Dynamic Control of a Make-to-Order System Under Model Uncertainty

Deriving control policies for a make-to-order manufacturing system is often predicated on a well-specified probabilistic model that governs demand realization. In practice, however, such a model may be a simplification of the actual scenario because of tractability considerations. Consequently, policies obtained under such simplifications may perform poorly if the assumed model does not accurately capture reality. In this paper, we propose a modeling paradigm that can generate control policies based on a simplified model, accounting for possible model errors that may result. The make-to-order system offers multiple products and has an outsourcing mechanism. Our focus is on addressing deliberate model simplification for the demand realization process. We formulate a robust control problem that takes the form of a two-player, zero-sum game. Because the original formulation is not tractable enough, we further develop an approximating problem under the heavy-traffic assumption that effectively results in a stochastic differential game. The solution to this game then translates into an implementable control policy for the original make-to-order system. We supplement the proposed modeling paradigm with a simulation-based method for selecting an appropriate uncertainty set. Numerical experiments expose, among other things, the value of building robustness into decision making. This paper was accepted by Barış Ata, stochastic models and simulation. Funding: X. Zhu’s work is supported by the National Natural Science Foundation of China (NSFC) [Grants 72401124 and 72394363/72394360]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.01820 .