The commodity-split multi-compartment capacitated arc routing problem

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.</p

The commodity-split multi-compartment capacitated arc routing problem

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.</p

A heuristic with a performance guarantee for the Commodity constrained Split Delivery Vehicle Routing Problem

The Commodity constrained Split Delivery Vehicle Routing Problem (C-SDVRP) is a routing problem where customer demands are composed of multiple commodities. A fleet of capacitated vehicles must serve customer demands in a way that minimizes the total routing costs. Vehicles can transport any set of commodities and customers are allowed to be visited multiple times. However, the demand for a single commodity must be delivered by one vehicle only. In this work, we developed a heuristic with a performance guarantee to solve the C-SDVRP. The proposed heuristic is based on a set covering formulation, where the exponentially-many variables correspond to routes. First, a subset of the variables is obtained by solving the linear relaxation of the formulation by means of a column generation approach which embeds a new pricing heuristic aimed to reduce the computational time. Solving the linear relaxation gives a valid lower bound used as a performance guarantee for the heuristic. Then, we devise a restricted master heuristic to provide good upper bounds: the formulation is restricted to the subset of variables found so far and solved as an integer program with a commercial solver. A local search based on a mathematical programming operator is applied to improve the solution. We test the heuristic algorithm on benchmark instances from the literature. Several new (best-known) solutions are found in reasonable computational time. The comparison with the state of the art heuristics for solving C-SDVRP shows that our approach significantly improves the solution time, while keeping a comparable solution quality

Freight Operations Modelling for Urban Delivery and Pickup with Flexible Routing: Cluster Transport Modelling Incorporating Discrete-Event Simulation and GIS

Urban pickup and delivery (PUD) activities are important for logistics operations. Real operations for general freight involve a high degree of complexity due to daily variability. Discrete-event simulation (DES) is a method that can mimic real operations and include stochastic parameters. However, realistic vehicle routing is difficult to build in DES models. The objective is to create a DES model for realistic freight routing, which considers the driver’s routing decisions. Realistic models need to predict the delivery route (including time and distance) for variable consignment address and backhaul pickup. Geographic information systems (GIS) and DES were combined to develop freight PUD models. GIS was used to process geographical data. Two DES models were developed and compared. The first was a simple suburb model, and the second an intersection-based model. Real industrial data were applied including one-year consignment data and global positioning system (GPS) data. A case study of one delivery tour is shown, with results validated with actual GPS data. The DES results were also compared with conventional GIS models. The result shows the intersection-based model is adequate to mimic actual PUD routing. This work provides a method for combining GIS and DES to build freight operation models for urban PUD. This has the potential to help industry logistics practitioners better understand their current operations and experiment with different scenarios