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

Abstract

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 due to 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 while 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.

Keywords: make-to-order manufacturing, robust control, heavy-traffic approximation, stochastic differential games