A Robust Replenishment and Production Control Policy for a Single-Stage Production/Inventory System with Inventory Inaccuracy

Inaccurate inventory data are often found in production/inventory systems, and have a significant negative impact on the performance of raw materials replenishment and production control. In this paper, robust replenishment and production control problem for a single-stage production/inventory system with inventory inaccuracy is investigated, with the objective of minimizing the average inventory and production cost. In addition to the inventory inaccuracy, the lead-time of raw materials ordering and machine unreliability are also taken into consideration. The problem is solved in two steps. First, for a single-stage production/inventory system with ordering lead-time and uncertain production capacity, but without inventory inaccuracy, an approximate optimal replenishment, and production control policy is constructed. Second, we reveal that it is the discontinuity of the control variables in different domains of the state space that makes the policy sensitive to inventory data error. Consequently, we develop a robust replenishment and production control policy to eliminate this sensitivity. This approach maintains the structural characteristics of the optimal policy, but allows the control variables to change smoothly when the state variables cross boundaries between different domains in the state space. Numerical experiments are conducted to examine the performance of the proposed robust policy for hedging against inventory inaccuracy, and a sensitivity analysis is used to study how the parameters of the production/inventory system and the robust policy impact on the average inventory and production cost.