomato processing industry, which includes tactical planning decisions like the size of tomato area, selection of tomato types, transporting harvests, and so on. Three optimization models for purchasing, transporting, and storing fresh produce were studied by Soto-Silva et al. (2017) to ensure an annual supply of fresh apple. An average of 8% savings in the real costs of purchasing, storing, and transporting arisen from conducting a real case study in apple dehydration in the Maule region of Chile has been achieved. Cheraghalipour et al. (2018) provided a citrus closed-loop supply chain model to minimize costs and maximize responsiveness to customers' demand. One of the most recent food supply chain model was introduced by Ma et al. (2019). They focused on the three-echelon supply chain for seasonal fresh products consisting of one supplier, third-party logistics service providers, and one retailer.

During the last few decades, only a limited number of researchers and academics have studied SFSC in miscellaneous ways. In a preliminary study of SFSC problems, Forsberg (1996) pointed out a multi-period linear programming approach to the production-planning of fish farms. In addition, Forsberg (1999) developed a multi-period linear programming model for fish growth that optimizes the harvest. Sanders et al. (2003) suggested a production model of white sturgeon caviar and meat for various management conditions. Using the network-flow approach, Yu et al. (2009) implemented a nonlinear mathematical model of partial harvesting. Cisternas et al. (2013) designed an integer programming model to improve resource usage, planning, and economic evaluation of grow-out centers. The results obtained from implementing this model in one of the Chile's largest salmon farmers showed a 18% reduction in net maintenance cost together with several qualitative benefits. Bravo et al. (2013) employed mixed integer programming to propose two models for the production planning in salmon farming suffering from a range of biological, economic, and health-related constraints. Bakhrankova et al. (2014) developed a stochastic production-planning model to overcome raw material supply and product market price uncertainties.

As can be noticed from the recent literature, SFSC has been considered in different manners and for various products. Real-world issues and case-based methods is the main factor to design an industrial problem for SSC networks. In our case, we formulated the SSC network according to both the nature and characteristics of the product and due to its importance in Iran and even in today’s food world industry. Developing countries like Iran have incredible capabilities for producing especial seafood like shrimps. There is an extraordinary domestic and oversea market demand for shrimp which can ensure a proper income. So, designing a SSC can be a good start and a preliminary preparation to accomplish this mission. The accurate analysis reported in Table 1 determines the gaps that highlight the significance of this paper. The main contributions of this study can be summarized as follows:

This paper addresses a new model to help the managers of shrimp production industries in designing an optimal supply chain network for shrimp products. It also undertakes wastes generated in two main levels of network i.e. wholesalers and shrimp factories. The decisions to be taken within this study consist of:

We believe that the mangers can extensively benefit from the suggested mathematical model and its results to make strategic decisions regarding the quality of shrimp flow in the supply network while minimizing the total cost. Additionally, since numerous countries do not have yet the technology to convert shrimp waste to poultry and livestock food, this study can give guidelines to the mangers and governors on how to invest their resources to set up a shrimp waste powder factories in highly potential areas.

The present SSC network embodies producers (shrimp fishers and farmers), distribution centers, wholesalers, processing centers (factories), shrimp waste powder factories, poultry and livestock food market, and customers. As can be observed in Fig. 5, captured or aquacultured shrimps are shipped in this network from the producing locations (fishery locations and aquacultures) to the distribution centers. The distribution centers, depending on their capacities, send shrimps to the wholesaler and factories. Furthermore, factories, after peeling, packing or canning, and freezing should transport finished goods to the final customers. Finally, shrimp wastes collected from both wholesalers and factories are shipped to shrimp waste powder factories. These factories make poultry and livestock food in addition to the required nutrients for shrimp farming.

The following real assumptions are set in the proposed SSC network:

The indices, parameters, and decision variables for the mathematical model are presented as follows:

The schematic view of the SSC network is illustrated in Fig. 6. The proposed mixed integer linear programming model of the SSC problem is formulated as follows:

Constraint (2) states that at least one distribution center should be opened. Constraint (3) state that the quantity of products transported from shrimp fishers to distribution centers should be less than or equal to the production capacity of each producer. Similarly, constraint (4) applies to the shrimp farmers case. Constraint (5) indicates that the quantity of products transported from the producers to the distribution centers should be less than or equal to the holding capacity of each distribution center, if it is opened. Constraint (6) implies that the quantity of products transported from the distribution centers to the wholesalers and factories should not exceed the quantity of products transported from the producers to distribution centers. Constraints (7) and (8) determine that at least one wholesaler and one factory should be opened, respectively. Constraint (9) indicates the quantity of products to be transported from the distribution centers to the factories should respect the holding capacity of each factory, if it is opened. Likewise, constraint (10) applies to the wholesaler. Constraint (11) ensures that the quantity of product transported from wholesaler and factories to each customer is less or equal to the demand at customers side. Constraint (12) ensures that products transported from distribution centers to wholesalers minus wasted shrimp product are equal to the amount of product transported from wholesalers to customers. Constraint (13) ensures that shrimp production by factories is equal to the quantity of product transported from factories to customers. Constraint (14) determines that at least one shrimp waste powder factory should be activated. Constraint (15) ensures the respect of the shrimp waste powder factories capacities. Constraint (16) ensures that wasted shrimp product transported from distribution centers to wholesalers is equal to waste products transported from wholesalers to shrimp waste powder factories. Constraint (17) ensures the flow balance of the waste shrimps between factories and shrimp waste powder factories. Constraint (18) establishes the equality between the produced shrimp waste powder and the quantity of product transported to poultry and livestock food market. Constraint (19) guarantees the demand satisfaction of the poultry and livestock food market. Finally, constraints (20) represent the 0/1 restriction on the binary variables and constraints (21) enforce the non-negativity of the continuous decision variables.

The above model results to be a mixed-integer linear model whose size increases quickly with the number of shrimp fishers, farms, distribution centers, wholesalers, shrimp factory, customers, shrimp waste powder factories and poultry and livestock food markets. Consequently, we will suggest in the sequel metaheuristic algorithms to solve real-world instances of SSC problems in a reasonable time.

Among the numerous approaches for encoding solutions in metaheuristics, we use the recent priority-based method (Cheraghalipour et al. 2018). Here, the proposed chromosome for the SSC network and application of the priority-based method for satisfying all the constraints is enlightened using a small-size example. Assume that the numbers of shrimp fishers, shrimp farms, distribution locations, wholesaler, factories, customers, and shrimp waste powder factories, and poultry and livestock food markets are 2, 3, 3, 2, 2, 3, 2, and 2, respectively. The proposed chromosome is a matrix with one row and (i + i' + 2 × j + 3 × k + 3 × l + m + 2 × n + p) columns that can be divided column-wise into five segments. The representation of proposed chromosome is presented in Fig. 7. Each segment in the proposed chromosome is designed according to the network illustrated in Fig. 6.

After generating the chromosome, whose all members are random numbers in the interval of (0,1), all values are transformed into a priority-based matrix. As shown in Fig. 8, Segment 1 states the amount of transported products from shrimp fishers and shrimp farmers (i + i') to the distribution centers (j). As reported in Fig. 9, in Segment 2, products are allocated to wholesalers and shrimp factories (k + l) from the distribution centers (j). According to Figs. 10 and 11, in segment 3, the allocation of products from wholesalers and shrimp factories (k + l) to customers is conducted and segment 4 obtains the allocation of wasted products from wholesalers and shrimp factories (k + l) to shrimp waste powder factories (n). Finally, the allocation of shrimp waste powder products from shrimp waste powder factories (n) to the poultry and livestock food markets is performed in segment 5 (Fig. 12). For more information about the priority-based method, refer to (Cheraghalipour et al. 2018).

During the last years, scholars have used numerous metaheuristic methods to solve NP-hard problems and attain a prominently proper solution. Timesaving, useful for more complex problems, and avoidance of local optimum are the most outstanding advantages of these methods (Van Engeland et al. 2018; Diarrassouba et al. 2019; and Fathollahi-Fard et al. 2020). For example, in order to solve the order acceptance and supply chain scheduling problem, Sarvestani et al. (2019) applied GA and Variable Neighborhood Search (VNS). Yousefi et al. (2018) used GA to tackle the fixed-charge transportation problem. Govindan et al. (2015) designed a sustainable supply chain problem for order allocation and sustainability including stochastic demand and used a multi-objective metaheuristic approach to solve the given problem. This study utilizes the benefits of metaheuristic algorithms and develops three metaheuristic algorithms including GA, SA, KA as well as two hybrid metaheuristics i.e. HGASA and HKASA to solve the SSC network design. In the following sections, the mentioned algorithms are discussed and the pseudo code of each algorithm is rendered.

In recent studies, a great development in nature-based metaheuristics can be seen. The advantages of the different metaheuristic algorithms draw many researchers’ attraction to improve the intensification and diversification phases of the algorithms using various hybrid ones (Hajiaghaei-Keshteli and Fathollahi Fard 2018). In this study, two hybrid algorithms are exercised, including HGASA and HKASA. These two hybrids are combination of GA and KA as two distinct population-based techniques together with SA as a single-solution algorithm. In the following subsections, detailed explanations of HGASA and HKASA are provided.

A set of test problems with different dimensions are considered to endorse the proposed model. Here, 15 test problems are designed. Table 2 shows the test problems generated to achieve the purpose of this study. The test problems are indiscriminately defined by using the parameters shown in Table 3. It should be mentioned that the approximated value of each parameter is estimated and extracted on the basis of the Iran Fisheries Organization databanks.

Tuning the parameters in metaheuristics is a crucial phase because it may lead to a wasteful execution of the metaheuristics if the parameters are not set rightfully (Fathollahi-Fard and Hajiaghaei-Keshteli 2018a). Although there are numerous researchers who tested all possible combinations of factors for parameter tuning (Jabbarizadeh et al. 2009; Naderi et al. 2008; Al-Aomarm and Al-Okaily 2006), when the number of factors increase in a problem, their findings are disclosed to be inefficient. Henceforward, for parameters tuning purpose, we use the efficient Taguchi experimental design method, developed by Taguchi (1986). The parameters and their levels for the algorithms have been evolved from (Fathollahi-Fard et al. 2018b). For each factor, three levels are taken into account to design the experiments. In GA and SA, we have four parameters with three levels, and for KA, we take five factors with three levels into account. The hybrid cases, HKASA and HGASA, contain seven factors with three levels, and six factors and three levels, respectively. Thus, L₂₇ is recommended as a proper array for both SA and KA and also L₉ for GA.

In this study, we generated, for the sake of validating the proposed model, 15 test problems put into three categories, consisting of small-size, medium-size, and large-size. Hence, the orthogonal array has been run for each test problem using Minitab software. Owing to the size difference of each problem, the Relative Percentage Deviation (RPD) or mean of means is operated to compare the results. The RPD is defined as follows for minimization problems: where \(Min_{sol}\) is the best solution among all solutions and \(Alg_{sol}\) is the result of algorithm. The mean RPD is computed on the basis of the RPDs from the objective values. Also, the optimal levels for metaheuristic algorithm are summarized in Table 4.

In this section, applied instances are exercised to corroborate the pertinency of the model and solving methodology. To this end, fifteen test problems in different dimension scales are solved with tuned parameters of each metaheuristic (Table 2). Among these examples, the second example is inspired by a small-sized case in southern Khuzestan province situated in southern Iran. Khuzestan province is surrounded by the Persian Gulf and has several rivers such as Arvand river, Karun river, etc. Thus, it has marine access with shrimp production capacity as well as numerous fishery farms which are active in this province. In the real-case example, four shrimp catching location is considered. These four location are Karun river in Ahvaz, Arvand river in Abadan, Bahmanshir river in Abadan, and Musa Bay in Mandar-e-Emam. Five shrimp farms exist in Ahvaz, Abadan, Mahshahr, Shadegan, and Hendijan. Other details on the case study are shown in Fig. 16 as a symbolic scheme for SSC network which contains producers, distribution centers, wholesalers, factories, shrimp waste powder factories, poultry and livestock food market, and customers in Khuzestan province.

At this point, we will attempt to solve the problems by our five the different algorithms, GA, SA, KA, HKASA, and HGASA. Note that the parameters are fixed but the size of test problems alters during the analysis. In fact, when a factory is added to the dimension of the model, all related parameters are selected through Table 3. To assess the performance of the metaheuristic algorithms, four measures including RPD, one-way ANOVA, hitting time, and the computational time of the algorithms are considered, as shown in Table 5 (Fig. 16).

Figures 17, 18 and 19 depict the objective function behavior for various problem sizes. It is obvious that there are slight differences between the values obtained by the different algorithms. Within this, it is clear that in terms of the cost values, SA and HKASA act better than the rest of the algorithms.

The RPD is a reliable criterion that can be defined to evaluate and compare the quality of the solution for the algorithms. Here, RPD is the relative deviation of the outcome of each algorithm from the optimal result among the five implemented approaches. These results for each test size are shown in Fig. 20. In terms of RPD, HKASA shows better performance than all other algorithms for all the three categories. Another avenue to evaluate the performance of the proposed metaheuristic algorithms is using one-way Analysis of Variance (ANOVA) to account for any statistically significant differences between the RPD of the algorithms. RPD is a response variable and all five metaheuristics algorithms are factors. Two hypotheses are considered for the ANOVA test. The p-value for ANOVA test is equal to zero; therefore, it can be concluded that there are statistically significant differences in the RPDs. For more precise analysis, the means plot and the least significant difference (LSD) intervals at 95% confidence level are presented in Figs. 21, 22 and 23 for small-size, medium size, and large size problems, respectively. In small-size problems, there is negligible difference between the performance of SA, KA, and HKASA (Fig. 21). As shown in Fig. 22, in medium-size cases, KA outperformes all other algorithms. Finally, the best performance among all algorithms belongs to HKASA for large-size problems (Fig. 23).

Hitting time is a tool used to investigate the speed of algorithms in different problem sizes. It is defined as the first time at which each algorithm obtains the best solution. Figure 24 demonstrates the hitting time comparison for the proposed algorithms. We can conclude that the increment of the hitting time coincides with the augmentation of problems sizes. Apparently, the growth rate of hitting time in KA and HKASA is more than that of GA, SA, and HGASA.

The last measure used to check the performance of our algorithms is the computation time. Figure 25 displays the information related to the computational time for all algorithms. Not surprisingly, the SA obviously has the least computational time and after followed by the GA, HGASA, KA, and HKASA.

In general, Sensitivity analysis is used to show how output variables change based on the variation of input parameters. In mathematical programming terms, sensitivity analysis is a way to explore the effect of changes in the values of parameters on objective function. To shed light on the functional capability of the proposed model and provide a managerial insight, a sensitivity analysis on the major parameters are performed. Since the HKASA demonstrated to be one of the most efficient algorithms with respect to different metrics, it has been applied here for the sensitivity analysis. Also, we selected the large-size experimental instance 14 as a test problem. Thus, we create three scenarios for sensitivity analysis in which we examine the behavior of cost function under the change of capacity parameters, production/waste rate, and demands for each sector.

The first scenario explores the changes in the production capacity of shrimp fisher (\(\lambda_{i}\)), the production capacity of shrimp farmer (\(\lambda ^{\prime}_{i^{\prime}}\)), the holding capacity at distribution center (\(\lambda d_{j}\)), the production capacity of factory (\(\lambda f\)), holding capacity at wholesaler (\(\lambda w_{k}\)), and production capacity of shrimp waste powder factory (\(\lambda s_{n}\)). In this scenario, each parameter varies between 5 to 35 tons and other parameters are kept unaltered. The performance of the objective function with respect to the change of capacity parameters are shown in Table 6 and Fig. 26. As shows Fig. 26 with the increase in the amount of capacity of each sector, the objective function also increases. However, there is significant difference between the effect of factories, distribution centers, and wholesalers on the objective function in comparison with the other factors. So, it can be inferred that the capacity of shrimp production factories, distribution centers, and wholesalers should be determined carefully to avoid risky increase in the cost of the supply chain network.

The second scenario seeks for the effect of changes in shrimp waste rate by the wholesaler (\(\alpha_{k}\)), shrimp production rate by factories (\(\beta_{l}\)), and shrimp waste powder production rate by factories (\(\xi_{n}\)). Here, we consider the decrease in shrimp waste rate by wholesaler, and increase in both shrimp production rate by factories, and shrimp waste powder production. The results of this scenario are presented in Table 7 and Fig. 27. According to Fig. 27, we realize that all considered factors are positively associated with an increase in the objective function value. However, shrimp production rate of factory is reasonably effective rather than the others.

The last scenario investigates the influence of shrimp product demand by customers (\(Db_{m}\)), and shrimp waste powder demand by poultry and livestock food market (\(Dp_{p}\)) on the supply chain network cost. The results of the third scenario are separately calculated for customer’s demands and shrimp waste powder demand and shown in Table 8 and Fig. 28. The results indicate that whenever the demand in both sides vary increasingly, there is advance in optimum objective function value. Additionally, it is derived from Fig. 27 that demands of customers have more significant effect on the overall cost of the supply chain network than the shrimp waste powder demand.