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In this paper we analyze the effect of two modelling approaches for supplyplanning problems under uncertainty: two-stage stochastic programming (SP) androbust optimization (RO). The comparison between the two approaches isperformed through a scenario-based framework methodology, which can be appliedto any optimization problem affected by uncertainty. For SP we compute theminimum expected cost based on the specific probability distribution of theuncertain parameters related to a set of scenarios. For RO we consider staticapproaches where random parameters belong to box or ellipsoidal uncertaintysets in compliance with the data used to generate SP scenarios. Dynamicapproaches for RO, via the concept of adjustable robust counterpart, are alsoconsidered. The efficiency of the methodology has been illustrated for a supplyplanning problem to optimize vehicle-renting and procurement transportationactivities involving uncertainty on demands and on buying costs forextra-vehicles. Numerical experiments through the scenario-based frameworkallow a fair comparison in real case instances. Advantages and disadvantages ofRO and SP are discussed.

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