Computing optimal (R,s,S) policy parameters by a hybrid of branch-and-bound and stochastic dynamic programming

• DOI: 10.1016/j.ejor.2021.01.012
• Publication Date: 2021-01-13T19:56:11Z
• Authors: Andrea Visentin; Steven Prestwich; Roberto Rossi; S. Armagan Tarim
• Keywords: (R,s,S) policy; Inventory; Stochastic lot sizing; 02 engineering and technology; stochastic lot sizing; demand uncertainty; inventory; Demand uncertainty; Optimization and Control (math.OC); FOS: Mathematics; 0202 electrical engineering, electronic engineering, information engineering; Mathematics - Optimization and Control

A well-know control policy in stochastic inventory control is the (R, s, S) policy, in which inventory is raised to an order-up-to-level S at a review instant R whenever it falls below reorder-level s. To date, little or no work has been devoted to developing approaches for computing (R, s, S) policy parameters. In this work, we introduce a hybrid approach that exploits tree search to compute optimal replenishment cycles, and stochastic dynamic programming to compute (s, S) levels for a given cycle. Up to 99.8% of the search tree is pruned by a branch-and-bound technique with bounds generated by dynamic programming. A numerical study shows that the method can solve instances of realistic size in a reasonable time.