A mathematical programming-based solution method for the nonstationary inventory problem under correlated demand

TL;DR

This paper introduces a mathematical programming approach to solve nonstationary inventory problems with correlated demand, relaxing independence assumptions and enabling efficient solutions with various demand models.

Contribution

It extends existing methods by incorporating demand correlation and multiple demand models into a mixed-integer linear programming framework.

Findings

The method achieves near-optimal solutions compared to stochastic dynamic programming.

It can handle demand modeled as multivariate normal, time-series, or Martingale processes.

The approach is compatible with off-the-shelf MILP solvers.

Abstract

This paper extends the single-item single-stocking location non-stationary stochastic inventory problem to relax the assumption of independent demand. We present a mathematical programming-based solution method that relaxes the assumption of demand independence between time periods in an existing piecewise linear approximation strategy under the receding horizon control framework. Our method can be solved via off-the-shelf mixed-integer linear programming solvers. It can tackle demand under various assumptions: the multivariate normal distribution, a collection of time-series processes, and the Martingale Model of Forecast Evolution. We compare against solutions via stochastic dynamic programming to demonstrate that our method leads to near-optimal solutions.