Multi-product inventory planning with downward substitution, stochastic demand and setup costs

In this paper we consider a single period multi-product inventory problem with stochastic demand, setup cost for production, and one-way product substitution in the downward direction. We model the problem as a two-stage integer stochastic program with recourse where the first stage variables determine which products to produce and how much to produce, and the second stage variables determine how the products are allocated to satisfy the realized demand. We exploit structural properties of the model and utilize a combination of optimization techniques including network flow, dynamic programming, and simulation-based optimization to develop effective heuristics. Through a computational study, we evaluate the performance of our heuristics by comparison with the corresponding optimal solution obtained from a large scale mixed integer linear program. The computational study indicates that our solution methodology can be very effective ( 98.8% on average) and can handle industrial-sized problems efficiently. We also provide several new qualitative insights on issues such as the effect of demand variance and cost parameters on the optimal number of products setup, the amount produced or inventoried, and the benefits of allowing substitution.