Periodic-review inventory systems with random yield and demand: Bounds and heuristics

We revisit the infinite-horizon decision problem of a single-stage single-item periodic-review inventory system under uncertain yield and demand. It is known that under some mild conditions the optimal replenishment policy is of the threshold type: an order is placed if and only if the starting inventory is below a threshold value. Although the structure of the optimal policy is well known, there has been little discussion about the optimal order quantities and the order threshold. In this paper, we construct upper and lower bounds for the optimal threshold value and the optimal order quantities through solving one-period problems with different cost parameters. These bounds provide interesting insights into the impact of yield uncertainty on the optimal policy. Heuristics are developed based on these bounds. Detailed computational studies show that, under some conditions, the performance of the heuristics is very close to that of the optimal solution and better than that of existing heuristics in the literature.