A Robust Production Control Policy for Hedging Against Inventory Inaccuracy in a Multiple-Stage Production System With Time Delay

Inventory inaccuracy has significant negative impact on the performance of production control. In this paper, we investigate the robust production control problem for a multiple-stage production system with inventory inaccuracy and time delay between stages. The objective of this problem is to minimize the average production cost. The problem is solved in two steps. First, an approximate optimal production control policy is developed for a multiple-stage production system with time delay but without inventory inaccuracy. Second, we reveal that the discontinuity of the controls makes the policy sensitive to the error of inventory data, and then propose a robust production control policy to eliminate this sensitivity, in which the control variables change smoothly when state variables cross boundaries between different domains in the state space. We also prove that the robustness of the proposed robust policy is better than that of the approximate optimal policy. Finally, numerical experiments are conducted to examine the performance of the proposed robust policy for hedging against inventory inaccuracy.