Coordination of a sustainable reverse supply chain with revenue sharing contract

Sushil Kumar Dey; Bibhas C. Giri

doi:10.3934/jimo.2020165

Article Contents

2022, Volume 18, Issue 1: 487-510. Doi: 10.3934/jimo.2020165

This issue Previous Article Second-Order characterizations for set-valued equilibrium problems with variable ordering structures Next Article Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation risk

Coordination of a sustainable reverse supply chain with revenue sharing contract

Sushil Kumar Dey and
Bibhas C. Giri^,

Department of Mathematics, Jadavpur University, Kolkata-700032, India

^* Corresponding author: Bibhas C. Giri
^* Corresponding author: Bibhas C. Giri

Received: February 2020

Revised: August 2020

Early access: November 2020

Published: January 2022

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Abstract

In this article, a three-echelon closed-loop supply chain is considered under sustainability consideration through remanufacturing of waste materials. Depending upon quality, the collector collects the used products and forwards to the manufacturer for remanufacturing. The collector offers a reward or incentive to consumers to influence them to return the used items. The shortfall amount of collected used items, if any, is meet up by the supplier by supplying fresh raw materials. In three separate cases viz centralized, decentralized and revenue-sharing contract, optimal incentives for end-customers and optimal profits of supply chain members are determined. The revenue-sharing contract is implemented in two different settings - one including the supplier and the other one excluding the supplier. The win-win outcome for the supply chain members is investigated and a specific range of the sharing parameter for win-win outcome is obtained. Optimal results are supported by numerical analysis, and sensitivity of the optimal results with respect to key parameters is analyzed.

Keywords:

Mathematics Subject Classification: Primary: 90B06; Secondary: 91A35.

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Figure 1. Diagram of the supply chain model

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Figure 2. Proposed supply chain model under revenue sharing contract

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Figure 3. Concavity of $ E(\Pi) $ w.r.to $ p $ and $ r $

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Figure 4. $ L $ vs. profits of the SC and its entities

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Figure 5. $ b $ vs. profits of the SC and its entities

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Figure 6. $ r^{max} $ vs. profits of the SC and its entities

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Table 1. Optimal results

Model	$ r^{*} $	$ p^{*} $	$ 1-\phi $	$ \phi_{1}+\phi_{2} $	$ E(\Pi_{c}) $	$ E(\Pi_{m}) $	$ E(\Pi_{s}) $	$ E(\Pi) $
Centralized	26.67	437	-	-	-	-	-	143535
Decentralized	46.67	463	-	-	6505	122018	10355	138878
RS-I	26.67	437	.01	-	7662	125518	10355	143535
RS-II	26.67	437	-	0.03	-	124536	-	143535

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