An optimal inventory policy for a multi-echelon closed-loop supply chain of postconsumer recycled content products
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An optimal inventory policy for a multi‑echelon closed‑loop supply chain of postconsumer recycled content products Mostafa Parsa1,2 · Ali Shahandeh Nookabadi2 · Zümbül Atan1 · Yaser Malekian2 Received: 27 November 2019 / Revised: 31 July 2020 / Accepted: 9 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This research studies a production-recycling inventory model for postconsumer recycled content products made from a mix of virgin and recycled materials with specific proportions. The proportion is known as the postconsumer recycled content level. We study a closed-loop supply chain (CLSC) where a recycling facility and a supplier respectively ship the recycled and virgin raw materials to a manufacturer. The manufacturer mixes them based on the proportion to produce these products for a retailer. The recycling facility recycles the used products collected by a material recovery facility. The paper develops a joint economic lot-size model (JELS) to maximize the chain-wide total profit. A branch-and-bound algorithm is developed, along with the convex analysis to find the exact solution. To coordinate the CLSC, we present models called disproportionate profit-sharing (DPS) and proportional profit-sharing (PPS) operating under quantity discount. The DPS would give more powerful members, a higher proportion of the extra profits resulting from the JELS. However, the PPS guarantees equitable increases in the individual profits accruing to all members from the JELS. Whereas the DPS works properly in vertically integrated CLSCs and decentralized ones with dominant player(s), the PPS is appropriate for decentralized ones with no dominant players. Additionally, we prove the optimal level of postconsumer recycled content is often either at its maximum or minimum allowable. However, the zero-derivative points within the range can be optimum in a particular case. Consequently, we present decision trees for managers to determine the right profit-sharing method and the optimal postconsumer recycled content level. Keywords Multi-echelon inventory · Closed-loop supply chain · Postconsumer recycled content products · Branch-and-bound algorithm · Profit-sharing
* Mostafa Parsa [email protected]; [email protected] Extended author information available on the last page of the article
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1 Introduction The term postconsumer material is defined by Federal Acquisition Regulation (48 C.F.R. § 52.223-9) as ‘a material or finished product that has served its intended use and has been discarded for disposal or recovery, having completed its life as a consumer item’. According to this definition, the postconsumer material includes waste generated by institutional, commercial, and industrial facilities or by households in their role as end-consumers of the products, which can no longer be used for their purposes. Some examples of these materials are wastepaper, discarded newspaper, used bottle, discarded furniture, worn-out clothes, and used disposables such
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