A scenario-based framework for supply planning under uncertainty: stochastic programming versus robust optimization approaches

TL;DR

This paper compares two modeling approaches, stochastic programming and robust optimization, for supply planning under uncertainty using a scenario-based framework, highlighting their relative advantages and limitations through real case experiments.

Contribution

It introduces a scenario-based framework for comparing stochastic programming and robust optimization in supply planning problems under uncertainty.

Findings

Scenario-based framework enables fair comparison of SP and RO.

RO is more conservative, providing solutions with less risk.

SP yields lower expected costs but is sensitive to probability assumptions.

Abstract

In this paper we analyze the effect of two modelling approaches for supply planning problems under uncertainty: two-stage stochastic programming (SP) and robust optimization (RO). The comparison between the two approaches is performed through a scenario-based framework methodology, which can be applied to any optimization problem affected by uncertainty. For SP we compute the minimum expected cost based on the specific probability distribution of the uncertain parameters related to a set of scenarios. For RO we consider static approaches where random parameters belong to box or ellipsoidal uncertainty sets in compliance with the data used to generate SP scenarios. Dynamic approaches for RO, via the concept of adjustable robust counterpart, are also considered. The efficiency of the methodology has been illustrated for a supply planning problem to optimize vehicle-renting and procurement transportation activities involving uncertainty on demands and on buying costs for extra-vehicles. Numerical experiments through the scenario-based framework allow a fair comparison in real case instances. Advantages and disadvantages of RO and SP are discussed.