A hybrid differential evolution algorithm for a stochastic location-inventory-delivery problem with joint replenishment

A practical stochastic location-inventory-delivery problem with multi-item joint replenishment is studied. Unlike the conventional location-inventory model with a continuous-review (r, Q) inventory policy, the periodic-review inventory policy is adopted with multi-item joint replenishment under stochastic demand, and the coordinated delivery cost is considered. The proposed model considers the integrated optimization of strategic, tactical, and operational decisions by simultaneously determining (a) the number and location of distribution centers (DCs) to be opened, (b) the assignment of retailers to DCs, (c) the frequency and cycle interval of replenishment and delivery, and (d) the safety stock level for each item. An intelligent algorithm based on particle swarm optimization (PSO) and adaptive differential evolution (ADE) is proposed to address this complex problem. Numerical experiments verified the effectiveness of the proposed two-stage PSO-ADE algorithm. A sensitivity analysis is presented to reveal interesting insights that can guide managers in making reasonable decisions.