The continuous delayed distribution problem

Nowadays, decision makers (DMs) at companies have access to extensive and accurate data, which means they have the opportunity to grow and improve if they use the latent potential effectively. We address the complex problem of optimizing decisions in a multi-period one-warehouse multi-retailer inventory system with stochastic continuous demand and an option of delayed distributions. At the beginning of each period, the DM determines each retailer's target stock levels, as well as the number of items to be held back at a central location for later distribution(s). Such a policy offers partial inventory pooling through the holdback quantity. The decisions in each period are data-driven, i.e., made based on sales data available through an information system up to that point in time. We model the problem as a multi-stage stochastic program with recourse. For the general case, we develop a new recursive solution algorithm, which is based on subgradient optimization and an analysis of system dynamics. For the special case of two identical retailers and two periods, we provide explicit optimality conditions based on the subgradients. Using a large numerical study, we evaluate the performance of our proposed policy and compare it to two benchmark policies. We also demonstrate the impact of various problem parameters on the optimal solution and objective value.