  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.
