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The optimization of a multi-period multi-product closed-loop supply chain network with cross-docking delivery strategy

  • * Corresponding author: Seyed Hamid Reza Pasandideh

    * Corresponding author: Seyed Hamid Reza Pasandideh 
Abstract Full Text(HTML) Figure(12) / Table(11) Related Papers Cited by
  • The main reason for the development of this research refers to the increased attention of businesses to the CLSC concept due to the social responsibilities, strict international legislations and economic motives. Hence, this study investigates the issue of optimizing a CLSC problem involving multiple manufacturers, a hybrid cross-dock/collection center, multiple retailers and a disposal center in deterministic, multi-product and multi-period contexts. The bi-objective MILP model developed here is to simultaneously minimize total costs and total processing time of CLSC. Both strategic and tactical decisions are considered in the model where retailer demands and capacity constraints are satisfied. Since the presented model is NP-hard, NSGAII and MOPSO are hired to find near-to-optimal results for practical problem sizes in polynomial time.Then, to increase the accuracy of solutions by tuning the algorithms' parameters, the Taguchi method is applied. The practicality of the developed

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

    Citation:

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  • Figure 1.  General structure for the considered CLSC network

    Figure 2.  The pseudo code of NSGA-II [62]

    Figure 3.  The pseudo code related to product's flow from manufacturer to retailer

    Figure 4.  A sample of crossover operator

    Figure 5.  A sample of mutation operator

    Figure 6.  The pseudo code of MOPSO [55]

    Figure 7.  Average S/N ratio levels for NSGAII's parameters

    Figure 8.  Average S/N ratio levels for MOPSO's parameters

    Figure 9.  Individual 95% CIs for mean based on Pooled StDev

    Figure 10.  Individual 95% CIs for mean based on Pooled StDev

    Figure 11.  Kruskal-Wallis test on computational time

    Figure 12.  Sensitivity analysis of the demand parameter

    Table 1.  A brief review of related literatures

    Reference Model Characteristics Decision variables Objective Method
    Flow Hybrid fac. Period Product Out. Disc. Cross. Example No. Des.
    [50] CLSC Yes Mu Mu Yes No No Test problem Loc/Alloc Si $\downarrow$ total costs LINGO software, Metaheuristic
    [59] CLSC No Mu Mu Yes No No Test problem Loc/Alloc Si $\downarrow$ total logistics costs LINGO software, Metaheuristic
    [24] CLSC No Si Mu Yes No No Test problem Loc/Alloc Mu $\downarrow$ total costs
    $\downarrow$ total tardiness
    Scatter search, Dual simplex, $\epsilon$-constraint
    [68] CLSC No Si Si No No No Test problem Loc/Alloc Mu $\downarrow$ total costs
    $\uparrow$ responsiveness
    Metaheuristics
    [67] CLSC Yes Mu Mu No No No an office document company Loc/Alloc/Inv Mu $\downarrow$ total costs
    $\uparrow$ service efficiency
    Goal programming, Compromise programming
    [5] CLSC No Si Mu No No No Copier remanufacturing Loc/Alloc Mu $\downarrow$ total costs
    $\uparrow$ environmental factors
    Weighted sums, $\epsilon$-constraint
    [22] CLSC No Si Si No No No Test problem Loc/Alloc Mu $\downarrow$total costs
    $\downarrow$ environmental impacts
    $\uparrow$ ↑social benefits
    GAMS software, Metaheuristics
    [7] CLSC No Mu Mu No No No Refrigerator industry Loc/Alloc/Inv Mu $\downarrow$total costs
    $\downarrow$total travel time
    $\epsilon$-constraint, GAMS software, Metaheuristics
    [20] CLSC Yes Si Mu No No No Test problem Loc/Alloc Mu $\uparrow$ total profit
    $\downarrow$ total spent energy
    $\downarrow$ harmful emissions
    LINGO software, Goal programming
    [89] CLSC Yes Si Mu No No No Test problem Loc/Alloc Mu $\downarrow$ total costs
    $\downarrow$ waiting time in services
    Interval-stochastic, robust optimization, Metaheuristic, Lower bound procedure, GAMS software
    [48] RL No Si Mu No No Yes Test problem Loc/Alloc Si $\downarrow$ total costs GAMS software
    [93] CLSC No Si Si No No No Gold industry Loc/Alloc Mu $\downarrow$ total costs
    $\uparrow$ total incomes
    $\downarrow$ CO2 emissions
    LINGO software, Metaheuristic
    [54] CLSC No Si Mu No No No Test problem Loc/Alloc Mu $\downarrow$ total costs
    $\downarrow$ environmental impacts
    LINGO software, LP-metrics
    [85] CLSC No Si Mu No No No Copiers industry Loc/Alloc Mu $\downarrow$ total costs
    $\downarrow$ CO2 emissions
    $\epsilon$-constraint
    [92] CLSC No Mu Mu No No No LCD and LED TV Loc/Alloc/ Route/Inv Mu $\downarrow$ total costs
    $\downarrow$ environmental impacts
    $\uparrow$ social impacts
    stochastic-possibilistic programming, modified game theory, lower bound procedure, GAMS software, Hybrid metaheuristic
    [18] CLSC No Si Si No No No Solar cell industry Loc/Alloc Mu $\downarrow$ total costs
    $\downarrow$ CO2 emissions
    branch & bound, CPLEX software, Metaheuristic
    [94] RL No Si Mu No No Yes Test problem Alloc Si $\downarrow$ total costs CPLEX software
    [37] CLSC No Mu Si Yes No No Filter Loc/Alloc/SS/Inv/Price Mu $\uparrow$ total profit
    $\downarrow$ CO2 emissions
    Karush–Kuhn–Tucker, conditions possibilistic method, $\epsilon$-constraint, CPLEX software
    [75] CLSC Yes Mu Mu No Yes No Test problem Loc/Alloc/SS Mu $\downarrow$total costs
    $\downarrow$ CO2 emissions
    $\uparrow$ customer satisfaction
    CPLEX software, LP-metrics
    [72] CLSC No Si Si No No Yes Test problem Loc/Alloc Mu $\downarrow$total costs
    $\downarrow$ environmental impacts
    $\uparrow$ social benefits
    GAMS software, Metaheuristics
    [40] CLSC Yes Mu Mu No No No Test problem Loc/Alloc/Inv Mu $\uparrow$ increase in the cash flow
    $\uparrow$ social responsibility
    $\downarrow$ amount of unreliable raw materials
    $\epsilon$-constraint, GAMS software, Metaheuristics
    [61] CLSC No Mu Mu Yes No No Battery Loc/Alloc/TPS Mu $\uparrow$ total profit
    $\uparrow$ environmental compliance
    Fully fuzzy stochastic programming
    [86] CLSC No Mu Si No Yes No CFL light bulb Alloc/Inv/Price Mu $\downarrow$total costs
    $\downarrow$ environmental impacts
    $\downarrow$ social impacts
    Fuzzy TH approach [88]
    [65] CLSC No Si Mu No No No Tanker industry Loc/Alloc/SS Mu $\downarrow$total costs
    $\downarrow$ environmental impacts
    $\uparrow$ social impacts
    Multi-choice goal programming with utility function
    [66] CLSC No Mu Si No No No Test problem Loc/Alloc Mu $\uparrow$supply chain surplus
    $\downarrow$ CO2 emissions
    MATLAB software
    This paper CLSC Yes Mu Mu Yes Yes Yes Test problem Loc/Alloc/TPS Mu $\downarrow$ total costs
    $\downarrow$ total processing times
    $\epsilon$-constraint, LINGO software, Metaheuristics
    Notes:
    fac. (facility); Out. (outsource); Disc. (discount); Cross. (cross-dock); Des. (description); RL (reverse logistic); CLSC (closed loop supply chain); Si (single); Mu (multi); Loc (location); Alloc (allocation); Inv (inventory); Route (routing); SS (supplier selection); TPS (third party selection); Price (pricing)
     | Show Table
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    Table 2.  Parameters and their levels for NSGAII

    Parameters Symbols Levels Value Tuned
    Level 1 Level 2 Level 3
    Pop Size (A) 100 150 200 100
    Iteration (B) 100 150 200 200
    Crossover Rate (C) 0.85 0.9 0.95 0.85
    Mutation Rate (D) 0.03 0.05 0.1 0.05
     | Show Table
    DownLoad: CSV

    Table 3.  Parameters and their levels for MOPSO

    Parameters Symbols Levels Value Tuned
    Level 1 Level 2 Level 3
    Pop Size (A) 50 100 150 100
    Iteration (B) 100 150 200 200
    Inertia Weight (C) 0.75 0.8 0.85 0.75
    C1 (D) 1.0 1.5 2.0 1.5
    C2 (E) 1.0 1.5 2.0 1.5
     | Show Table
    DownLoad: CSV

    Table 4.  Size and level of problems

    Problem levels Problem size (I, C, J, K, M, N, P, T)
    Small scale P1. (2, 2, 5, 2, 2, 2, 4, 3) P6. (4, 3, 10, 2, 2, 2, 4, 3)
    P2. (2, 2, 7, 3, 2, 2, 4, 3) P7. (5, 2, 5, 2, 2, 2, 4, 3)
    P3. (3, 3, 10, 2, 2, 2, 4, 3) P8. (5, 2, 7, 3, 2, 2, 4, 3)
    P4. (3, 2, 5, 2, 2, 2, 4, 3) P9. (6, 3, 10, 2, 2, 2, 4, 3)
    P5. (4, 2, 7, 3, 2, 2, 4, 3) P10. (6, 3, 10, 3, 2, 2, 4, 3)
    Medium scale P11. (7, 4, 15, 3, 2, 3, 4, 5) P16. (11, 5, 30, 3, 3, 3, 4, 5)
    P12. (7, 4, 20, 4, 2, 4, 4, 5) P17. (13, 4, 15, 3, 2, 3, 4, 5)
    P13. (9, 5, 30, 3, 3, 3, 4, 5) P18. (13, 4, 20, 4, 2, 4, 4, 5)
    P14. (9, 4, 15, 3, 2, 3, 4, 5) P19. (15, 5, 30, 3, 3, 3, 4, 5)
    P15. (11, 4, 20, 4, 2, 4, 4, 5) P20. (15, 5, 30, 4, 3, 4, 4, 5)
    Large scale P21. (16, 6, 50, 5, 3, 5, 4, 10) P26. (20, 9,100, 5, 4, 5, 4, 10)
    P22. (16, 6, 75, 7, 3, 7, 4, 10) P27. (22, 6, 50, 5, 3, 5, 4, 10)
    P23. (18, 9,100, 5, 4, 5, 4, 10) P28. (22, 6, 75, 7, 3, 7, 4, 10)
    P24. (18, 6, 50, 5, 3, 5, 4, 10) P29. (24, 9,100, 5, 4, 5, 4, 10)
    P25. (20, 6, 75, 7, 3, 7, 4, 10) P30. (24, 9,100, 7, 4, 7, 4, 10)
     | Show Table
    DownLoad: CSV

    Table 5.  Parameters' range in test problems

    Parameter Random generation function
    Demand (DE) U [50,150]
    Production capacity (MC) U [200*J/I, 200*J/I+275*J/I]
    Transportation capacity (VC) U [200*N*J/I, 200*N*J/I+275*N*J/I]
    Upper bound (U) Transportation capacity/P+1
    Transportation fixed cost I (FCC) U [15, 20]
    Transportation fixed cost II (FCR) U [8, 15]
    Transportation fixed cost III (FCD) U [5, 10]
    Transportation cost I (TIC) U [10, 15]
    Transportation cost II (TCJ) U [4, 8]
    Transportation cost III (TCD) U [3, 5]
    Production cost (PC) U [80,100]
    Opening cost of hybrid facility (EC) U [5, 30]
    Recovery cost (RC) U [20, 30]
    Consolidation time (TA) U [0.08, 0.11]
    Inspection time (TI) U [0.03, 0.06]
    Transportation time I (TC) U [2, 20]
    Transportation time II (TM) U [1.5, 12]
    Transportation time III (TD) U [3, 5]
    Fraction of returned product ($ \alpha $) U [0.02, 0.04]
    Fraction of recoverable product ($ \beta $) U [0.25, 0.8]
    Weight/volume of each unit of product ($ \gamma $) U [0.5, 3]
     | Show Table
    DownLoad: CSV

    Table 6.  The obtained metrics for algorithms' performance (MID, SM, NPS, QM and Time)

    Problem size $\sharp$ P. MID SM NPS QM Time
    NSGA-II MOPSO NSGA-II MOPSO NSGA-II MOPSO NSGA-II MOPSO NSGA-II MOPSO
    Small P1. 0.2965 0.9135 0.52047 0.79424 2 13 0.11743 0.88256 152.2674 83.61384
    P2. 0.7985 0.7594 1.44002 1.42646 11 5 0.21714 0.78285 170.5 93.31762
    P3. 0.6678 0.8303 0.90528 1.30920 11 20 0.16347 0.83652 170.5483 112.2679
    P4. 0.7380 0.8242 0.34031 1.31610 4 12 0.03538 0.96461 169.0048 89.31582
    P5. 0.8355 0.9241 0.04645 0.77740 3 13 0.18888 0.81111 170.3636 105.0191
    P6. 0.8890 0.6733 0.73833 1.26314 9 11 0.14164 0.85835 170.8992 117.5417
    P7. 0.5898 0.8458 0.92847 1.49796 9 19 0.025 0.975 170.4384 115.9775
    P8. 0.6611 0.8644 1.26429 1.74167 8 12 0.03760 0.96239 170.6712 132.081
    P9. 0.8354 0.8519 0.63885 0.40465 4 7 0 1 170.698 131.0991
    P10. 0.9213 0.8708 0.24135 0.98781 9 3 0.01818 0.98181 170.9277 133.0108
    Medium P11. 1.2217 0.6809 0.24001 0.59929 2 5 0.08008 0.91991 171.9736 171.6591
    P12. 1.0055 0.6922 0.76749 0.72169 7 10 0.25 0.75 174.4272 164.5119
    P13. 0.9574 0.6393 0.27271 0.12447 4 7 0.38650 0.61349 173.6264 172.9455
    P14. 1.0100 0.8820 0.57146 0.46826 5 8 0.27200 0.72799 172.9297 173.0899
    P15. 1.0500 0.7352 0.65799 1.15036 4 4 0.15320 0.84679 173.1716 174.1405
    P16. 0.9179 0.6964 0.56273 0.59754 6 10 0.38333 0.61666 178.755 175.1082
    P17. 0.8986 0.8084 0.53351 0.79303 2 7 0.05714 0.94285 173.6318 173.4457
    P18. 0.9193 0.7470 0.75717 0.54668 7 7 0.28666 0.71333 175.8487 164.4145
    P19. 1.0065 0.6942 0.76486 0.44983 3 4 0.24 0.76 172.0987 173.5797
    P20. 0.9107 0.6542 0.41413 1.07685 7 10 0.51414 0.48585 171.5135 174.0156
    Large P21. 0.9056 0.5901 0.54131 1.23029 6 4 0.64047 0.35952 183.5318 182.9749
    P22. 0.7044 0.8123 0.98102 0.64139 4 8 0.375 0.625 196.9311 178.7448
    P23. 0.8133 0.5921 0.70779 0.39384 5 9 0.40090 0.59909 189.7017 195.596
    P24. 0.8936 0.6095 0.74845 0.32664 7 5 0.60333 0.39666 196.8208 173.8915
    P25. 0.8663 0.6634 0.43799 0.39058 7 3 0.61555 0.38444 180.2806 180.9208
    P26. 0.8217 0.7219 0.10674 0.63042 7 3 0.31666 0.68333 184.1588 183.5843
    P27. 0.7576 0.7515 1.17926 0.91817 9 7 0.23690 0.76309 180.4263 193.2142
    P28. 0.9310 0.6332 0.85185 0.95080 8 5 0.59047 0.40952 192.3841 180.048
    P29. 0.7122 0.7540 0.77547 0.99490 7 4 0.34381 0.65619 177.788 186.2371
    P30. 0.9133 0.7173 0.48094 0.91014 5 5 0.59285 0.40714 211.5774 188.7306
     | Show Table
    DownLoad: CSV

    Table 7.  ANOVA results for MID criterion

    Source DF SS MS F-Test P-Value
    Factor 1 0.1517 0.1517 8.09 0.006
    Error 58 1.0869 0.0187
    Total 59 1.2386
     | Show Table
    DownLoad: CSV

    Table 8.  ANOVA results for QM criterion

    Source DF SS MS F-Test P-Value
    Factor 1 3.0071 3.0071 75.25 0.000
    Error 58 2.3179 0.0400
    Total 59 5.3250
     | Show Table
    DownLoad: CSV

    Table 9.  ANOVA results for NPS criterion

    Source DF SS MS F-Test P-Value
    Factor 1 56.1 56.1 4.35 0.041
    Error 58 747.9 12.9
    Total 59 803.9
     | Show Table
    DownLoad: CSV

    Table 10.  ANOVA results for QM criterion

    Source DF SS MS F-Test P-Value
    Factor 1 3.0071 3.0071 75.25 0.000
    Error 58 2.3179 0.0400
    Total 59 5.3250
     | Show Table
    DownLoad: CSV

    Table 11.  Results of sensitivity analysis

    Objective functions Demand's change interval
    -20% -10% 0% 10% 20%
    Total cost 431,871 553,901 806,133 849,666 948,245
    Total processing time 186 221 240 276 298
     | Show Table
    DownLoad: CSV
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