A Coordinated Non-Stationary Stochastic Lot-Sizing and Location Problem with Joint Replenishment

Firms increasingly coordinate lot-sizing, distribution center (DC) location, and joint replenishment over time to reduce costs. This paper studies this integrated problem under the (R, S) policy with demand, which stochasticity varies from period to period. We build a model where only the timing of replenishment is the core decision; all else follows from it. To solve efficiently, we design a hybrid differential evolution algorithm with a random neighborhood search. Experiments show our algorithm outperforms eight benchmark methods in solution quality and speed. A sensitivity analysis reveals how key parameters affect the total cost, replenishment frequency, and the number of DCs. Higher ordering costs reduce replenishment frequency, and larger DC setup costs lead to fewer DCs. However, fewer DCs do not always lower the total cost—when dealers are geographically dispersed, more DCs can reduce the overall total system cost. These insights help managers balance the cost components in a supply chain network design.