Optimal production-inventory policy for the multi-period fixed proportions co-production system

Hengyu Liu, Juliang Zhang, T.C.E. Cheng and Yihong Ru

European Journal of Operational Research, 2020, vol. 280, issue 2, 469-478

Abstract: Consider the multi-period production-inventory problem where a manufacturer purchases and processes a raw material into two products in fixed proportions when facing uncertain demands. In each period, the manufacturer first reviews the on-hand inventories of the products and then decides the purchase/processing quantity of the raw material. After processing the raw material into the end products, the demands of the two products are realized and satisfied by the available inventories. Any leftover inventories are carried to the next period while the unsatisfied demands are backordered. By proving the concavity and submodularity of the expected profit-to-go function, we establish that the one-dimensional produce-up-to policy is optimal. We also study the case where the raw material is seasonal and the manufacturer has only one chance to purchase. Modeling it as a dynamic program, we establish that the one-dimensional produce-down-to policy is optimal. Finally, we conduct numerical studies to examine the impacts of supply-demand balance and price fluctuation on the optimal policy, and derive managerial insights from the analytical findings.

Keywords: Production-inventory management; Co-production system; Markov decision problem; Dynamic programming (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:280:y:2020:i:2:p:469-478

DOI: 10.1016/j.ejor.2019.07.025

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