Our joint paper with Said Dabia and Emrah Demir, “An Exact Approach for a Variant of the Pollution-Routing Problem” is accepted in Transportation Science!
The Pollution-Routing Problem (PRP) is a recently introduced green 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. Due to 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. Specifically, computational results are reported for a new set of instances with up to 100 customers obtained by modifying Solomon’s instances, and for small instances with up to 20 customers taken from the PRPLIB. While some instances with up to 100 customers can be solved to optimality, several instances with only 25 customers remain unsolved.
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