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A robust multi-objective model for managing the distribution of perishable products within a green closed-loop supply chain

  • * Corresponding author: Fatemeh Harsej

    * Corresponding author: Fatemeh Harsej 
Abstract Full Text(HTML) Figure(7) / Table(13) Related Papers Cited by
  • The required processes of supply chain management include optimal strategic, tactical, and operational decisions, all of which have important economic and environmental effects. In this regard, efficient supply chain planning for the production and distribution of perishable productsis of particular importance due to its leading role in the human food pyramid. One of the main challenges facing this chain is the time when products and goods are delivered to the customers and customer satisfaction will increase through this.In this research, a bi-objective mixed-integer linear programming (MILP)model is proposedto design a multi-level, multi-period, multi-product closed-loop supply chain (CLSC) for timely production and distribution of perishable products, taking into account the uncertainty of demand. To face the model uncertainty, the robust optimization (RO) method is utilized. Moreover, to solve and validate the bi-objective model in small-size problems, the $ \epsilon $-constraint method (EC) is presented. On the other hand, a Non-dominated Sorting Genetic Algorithm (NSGA-II) is developed for solving large-size problems. First, the deterministic and robust models are compared by applying the suggested solutions methods in a small-size problem, and then, the proposed solution methods are compared in large-size problems in terms of different well-known metrics. According to the comparison, the proposed model has an acceptable performance in providing the optimal solutions and the proposed algorithm obtains efficient solutions.Finally, managerial insights are proposed using sensitivity analysis of important parameters of the problem.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:

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  • Figure 1.  The proposed supply chain network

    Figure 2.  Flowchart of the proposed NSGA-II (Rabbani et al., 2021)

    Figure 3.  The Pareto solution obtained by two methods

    Figure 4.  The comparison of NSGA-II and EC at uncertainty level 0.2

    Figure 5.  The comparison of NSGA-II and EC at uncertainty level 0.4

    Figure 6.  The comparison of NSGA-II and EC at uncertainty level 0.5

    Figure 7.  The comparison of solution time for NSGA-II and EC

    Table 1.  A brief comparison between previously-performed studies and our study

    Reference Year Levels of Network Features Objectives Solution methods
    Supply centers Production centers Collection centers Recycling centers Distribution centers Recovery centers Repair center Disposal center Uncertainty Perishable products Responsiveness Environmental Social Economic
    Pishvaee et al. 2014 * * * * * * * * LINGO
    Govindan et al. 2014 * * * * Benders decomposition
    Devika et al. 2014 * * * * * * * * * * LINGO
    Azadeh et al. 2015 * * * * * * * $ \epsilon $-constraint
    Wu et al. 2017 * * * * * NSGA-II
    Keshavarz Ghorabaee et al. 2017 * * * * * * * GAMS
    Cheraghalipour et al. 2018 * * * * * * NSGA-II
    Kayvanfar et al. 2018 * * * * * * * * Benders decomposition
    Dai et al. 2018 * * * * LINGO
    Yavari andGeraeli 2019 * * * * * * * * Heuristics
    Parsa et al. 2020 * * * * * * Branch-and-bound (B & B) algorithm
    Lotfi et al. 2021 * * * * * * * * * * LP-Metric method
    Current work 2021 * * * * * * * * * * $ \epsilon $-constraint and NSGA-II
     | Show Table
    DownLoad: CSV

    Table 2.  An example of chromosome

    First Part 0.41 0.72 0.93
     
    Second Part Customer 1 Customer 2 Customer 3 Customer 4 Customer 5
    Distribution Center 1 0.61 0.29 0.43 0.27 0.35
    Distribution Center 2 0.45 0.73 0.28 0.34 0.19
    Distribution Center 3 0.35 0.91 0.73 0.58 0.39
     | Show Table
    DownLoad: CSV

    Table 3.  Interpretation of chromosome

    First Part 0 1 1
     
    Second Part Customer 1 Customer 2 Customer 3 Customer 4 Customer 5
    Distribution Center 1 0 0 0 0 0
    Distribution Center 2 0.52 0.44 0.27 0.37 0.32
    Distribution Center 3 0.48 0.56 0.73 0.63 0.68
     | Show Table
    DownLoad: CSV

    Table 4.  The value of parameters for NSGA-II

    Parameter Value
    Npop 50 80 100
    Max iteration 100 200 300
    Cross rate 0.5 0.7 0.9
    Mut rate 0.5 0.3 0.1
     | Show Table
    DownLoad: CSV

    Table 5.  The optimal value of parameters of NSGA-II

    Parameter Value
    Npop 100
    Max iteration 200
    Cross rate 0.7
    Mut rate 0.3
     | Show Table
    DownLoad: CSV

    Table 6.  The small-size instance for the supply chain network

    Set Number
    Suppliers 4
    Production centers 3
    Distribution centers 3
    Customers 5
    Collection centers 2
    Recovery centers 2
    Disposal centers 2
    Products 2
    Raw materials 2
    Time periods 1
    Technology levels 2
    Transportation modes 2
     | Show Table
    DownLoad: CSV

    Table 7.  Value of parameters

    Parameter Value
    Parameter Value
    Customer demand U(1,200)
    Quantity of raw material U(50,350)
    Capacity of suppliers U(1000, 2500)
    Capacity of production centers U(500, 2000)
    Capacity of distribution centers U(1000, 2500)
    Capacity of collection centers U(1000, 2500)
    Capacity of disposal centers U(1000, 2000)
    Capacity of recovery centers U(1000, 2000)
    Cost of transporting raw materials from the supply center to the production center U(50,150)
    Cost of transporting products from production center to distribution center U(50,150)
    Cost of transporting from distribution center to customer U(50,150)
    Cost of transporting from customer to collection center U(50,150)
    Cost of transporting from the collection center to the disposal center U(50,150)
    Cost of transporting from the collection center to the recovery center U(50,150)
    Cost of transporting from the recovery center to the production center U(50,150)
    Volume of $CO_2$ emission released to transport raw material from the supply center to the production center U(50,100)
    Volume of $CO_2$ emission released to transport products from the production center to the distribution center U(50,100)
    Volume of $CO_2$ emission released to transport from the distribution center to the customer U(50,100)
    Volume of $CO_2$ emission released to transport from customer to the collection center U(50,100)
    Volume of $CO_2$ emission released to transport from the collection center to the disposal center U(50,100)
    Volume of $CO_2$ emission released to transport from the collection center to the recovery center U(50,100)
    Volume of $CO_2$ emission released to transport from the recovery center to the production center U(50,100)
    Preparation time for transportation of raw material from the supply center to production center U(10, 20)
    Preparation time for the transportation of products from distribution center to customers U(10, 20)
    Distance between supply center and production center U(500, 1500)
    Distance between production center and distribution center U(500, 1500)
    Distance between the distribution center and customer U(500, 1500)
    Distance between customer and collection center U(500, 1500)
    Distance between collection center and disposal center U(500, 1500)
    Distance between collection center and recovery center U(500, 1500)
    Distance between recovery center and production center U(500, 1500)
    Production cost in production centers U(50,100)
    Processing cost in distribution centers U(50,100)
    Processing cost in production centers U(50,100)
    Processing cost in disposal centers U(50,100)
    Processing cost in recovery centers U(50,100)
    Fixed cost of establishing a production center U(5000, 15000)
    Fixed cost of establishing a distribution center U(5000, 15000)
    Fixed cost of establishing a collection center U(5000, 15000)
    Fixed cost of establishing a disposal center U(5000, 15000)
    Fixed cost of establishing a recovery center U(5000, 15000)
    Inventory holding cost U(100,200)
    Inventory shortage cost U(100,150)
    Consumption coefficient of raw materials U(0.3, 0.7)
    Recovery coefficient of products U(0.1, 0.4)
    Flow rate of retuned products U(0, 0.5)
    Flow rate of disposable products U(0, 0.3)
     | Show Table
    DownLoad: CSV

    Table 8.  Results of the solution methods for the robust model

    No. NSGA-II EC
    Objective 1 Objective 2 Objective 1 Objective 2
    1 860870 26703 860824 26700
    2 861031 26288 861029 26277
    3 864920 25883 864875 25854
    4 869473 25445 869468 25441
    5 874268 25014 874115 25010
     | Show Table
    DownLoad: CSV

    Table 9.  Results of the solution methods for deterministic and robust models

    Model NSGA-II EC
    Objective 1 Objective 2 CPU time Objective 1 Objective 2 CPU time
    Deterministic 858651.6 25271.3 12.94 858242.1 24971.3 31.84
    Robust 866112.4 25866.6 14.04 866062.2 25856.4 40.56
     | Show Table
    DownLoad: CSV

    Table 10.  Information of the problem instances in medium- and large- size

    Sets P1 P2 P3 P4
    Suppliers 8 15 20 40
    Production centers 5 10 15 25
    Distribution centers 5 10 15 30
    Customers 8 20 35 50
    Collection centers 4 6 10 15
    Recovery centers 4 6 10 15
    Disposal centers 4 6 10 15
    Products 4 6 10 15
    Raw materials 4 6 10 15
    Time periods 3 4 5 8
    Technology levels 3 4 5 8
    Transportation modes 3 4 5 8
     | Show Table
    DownLoad: CSV

    Table 11.  The average value of criteria for the two algorithms in the uncertainty level of 0.2

    Criteria DM MID SM NPS
    Problem/ Method EC NSGA-II EC NSGA-II EC NSGA-II EC NSGA-II
    1 1.09 1.13 0.82 0.88 1.12 1.01 4 8
    2 1. 23 1.2 1.13 1.09 1.07 0.99 2 14
    3 0.92 0.95 0.94 0.9 0.71 0.66 3 23
    4 - 1.13 - 1.55 - 2.39 - 32
     | Show Table
    DownLoad: CSV

    Table 12.  The average value of criteria for the two algorithms in the uncertainty level of 0.4

    Criteria DM MID SM NPS
    Problem/ Method EC NSGA-II EC NSGA-II EC NSGA-II EC NSGA-II
    1 1.03 1.09 0.86 0.74 2.33 2.14 3 7
    2 1.16 1.21 0.93 0.82 2.02 1.91 2 16
    3 0.75 0.69 0.79 0.83 0.72 0.92 2 28
    4 - 1.31 - 1.02 - 1.24 - 43
     | Show Table
    DownLoad: CSV

    Table 13.  The average value of criteria for the two algorithms in the uncertainty level of 0.5

    Criteria DM MID SM NPS
    Problem/ Method EC NSGA-II EC NSGA-II EC NSGA-II EC NSGA-II
    1 1.17 1.24 0.59 0.69 1.25 1.03 2 6
    2 0.84 0.93 0.32 0.23 1.97 1.51 4 15
    3 1.2 1.31 0.43 0.31 0.9 0.87 2 37
    4 - 0.71 - 0.92 - 2.34 - 52
     | Show Table
    DownLoad: CSV
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