Integration of pricing, sustainability and 3PL delivery time according to freshness date in a dual-channel fruit supply chain: A game theoretic approach

Parsa Leylaparast; Mohammad Reza Gholamian; Maryam Noroozi

doi:10.3934/jimo.2024092

Article Contents

2025, Volume 21, Issue 1: 504-523. Doi: 10.3934/jimo.2024092

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Integration of pricing, sustainability and 3PL delivery time according to freshness date in a dual-channel fruit supply chain: A game theoretic approach

1.
Department of Industrial Engineering, Iran University of Science and Technology (IUST), Iran

^*Corresponding author: Mohammad Reza Gholamian
^*Corresponding author: Mohammad Reza Gholamian

Received: June 2023

Revised: December 2023

Early access: July 2024

Published: January 2025

Abstract / Introduction Full Text(HTML) Figure(11) / Table(5) Related Papers Cited by

Abstract

The perishable nature of agricultural products poses a significant challenge in the management of agricultural supply chains, necessitating the timely delivery of these products. The increasing global population has led to a greater demand for food supplies, prompting the need for sustainable supply chains that take into account environmental concerns and social responsibility. By examining various strategies, such as cooperation, the field of agricultural supply chain management can experience growth. This study investigates a three-level agricultural supply chain model, comprising the farmer, third-party logistics (3PL), and two retailers (online and offline sellers). The 3PL plays a crucial role in this supply chain by ensuring the delivery of fresh produce to customers before the expiration date, as well as implementing environmentally friendly packaging practices. Additionally, the farmer contributes to charitable causes through cash donations. To explore the relationships among the members of the supply chain, two approaches, namely Stackelberg and Nash equilibrium games, are employed. Consequently, two distinct supply chain strategies are developed and compared. In the first scenario, the two retailers cooperate as a single entity, whereas in the second scenario, the retailers compete against each other with the Nash equilibrium utilized to analyze their interactions. In both scenarios, the farmer assumes the role of the Stackelberg game leader, while the retailers act as the first followers, and the 3PL functions as the second follower. The findings of the analysis indicate that cooperation between the two retailers results in higher profits for both parties and the entire supply chain, whereas the profit levels of the farmer and 3PL are comparatively lower in the first scenario. This model can be applied to other case studies that consider these two scenarios as well.

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

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Figure 1. Supply chain schematic

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Figure 2. Game scenarios

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Figure 3. Equilibrium values of profit functions in two scenarios

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Figure 4. The effect of $ a_1 $ on Prices in CM scenario

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Figure 5. The effect of $ a_1 $ on Prices in DM scenario

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Figure 6. The effect of $ a_1 $ on profit functions in CM scenario

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Figure 7. The effect of $ a_1 $ on profit functions in DM scenario

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Figure 8. The effect of $ k $ on Delivery time

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Figure 9. The effect of $ \lambda $ on Delivery time

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Figure 10. The effect of $ h $ on quality of green packaging

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Figure 11. The effect of $ \tau_1 $ on quality of green packaging

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Table 1. Most important articles in literature

Authors	Demand dependency				3PL	Freshness date	Game
	Price	Green	CSR	Delivery time
Modak and Kelle [19]	$ \ast $			$ \ast $			Stackelberg and Nash
Raza [20]			$ \ast $				Stackelberg
Li et al. [13]	$ \ast $	$ \ast $					Stackelberg and Nash
Heydari et al. [8]	$ \ast $	$ \ast $					Stackelberg
Xu et al. [29]	$ \ast $						Stackelberg
He et al. [7]	$ \ast $	$ \ast $		$ \ast $			Stackelberg
Yang et al. [30]	$ \ast $	$ \ast $					Stackelberg
Wang et al. [26]	$ \ast $	$ \ast $					Stackelberg and Nash
Dabaghian et al. [3]	$ \ast $		$ \ast $				Stackelberg
Dingjun [9]	$ \ast $		$ \ast $				Stackelberg
This article	$ \ast $	$ \ast $	$ \ast $	$ \ast $	$ \ast $	$ \ast $	Stackelberg and Nash

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Table 2. Parameter values

$ a_1 $	$ a_2 $	$ b $	$ q $	$ \tau_1 $	$ \tau_2 $	$ \gamma_1 $	$ \gamma_2 $
2400	2000	2	1	0.8	0.7	0.4	0.3
$ \mu $	$ h $	$ k $	$ m $	$ c $	$ w $	$ \phi $	$ \lambda $
12	3	6	7	200	800	250	150

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Table 3. Decision variables in both scenarios

	Non-cooperative scenario	cooperative scenario
$ p_1 $	2462.01	3160.07
$ p_2 $	2338.19	3040.23
$ l $	1.33	1.33
$ e $	13.33	13.33
$ x $	249.975	249.975

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Table 4. Values of profit functions

	Non-cooperative scenario	cooperative scenario
$ \pi_{r_1} $	3987560	4494280
$ \pi_{r_2} $	3854160	4329660.61
$ \pi_{r} $	7841690	8821850
$ \pi_{f} $	1960280	1470210
$ \pi_{3PL} $	281735	212325
$ \pi_{sc} $	10083705	10504385

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Table 5. The results on demand levels

	Non-cooperative scenario	cooperative scenario
$ D_1 $	2824.01	2129.92
$ D_2 $	2776.39	2070.38

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