Stochastic Dynamic Programming Heuristic for the (R, s, S) Policy Parameters Computation

TL;DR

This paper presents a fast, heuristic stochastic dynamic programming method for computing (R, s, S) inventory policy parameters in non-stationary, backlogged demand scenarios, improving computational efficiency over existing approaches.

Contribution

It introduces a novel SDP-based heuristic that combines greedy relaxation and K-convexity to efficiently determine policy parameters, extending practical applicability.

Findings

The proposed method significantly reduces computation time.

It achieves comparable or better policy quality than existing algorithms.

The approach is validated through extensive computational experiments.

Abstract

The (R, s, S) is a stochastic inventory control policy widely used by practitioners. In an inventory system managed according to this policy, the inventory is reviewed at instant R; if the observed inventory position is lower than the reorder level s an order is placed. The order's quantity is set to raise the inventory position to the order-up-to-level S. This paper introduces a new stochastic dynamic program (SDP) based heuristic to compute the (R, s, S) policy parameters for the non-stationary stochastic lot-sizing problem with backlogging of the excessive demand, fixed order and review costs, and linear holding and penalty costs. In a recent work, Visentin et al. (2021) present an approach to compute optimal policy parameters under these assumptions. Our model combines a greedy relaxation of the problem with a modified version of Scarf's (s, S) SDP. A simple implementation of the model requires a prohibitive computational effort to compute the parameters. However, we can speed up the computations by using K-convexity property and memorisation techniques. The resulting algorithm is considerably faster than the state-of-the-art, extending its adoptability by practitioners. An extensive computational study compares our approach with the algorithms available in the literature.