An aggregation-based approximate dynamic programming approach for the periodic review model with random yield

A manufacturer places orders periodically for products that are shipped from a supplier. During transit, orders get damaged with some probability, that is, the order is subject to random yield. The manufacturer has the option to track orders to receive information on damages and to potentially place additional orders. Without tracking, the manufacturer identifies potential damages after the order has arrived. With tracking, the manufacturer is informed about the damage when it occurs and can respond to this information. We model the problem as a dynamic program with stochastic demand, tracking cost, and random yield. For small problem sizes, we provide an adjusted value iteration algorithm that finds the optimal solution. For moderate problem sizes, we propose a novel aggregation-based approximate dynamic programming (ADP) algorithm and provide solutions for instances for which it is not possible to obtain optimal solutions. For large problem sizes, we develop a heuristic that takes tracking costs into account. In a computational study, we analyze the performance of our approaches. We observe that our ADP algorithm achieves savings of up to 16% compared to existing heuristics. Our heuristic outperforms existing ones by up to 8.1%. We show that dynamic tracking reduces costs compared to tracking always or never and identify savings of up to 3.2%.