Mathematical programming heuristics for nonstationary stochastic inventory control

Abstract

This work focuses on the computation of near-optimal inventory policies for a wide range of problems in the field of nonstationary stochastic inventory control. These problems are modelled and solved by leveraging novel mathematical programming models built upon the application of stochastic programming bounding techniques: Jensen's lower bound and Edmundson-Madanski upper bound. The single-item single-stock location inventory problem under the classical assumption of independent demand is a long-standing problem in the literature of stochastic inventory control. The first contribution hereby presented is the development of the first mathematical programming based model for computing near-optimal inventory policy parameters for this problem; the model is then paired with a binary search procedure to tackle large-scale problems. The second contribution is to relax the independence assumption and investigate the case in which demand in different periods is correlated. More specifically, this work introduces the first stochastic programming model that captures Bookbinder and Tan's static-dynamic uncertainty control policy under nonstationary correlated demand; in addition, it discusses a mathematical programming heuristic that computes near-optimal policy parameters under normally distributed demand featuring correlation, as well as under a collection of time-series-based demand process. Finally, the third contribution is to consider a multi-item stochastic inventory system subject to joint replenishment costs. This work presents the first mathematical programming heuristic for determining near-optimal inventory policy parameters for this system. This model comes with the advantage of tackling nonstationary demand, a variant which has not been previously explored in the literature. Unlike other existing approaches in the literature, these mathematical programming models can be easily implemented and solved by using off-the-shelf mathematical programming packages, such as IBM ILOG optimisation studio and XPRESS Optimizer; and do not require tedious computer coding. Extensive computational studies demonstrate that these new models are competitive in terms of cost performance: in the case of independent demand, they provide the best optimality gap in the literature; in the case of correlated demand, they yield tight optimality gap; in the case of nonstationary joint replenishment problem, they are competitive with state-of-the-art approaches in the literature and come with the advantage of being able to tackle nonstationary problems.