Multidepot Vehicle Routing with Uncertain Demands: Chance Constrained Approach

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Abstract
Distribution system design is a relevant problem that has been widely studied by researchers and practitioners in logistics and supply chain management. A stochastic programming model used to design part of the distribution system of a firm with multiple depots that face stochastic demands is presented. It is assumed that there is a fixed set of depots that serve a fixed set of customers with uncertain demands. The problem consists of finding the number of vehicles and assigning customers to capacitated vehicle routes such that the total system cost is minimum. The vehicle capacity is treated stochastically through chance constraint programming, in which the model finds a solution that presents a probability of exceeding capacity constraints lower than a fixed probability. The customers are characterized by the means and variances of their demands. The problem is modeled on the basis of a hub-and-spokes network topology, in contrast to the standard objective function of the vehicle routing problem. This modeling is considered to be included in a strategic distribution network design problem, which is typically solved by using facility location problems. Unlike previous work found in the literature, this approach simultaneously considers multiple depots and stochastic constraints. A heuristic procedure is presented along with an algorithm to find the objective function's lower bound, which allows the computation of an upper bound of the error of the heuristic solutions.

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