Pickup and delivery network segmentation using contiguous geographic clustering

• Published in: The Journal of the Operational Research Society Vol. 62; no. 10; pp. 1827 - 1843
• Main Authors: Jarrah, A I, Bard, J F
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 01-10-2011; Palgrave Macmillan; Palgrave Macmillan UK; Taylor & Francis Ltd
• Series: Journal of the Operational Research Society
• Subjects: Aggregation; Algorithms; Applied sciences; Aspect ratio; Business and Management; Case-Oriented Paper; Case-Oriented Papers; Clustering; Customer services; Exact sciences and technology; Flows in networks. Combinatorial problems; Fuzzy sets; Geodetic position; Geographic regions; heuristic column generation; Heuristics; Integers; Logistics; Management; Mathematical programming; Operational research and scientific management; Operational research. Management science; Operations research; Operations Research/Decision Theory; pickup and delivery operations; Quadrants; Rectangles; Studies; Transportation problem (Operations research); Vehicles; clustering; aggregation; heuristic column generation; pickup and delivery operations; Averaging method; Segmentation; Transit time; Modeling; Adaptive method; Aggregation; Column generation; Uncertain system; Partitioning; User service; Classification; Pricing; Set covering; Travel time; Balancing; Fleet; Probabilistic approach; Compact space; Cluster; Linear programming; Supply demand balance; Seed; Heuristic method; Reverse logistics; Capacity constraint
• ISSN: 0160-5682; 1476-9360
• DOI: 10.1057/jors.2010.123

This paper addresses the problem of partitioning a local service region into nonoverlapping work areas in which pickups and deliveries are made throughout the day. For a fleet of homogeneous vehicles, a given set of customers, and expected demand for service, the objective is to find the least number of work areas or clusters that satisfy a variety of geometric and capacity constraints. Using rectangles as the basic shape, each cluster must have an aspect ratio that falls within certain bounds, as well as meet load and time requirements dictated by the capacity of a vehicle and the working hours in a day, respectively. The latter requirement presents a unique hurdle because travel times are a function of the actual routes followed by the drivers, and are not known, even in a probabilistic sense, until the clusters are formed. A novel aspect of the paper is the method proposed for dealing with this uncertainty. The problem is modelled using a compact set-covering formulation and is solved with an adaptive column generation heuristic. Because it is not possible to efficiently represent all the constraints in algebraic form, thus allowing a Dantzig-Wolfe decomposition, a constructive approach was taken. The first step involved generating a subset of attractive clusters from seed customers scattered throughout the service region and then iteratively pricing them out to obtain a relaxed solution to the set-covering model. To find integer solutions, a three-phase variable fixing scheme was designed with the aim of balancing solution quality with runtimes. The full methodology was tested on six data sets provided by an internationally known express package carrier. The results showed that vehicle reductions averaging 7.6% could be realized by adopting the configurations derived from the proposed approach.