A novel mathematical model for a discrete speed pollution routing problem with time windows in a Colombian context

Pollution affects globally, contributing to its reduction is a challenge. The Pollution Routing Problem (PRP) consists of a multi-objective problem that considers the minimization of transport costs and the reduction of polluting emissions. It is a generalization of the classic vehicle routing problem (VRP). It gets involved an additional level of decision making since the generation of pollutants is linked to the speed that vehicles use. Other generalizations of VRP consider time windows, in which each customer is associated with a time interval that determines their availability to receive the product. This paper addresses the integration of these problems in the so-called Discrete Speed Pollution Routing Problem with Time Windows (DSPRPTW). A novel model of linear integer-mixed programming is proposed. It considers inclination of the roads, three discrete speeds between each pair of nodes, the generation of pollutants, homogeneous fleet and the cost of transport in the Colombian context. Finally, a validation of the model is made using the CPLEX solver in 160 instances adapted from the literature, optimally solving 38.1% of them in less than 5 minutes.