A Chance‐Constrained Model for a Production Routing Problem With Uncertain Availability of Vehicles

ABSTRACT

The Production Routing Problem (PRP) is a complex integrated problem that allows for the achievement of competitive advantages, such as better management of inventory, reduction in operational costs and lead times, improvement in efficiency and customer service, and better response to market changes. Most of the literature on PRP considers only deterministic data, and the papers that take stochastic parameters into account focus mainly on uncertain demand. In this study, we consider a PRP with a single capacitated production facility, a single product type, and a homogeneous fleet of capacitated vehicles. The availability of these vehicles is assumed uncertain and formulated as a stochastic parameter. The problem is modeled using two types of chance constraints, and the sample approximation approach method is used to linearize the formulations, which are then solved using Benders decomposition (BD) and partial BD (PBD). Results show that PBD outperforms the standard BD method, and it is able to produce good optimality gaps for most instances within two hours of CPU time. In the remaining experiments, which are performed using PBD, results show that the problem becomes significantly more difficult to solve as the number of periods and retailers increase. Moreover, one of the mathematical formulations allows more flexibility to decision makers, resulting in higher feasibility and smaller costs.