� 2008 INFORMS | isbn 978-1-877640-23-0 c INFORMS 2008 doi 10.1287/educ.1080.0046 Recent Developments in Modeling and Solving the Split Delivery Vehicle Routing Problem Damon J. Gulczynski Department of Mathematics, University of Maryland, College Park, Maryland 20742, damon@math.umd.edu Bruce Golden Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742, bgolden@rhsmith.umd.edu Edward Wasil Kogod School of Business, American University, Washington, D.C., 20016, ewasil@american.edu Abstract In the split delivery vehicle routing problem, a customer’s demand can be split among several vehicles. In the last five years or so, researchers have proposed exact and approximate solution methods, modeled variants with time windows and pickups, and developed large-scale benchmark problems. In this tutorial, we summarize the recent literature on the split delivery vehicle routing problem, describe solution procedures and results of computational experiments, and suggest directions for future research. Keywords vehicle routing problem; heuristics; mixed-integer program 1. Introduction In the standard version of the vehicle routing problem (VRP), vehicles with the same capac- ity based at a single depot service many customers. A customer’s demand is delivered in one visit by a single vehicle. We must find the minimal cost set of routes for the vehicles that start and end at the depot and do not violate vehicle capacity. The VRP has been studied for nearly 50 years. The book by Golden et al. [15] contains 25 papers that describe the latest applications, algorithms, and computational results. In the late 1980s, researchers considered the possibility of serving a customer by more than one vehicle to potentially reduce the total distance traveled by the fleet of vehicles. The split delivery vehicle routing problem (SDVRP) retains all features of the standard VRP but allows a customer’s demand to be split among several vehicles. In Figure 1, we give an example of the SDVRP with four customers (labeled 1, 2, 3, 4) and a single depot. Each customer has a demand of three units, each vehicle has a capacity of four units, and distances are shown adjacent to edges. In Figure 1(b), the optimal solution to the standard VRP with no split deliveries has one vehicle traveling directly out to each customer, delivering three units, and returning back to the depot for a total distance of 16. In Figure 1(c), split deliveries are allowed. Customers 2 and 3 are now serviced by two different vehicles and the total distance has been reduced to 15. In the last five years or so, research work on the SDVRP has increased significantly, so that there are currently more than a dozen articles in which the modeling and solving of the SDVRP and its variants (such as the SDVRP with time windows) are addressed. We believe that part of the renewed interest in the SDVRP is due to the increased costs (such as higher fuel and maintenance costs) associated with operating commercial fleets and the need for management to reduce these costs as much as possible. In addition, the availability of powerful metaheuristics has made this problem easier to study computationally. Our goal 170
Gulczynski et al.: Recent Developments in Modeling and Solving the SDVRP 171 Tutorials in Operations Research, c � 2008 INFORMS Figure 1. Splitting deliveries may reduce the distance traveled by a fleet. VRP SDVRP Total distance = 16 Total distance = 15 2 3 2 1 3 2 (2) (2) 3 (1) (1) 1 1 2 2 (3) (3) 2 1 4 1 4 1 4 2 2 2 2 Depot Depot Depot (a) (b) (c) Note. Customer demand is three units, vehicle capacity is four units, and edge labels are distances. in this tutorial is threefold: (1) summarize the open literature on the SDVRP, (2) provide details of solution procedures and report computational results on benchmark problems, and (3) suggest future research directions. 2. Summary of the Recent Literature The SDVRP was introduced by Dror and Trudeau [11] in 1989. For the next 15 years, there was a steady trickle of published papers, and their algorithmic accomplishments and applications have been described by Chen et al. [7] and Archetti and Speranza [1]. In this section, we summarize recent work on the SDVRP. We focus on the 15 papers given in Table 1 that model and solve the SDVRP and its variants from 2004 to 2008. Our summary of each paper will fall into one of three categories: (1) heuristics, (2) exact methods and bound-generating procedures, and (3) SDVRP variants. 2.1. Heuristics 2.1.1. Tabu Search. Archetti et al. [2] formulate a mixed-integer program (MIP) for the SDVRP in which the quantity delivered on a route cannot exceed a value k (they call this Table 1 . Summary of 15 papers that model and solve the SDVRP from 2004 to 2008. Authors Year Algorithm Variant Ho and Haugland [16] 2004 Tabu search Time windows Mitra [21] 2005 Cheapest-insertion Backhauls Archetti et al. [2] 2006 Tabu search Lee et al. [19] 2006 Dynamic program, shortest path Exact algorithm Boudia et al. [5] 2007 Memetic algorithm Chen et al. [7] 2007 MIP, record-to-record travel Jin et al. [17] 2007 LP with valid inequalities Exact algorithm Mitra [22] 2007 Cluster and route Backhauls Mota et al. [23] 2007 Scatter search Tavakkoli-Moghaddam et al. [28] 2007 Simulated annealing Heterogeneous fleet Thangiah et al. [29] 2007 First insertion, local search Real-time events Archetti et al. [3] 2008 IP route optimization Jin et al. [18] 2008 Column generation Bounds generation Liu et al. [20] 2008 Greedy heuristic, bin-packing Fixed route Nowak et al. [24] 2008 Local search, Clarke-Wright Pickups
Recommend
More recommend
