# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2020165

## Coordination of a sustainable reverse supply chain with revenue sharing contract

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

* Corresponding author: Bibhas C. Giri

Received  February 2020 Revised  August 2020 Published  November 2020

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.

Citation: Sushil Kumar Dey, Bibhas C. Giri. Coordination of a sustainable reverse supply chain with revenue sharing contract. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020165
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##### References:
Diagram of the supply chain model
Proposed supply chain model under revenue sharing contract
Concavity of $E(\Pi)$ w.r.to $p$ and $r$
$L$ vs. profits of the SC and its entities
$b$ vs. profits of the SC and its entities
$r^{max}$ vs. profits of the SC and its entities
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
 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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