Optimal outbound shipment policy for an inventory system with advance demand information

Abstract

This paper examines a single-echelon inventory system that fulfills stochastic orders from a production facility using a time-based shipment consolidation strategy. In this system, the production facility provides advance demand information to the warehouse, ensuring that all orders are placed with a positive demand lead time. Using value iteration, we identify the optimal outbound shipment quantities while accounting for costs related to early deliveries, late deliveries, and shipments. Additionally, this research highlights the impact of advance demand information on transportation capacity planning and the optimization of load factors

The results from value iteration enable us to observe the general structure of the optimal dispatch policy, and we determine that it is a multidimensional threshold policy. Based on this observation, we introduce an approximated three-level threshold policy with acceptable performance. Furthermore, the decision itself is easier to interpret and to explain. To analyze large-scale instances, we compare several heuristic policies. First, we develop a deep reinforcement learning algorithm that approximates the value of the post-decision state instead of the pre-decision state. We compare our approach to value iteration and find that our method works very well; the average optimality gap is 0.08%. Additionally, three simple heuristic policies are proposed that might be justifiable in specific situations.

Finally, we find that the value of advance demand information does not follow a linear pattern but decreases as the demand lead time increases. Furthermore, the transportation capacity should be planned in the range of the mean demand between two shipments.