Optimal production-inventory policy for the multi-period fixed proportions co-production system |
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| Institution: | 1. Department of Logistics Management, School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China;2. Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Special Administrative Region;1. School of Economic Mathematics and Collaborative Innovation Center of Financial Security, Southwestern University of Finance and Economics, Chengdu 611130, China;2. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China;3. Department of Mathematics, Imperial College, London SW7 2BZ, UK;1. Universidad Pontificia Comillas, ICADE. c/ Alberto Aguilera 23, 28015 Madrid, Spain;2. Department of Economics, Universidad Carlos III de Madrid. Calle Madrid, 126, Getafe, E-28903 Madrid, Spain;1. Department of Economics, Oregon State University, Corvallis, OR, USA;2. Department of Applied Economics, University of Maryland, College Park, MD, USA;3. Department of Economics, Southern Illinois University, Carbondale, IL, USA;4. Department of Accounting, Economics and Finance, Southeast Missouri State University, Cape Girardeau, MO, USA;1. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;2. Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia |
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| 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. |
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