Optimal policy for production systems with two flexible resources and two products

Abstract

Manufacturing companies are facing increasing volatility in demand. As a result, there has been an emerging need for a flexible multi-period manufacturing system that uses multiple resources to produce multiple products with stochastic demands. To manage such multi-product, multi-resource systems, manufacturers need to make two decisions simultaneously: setting a production quantity for each product and allocating the limited resources dynamically among the products. Unfortunately, although the flexibility design and investment have been extensively studied, the literature has been muted on how to make production and allocation decisions optimally from an operational perspective. This article attempts to fill this literature gap by investigating a multi-period system using multiple flexible resources to produce two products. We identify the structural property of the cost functions, namely $\rho$-differential monotone. Based on this property, the optimal production and allocation policy can be characterized by switching curves, which divide the state space into eight or nine sub-regions based on the segmentation of decision rules. We analyze different cases in terms of production costs and resource utilization ratios, and show how they affect the optimal production and allocation decisions. Finally, we compare three heuristic policies to the optimal one to display the advantage of resource flexibility and the effectiveness of a heuristic policy. Supplementary materials are available for this article. Go to the publisher’s online edition of IISE Transaction, datasets, additional tables, detailed proofs, etc.

Keywords:

• Production/inventory control
• manufacturing flexibility
• resource flexibility
• optimal allocation policy
• dynamic programming

Acknowledgments

The authors gratefully acknowledge the constructive comments from the area editor and two anonymous referees that helped us improve the manuscript significantly.

Additional information

Funding

The research of Jianjun Xu was supported by National Natural Science Foundation of China (grant nos. 71871047 and 71831003). The third author G. Cai acknowledges support from the National Natural Science Foundation of China (grant no. 71629001) and the National Social Science Fund of China (grant no.18ZDA058).

Notes on contributors

Jianjun Xu

Jianjun Xu is an associate professor at International Business College and Institute of Supply Chain Analytics, Dongbei University of Finance and Economics, China. He received his Ph.D. degree in Operations Management from Nanyang Technological University. His research interests include dynamic inventory control, stochastic optimization, and data-driven operations management.

Shaoxiang Chen

Shaoxiang Chen is a professor of operations management in the Nanyang Business School at Nanyang Technological University, Singapore. He received his B.S. in 1982 from Nanjing University, China, MBA in 1987 and Ph.D. in 1993 from Catholic University of Leuven, Belgium. His main research interest in the past has been in developing the fundamental theories on some of the basic stochastic production and inventory systems. His papers have appeared in Operations Research and Management Science, among others. Recently, he is doing research on how internet is changing the way the economy is running and its impacts to the social and political systems.

Gangshu (George) Cai

Dr. Gangshu (George) Cai is a Professor at the Leavey School of Business in Santa Clara University. His research interests include supply chain management, interface between operations management and marketing, and supply chain finance. His scholarship has been financially supported by the NSF and NSF China. Professor Cai has received a number of school-level and international awards in research, teaching, and service, including the Wickham Skinner Award for Teaching Innovation of the Production & Operations Management Society. Professor Cai has chaired multiple international conferences and founded several international research institutes. He is an Associate Editor of Decision Sciences Journal and a Senior Editor of Production and Operations Management Journal.