A Simulated Annealing Heuristic for the Heterogeneous Fleet Pollution Routing Problem

Abstract

Public consciousness on environmental sustainability and industry impact on environment has been increasing for the last few decades. As a result, more and more companies are taking pollution factor into account when planning their logistic activities. Pollution Routing Problem (PRP) is an extension of the classical Vehicle Routing Problem with Time Windows by determining a set of optimal routes and vehicle speed on each route segment for a fleet of vehicles serving a set of customers within specific time windows. In practice, many vehicle routing problems are addressed by a fleet of heterogeneous vehicles with different capacities and travel costs. Emission levels vary by vehicle type due to differences in curb weight and capacity. Therefore, Heterogeneous Fleet Pollution Routing Problem (HFPRP) has been proposed as an extension of Pollution Routing Problem (PRP). Its goal is to minimize the total costs of fuel, greenhouse gas (GHG) emissions, and vehicle variable cost put together in a more comprehensive objective function. This research developed a mathematical model and proposed a Simulated Annealing (SA) heuristic for HFPRP. The performance of the proposed SA heuristic was first verified using benchmark data of the Pollution Routing Problem. The result shows that SA performs better for 7 instances than previous method. SA was then used to solve HFPRP and the results were compared to those obtained by CPLEX. We found that the consideration of a heterogeneous fleet reduces total costs for all instances.