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

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)469-478
Number of pages10
JournalEuropean Journal of Operational Research
Issue number2
Publication statusPublished - 16 Jan 2020


  • Co-production system
  • Dynamic programming
  • Markov decision problem
  • Production-inventory management

ASJC Scopus subject areas

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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