A stochastic dynamic programming based heuristic for the inventory decision-making encountered in a two-echelon warehouse system

The inventory control problem is a classic intelligent decision-making scenario. A good inventory policy can greatly improve the efficiency of supply chain and enhance the competitiveness of enterprises. This paper introduces an algorithm to compute the (R, s, S) policy parameters for a two-echelon warehouse non-stationary stochastic lot-sizing problem with backorder. The two-echelon warehouse system refers to a system where the warehouses are divided into business-oriented and customer-oriented two tiers, which are widely used in the real world but poorly studied in the literature. The businessoriented warehouse supplies both the business partners and the customer-oriented warehouse while the customer's demands are met only by the latter. The heuristic combines a backward stochastic dynamic programming and a greedy relaxation of the problem. A technique is proposed to convert customer-oriented sales into the replenishment demands for the businessoriented warehouse. The (R, s, S) policy parameters are then computed for product sales of the customer-oriented warehouse and total demand of the business-oriented warehouse. Moreover, we speed up the procedure by applying a convexity property and some techniques to avoid recomputation, which extends its adoptability to large-scale problems. The results show that the computational efforts remain acceptable as the problems’ sizes increase. Sensitivity analysis shows that the performance is less affected by parameter settings, which represents the stability of the algorithm.