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

Fatemeh Kangi; Seyed Hamid Reza Pasandideh; Esmaeil Mehdizadeh; Hamed Soleimani

doi:10.3934/jimo.2021118

Article Contents

2022, Volume 18, Issue 5: 3393-3431. Doi: 10.3934/jimo.2021118

This issue Previous Article Collection decisions and coordination in a closed-loop supply chain under recovery price and service competition Next Article The application of model predictive control on stock portfolio optimization with prediction based on Geometric Brownian Motion-Kalman Filter

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
^* Corresponding author: Seyed Hamid Reza Pasandideh

Received: November 30, 2020

Revised: February 28, 2021

Early access: July 2021

Published: November 2022

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Abstract

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

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

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Figure 1. General structure for the considered CLSC network

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

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

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Figure 4. A sample of crossover operator

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Figure 5. A sample of mutation operator

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Figure 6. The pseudo code of MOPSO [55]

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

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

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

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

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Figure 11. Kruskal-Wallis test on computational time

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Figure 12. Sensitivity analysis of the demand parameter

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Table 1. A brief review of related literatures

Reference	Model Characteristics								Decision variables	Objective		Method
Reference	Flow	Hybrid fac.	Period	Product	Out.	Disc.	Cross.	Example	Decision variables	No.	Des.	Method
^[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)

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Table 2. Parameters and their levels for NSGAII

Parameters	Symbols	Levels			Value Tuned
Parameters	Symbols	Level 1	Level 2	Level 3	Value Tuned
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

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Table 3. Parameters and their levels for MOPSO

Parameters	Symbols	Levels			Value Tuned
Parameters	Symbols	Level 1	Level 2	Level 3	Value Tuned
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

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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)

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Table 5. Parameters' range in test problems

Parameter	Random generation function
Demand (DE)	U [50,150]
Production capacity (MC)	U [200J/I, 200J/I+275*J/I]
Transportation capacity (VC)	U [200NJ/I, 200NJ/I+275NJ/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]

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

Problem size	$\sharp$ P.	MID		SM		NPS		QM		Time
Problem size		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

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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

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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

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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

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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

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Table 11. Results of sensitivity analysis

Objective functions	Demand's change interval
Objective functions	-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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