The non-stationary stochastic lot-sizing with joint replenishment under (R, S) policy and the heuristic

This study investigates for the first time the non-stationary stochastic lot-sizing problem involving multi-dealer joint replenishment under the policy (R, S) without fill rate constraints. The planning horizon for each dealer is divided into the replenishment cycle series, accounting for the lead time associated with each joint replenishment cycle. A shortest path model is developed. Through mathematical analysis, the safety stock variables are eliminated, and the multiple variables are reduced to replenishment variables only. The stochastic problem is converted to the deterministic dynamic lot-sizing through expectation analysis. Furthermore, the MLS-MRS heuristic is proposed based on Robinson's Left-Right shift (LS-RS) heuristic by adding a module, the positive cost-saving family shifts. This algorithm improves the optimal solution and notably greatly increases the search speed.