Dynamic Substitution for Selling Multiple Products under Supply and Demand Uncertainties

Abstract

Substitution is a commonly adopted strategy to match the demand mix by remixing the supplies. The recent development of information technology has allowed firms to easily swap products to meet the consumers' preference. When formulating the substitution policies, firms have to take into account the supply and demand conditions, as well as the cost and benefit of substitution. We formulate a dynamic model, in which the firm replenishes product inventories from uncertain sources and dynamically allocates available products to meet the uncertain demands with the flexibility of substitution. To address the analytical challenge associated with multi-product management, we develop an approximation algorithm that leverages the value of substitution, while allowing separability of the future profit among the products. This approximation algorithm iteratively solves a transportation problem in a network with the Monge property. The application of the Monge property allows for dealing with general substitution structures, which generalizes the commonly studied downward substitution models. Through extensive numerical analysis, we demonstrate that our approximation yields good performance measured by the percentage profit gap against an upper bound problem. We also show that substitution can generate significant benefit when the supply capacities are moderate, the supply and demand uncertainties are high, or the replenishment cycle is short.

Keywords: Dynamic Substitution, Multi-Product Inventory Allocation, Monge Property, Stochastic Linearity