A bi-level programming framework for stochastic replenishment policy in a supply chain: approach and computational test

This paper considers a two-stage stochastic dynamic lot-sizing problem with transportation costs and service level constraints under a non-deterministic demand. Bi-level programming is used to solve the stochastic problem. The user can not understand the interactions among the decision variables and their influence on the objective function value by the methods in the history literature. Consequently, to effectively optimize the stochastic bi-level programming problem and to let the user understand the whole process, this paper proposes an integrated approach. This paper proposes a replenishment method based on modified ant colony optimization (ACO) and response surface methodology (RSM), RSM&ACO, which includes the optimization of a forecast model, and the replenishment quantity and cycle. A series of functions are used to test the quality of the solution of modified ACO algorithm. The numerical analysis shows that the placement function of the pheromone trail proposed in this paper helps improve the solution quality.