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

Highlights

• We consider the inventory control problem under stochastic non-stationary demand.

• We introduce a new algorithm to compute optimal (R, s, S) policy parameters.

• The algorithm is a hybridisation of branch-and-bound and dynamic programming.

• The computational results prove the performance of our method.

Abstract

A well-known 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.