A unified modeling approach for the static-dynamic uncertainty strategy in stochastic lot-sizing

TL;DR

This paper introduces mixed integer linear programming models for the non-stationary stochastic lot sizing problem under the static-dynamic uncertainty strategy, providing accurate cost estimates and adaptable formulations.

Contribution

It develops a unified modeling framework using piecewise linear bounds, enabling flexible and accurate solutions for various stochastic lot sizing variants.

Findings

Models produce tight upper and lower bounds on expected total costs.

Framework effectively handles different service level measures.

Computational results demonstrate high accuracy and flexibility.

Abstract

In this paper, we develop mixed integer linear programming models to compute near-optimal policy parameters for the non-stationary stochastic lot sizing problem under Bookbinder and Tan's static-dynamic uncertainty strategy. Our models build on piecewise linear upper and lower bounds of the first order loss function. We discuss different formulations of the stochastic lot sizing problem, in which the quality of service is captured by means of backorder penalty costs, non-stockout probability, or fill rate constraints. These models can be easily adapted to operate in settings in which unmet demand is backordered or lost. The proposed approach has a number of advantages with respect to existing methods in the literature: it enables seamless modelling of different variants of the above problem, which have been previously tackled via ad-hoc solution methods; and it produces an accurate estimation of the expected total cost, expressed in terms of upper and lower bounds. Our computational study demonstrates the effectiveness and flexibility of our models.