An Exact Approach for a Variant of the Pollution-Routing Problem

Abstract

The pollution-routing problem (PRP) is a recently introduced green vehicle routing problem in the field of green logistics. It concerns routing a number of vehicles to serve a set of geographically dispersed customers within their time windows, jointly with determining their speed on each arc so as to minimize fuel and driving costs. Because of its complexity, all known solution methods are based on (meta-)heuristics. This paper presents an exact solution based on a branch-and-price algorithm for a variant of the PRP. The master problem is a set-partitioning problem, and the pricing problem is a speed- and start-time elementary shortest path problem with resource constraints, in which the speed and start time at the depot needs to be decided on for each individual route. The master problem is solved by means of column generation, and a tailored labeling algorithm is used to solve the pricing problem. New dominance criteria are developed to discard unpromising labels by exploiting the structure of the ready time and the fuel consumption functions. Extensive computational experiments show the value of the proposed algorithm.

Sustainable Transportation and Smart Logistics

“…They also develop a set of valid inequalities. Dabia et al (2017) describe a branch-and-price algorithm to solve a variant of the PRP where the speed along all arcs of a given route is assumed to be constant. In the algorithm, the master problem is of a set-partitioning type, and where the pricing is performed through solving a speed and start-time elementary shortest path problem with resource constraints using a tailored labeling algorithm.…”

“…Transportation Research Part C: Emerging Technologies 14 (6), 369e383. Eshtehadi, R., Fathian, M., Demir, E., 2017…”

A Joint Vehicle Routing and Speed Optimization Problem

“…Motivated by the integrated models in maritime transportation and the PRP, we propose the JRSP with general strictly convex cost functions, accommodating many fuel consumption and emission models (Hickman et al 1999, Barth et al 2000, Notteboom and Vernimmen 2009, Fagerholt et al 2010, Psaraftis and Kontovas 2013. Two algorithmic results closely related to our work are Dabia et al (2016) and Fukasawa et al (2016b). In Dabia et al (2016), a branchand-price algorithm is developed for a variant of the PRP which assumes that the speed must be constant throughout every arc of a given route.…”

A two‐phase Pareto local search heuristic for the bi‐objective pollution‐routing problem

“…Most of the methods adopted to solve these problems are based on heuristics. Concerning the exact approaches, one can cite the column generation‐based algorithms proposed by Fukasawa et al , Fukasawa et al , and Dabia et al , and the disjunctive convex programming models by Fukasawa et al . The interested reader is referred to the surveys of Demir et al and Lin et al for a more complete analysis of the state‐of‐the‐art on VRPs with environmental considerations.…”