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doi: 10.3934/jimo.2021118
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## The optimization of a multi-period multi-product closed-loop supply chain network with cross-docking delivery strategy

 1 Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran 2 Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran 3 School of Mathematics and Statistics, University of Melbourne, Melbourne, Parkville, VIC 3010, Australia

* Corresponding author: Seyed Hamid Reza Pasandideh

Received  December 2020 Revised  March 2021 Early access July 2021

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

Citation: Fatemeh Kangi, Seyed Hamid Reza Pasandideh, Esmaeil Mehdizadeh, Hamed Soleimani. The optimization of a multi-period multi-product closed-loop supply chain network with cross-docking delivery strategy. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2021118
##### References:

show all references

##### References:
General structure for the considered CLSC network
The pseudo code of NSGA-II [62]
The pseudo code related to product's flow from manufacturer to retailer
A sample of crossover operator
A sample of mutation operator
The pseudo code of MOPSO [55]
Average S/N ratio levels for NSGAII's parameters
Average S/N ratio levels for MOPSO's parameters
Individual 95% CIs for mean based on Pooled StDev
Individual 95% CIs for mean based on Pooled StDev
Kruskal-Wallis test on computational time
Sensitivity analysis of the demand parameter
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)
 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)
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
 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
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
 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
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)
 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)
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]
 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]
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
 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
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
 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
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
 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
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
 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
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
 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
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
 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

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