Stochastic versus Robust Optimization for a Transportation Problem

In this paper we consider a transportation problem under uncertainty related to gypsum replenishment for a cement producer. The problem is to determine the number of vehicles to book at the beginning of each week to replenish gypsum at all the cement factories of the producer in order to minimize the total cost, given by the sum of the transportation costs and buying cost from external sources in extreme situations. Two sources of uncertainty are considered: the demand of gypsum at cement factories of the producer and the buying costs from external sources. We solve the problem both via a two-stage stochastic programming and different robust optimization models. The proposed robust formulations have the advantage to be solvable in polynomial time and to have theoretical guarantees for the quality of their solutions, which is not the case for the stochastic formulation. Numerical experiments show that the robust approach results in larger objective function values than the stochastic approach due to the certitude of constraints satisfaction and more conservative decision strategies on the number of booked vehicles. Conversely, the computational complexity is higher for the stochastic approach.


Submission date: November 15, 2014



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