Inventory systems with stochastic and batch demand: computational approaches

Abstract

Modeling the behavior of customer demand is a key challenge in inventory control, where an accurate characterization of the demand process often involves accounting for a wide range of statistical descriptors. This motivates the use of Markovian processes, due to their proven versatility in matching key components of point processes, to capture the behavior of customer demand. Accordingly, this work presents computational frameworks for continuous inventory models with a batch Markovian demand. A Markovian formulation of the system state-space is presented along with computational approaches to obtain key inventory performance measures. Compact matrix representations are considered for the steady-state solution of the system performance measures. The transient and non-stationary behavior of the inventory system is calculated by numerically integrating the corresponding set of Kolmogorov forward equations. A byproduct of this work is explicitly expressing the solution of the moments of the batch Markovian counting process by a compact matrix exponential equation. Numerical examples illustrate the computational efficiency of the mathematical frameworks when evaluating and comparing the performance of different re-ordering policies. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.