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

Maedeh Agahgolnezhad Gerdrodbari; Fatemeh Harsej; Mahboubeh Sadeghpour; Mohammad Molani Aghdam

doi:10.3934/jimo.2021107

Article Contents

2022, Volume 18, Issue 5: 3155-3186. Doi: 10.3934/jimo.2021107

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

1.
Department of Industrial Engineering, Nour Branch, Islamic Azad University, Nour, Iran
2.
Department of Industrial Engineering and Quality Research Centre, Nour Branch, Islamic Azad University, Nour, Iran
3.
Department of Industrial Engineering, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
4.
Innovation and Management Research Center, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran

^* Corresponding author: Fatemeh Harsej
^* Corresponding author: Fatemeh Harsej

Received: November 30, 2020

Revised: March 31, 2021

Early access: June 2021

Published: November 2022

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Abstract

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.

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

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Figure 1. The proposed supply chain network

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

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Figure 3. The Pareto solution obtained by two methods

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

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

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

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

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

Reference	Year	Levels of Network								Features		Objectives				Solution methods
Reference	Year	Supply centers	Production centers	Collection centers	Recycling centers	Distribution centers	Recovery centers	Repair center	Disposal center	Uncertainty	Perishable products	Responsiveness	Environmental	Social	Economic	Solution methods
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

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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
Second Part	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

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Table 3. Interpretation of chromosome

First Part		0	1	1

Second Part		Customer 1	Customer 2	Customer 3	Customer 4	Customer 5
Second Part	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

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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

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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

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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

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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)

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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

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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

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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

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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

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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

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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

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