The commodity-split multi-compartment capacitated arc routing problem

Abstract

The purpose of this paper is to develop a data-driven matheuristic for the Commodity-Split Multi-Compartment Capacitated Arc Routing Problem (CSMC-CARP). This problem arises in curbside waste collection, where there are different recyclable waste types called fractions. The CSMC-CARP is defined on an undirected graph with a limited heterogeneous fleet of multi-compartment vehicle types based at a depot, where each compartment’s capacity can vary depending on the waste fraction assigned to it and on the compression factor of that fraction in that vehicle type. The aim is to determine a set of least-cost routes starting and ending at the depot, such that the demand of each edge for each waste fraction is collected exactly once by one vehicle, without violating the capacity of any compartment. The CSMC-CARP consists of three decision levels: selecting the number of vehicles of each type, assigning waste fractions to the compartments of each selected vehicle, and routing the vehicles. Our three-phase algorithm decomposes the problem into incomplete solution representations and heuristically solves one or more decision levels at a time. The first phase selects a subset of attractive compartment assignments from all assignments of all vehicle types. The second phase solves the CSMC-CARP with an unlimited fleet of the selected assignments. This is done by our C-split tour splitting algorithm, which can simultaneously split a giant tour of required edges into feasible routes while making decisions on the fractions that are collected by each route. The third phase selects the set of best routes servicing all fractions of all required edges without exceeding the number of vehicles available of each type. The algorithm is applied to real-life instances arising from recyclable waste collection operations in Denmark, with graph sizes up to 6,149 nodes and 3,797 required edges, the waste sorted in three to six fractions, and four to six vehicle types with one to four compartments. Computational results show that the generated solutions favor combining different fractions together in vehicles with higher numbers of compartments, and that the algorithm adapts well to the characteristics of the data, in terms of the graph, vehicle types, degree of sorting, and to skewness in demand among waste fractions.