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

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 ρ-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.