Robust Capacitated Vehicle Routing Problem with Uncertain Demands

Abstract

This thesis addresses the Static and Stochastic Capacitated Vehicle Routing Problem with Stochastic Demands (SSCVRPSD). In this problem, an initial a priori route plan is designed. During plan execution, corrective actions are applied as each demand is revealed, if the real total demand of a route exceeds the vehicle capacity. The goal is to calculate a robust a-priori route plan that will only undergo small changes when the true demands are revealed during its implementation. For that, we propose a mathematical formulation based on a Mean Absolute Deviation (MAD) objective function. This objective function combines two conflicting objectives, minimization of the expected planned transportation cost (optimality) and minimization of the mean absolute deviation of the second-stage transportation cost (robustness). In the MAD model, the variability term is multiplied by a parameter of decision-maker's choice A , used to obtain a spectrum of route plans that can be more or less robust. In this manner, the proposed formulation delivers flexibility to the decision-maker to define desired safety levels and allows to trade off cost minimization and protection.