Chapter 1: The Family of Vehicle Routing Problems

Abstract

A generic verbal definition of the family of vehicle routing problems can be the following:Given: A set of transportation requests and a fleet of vehicles.The problem is then to find a plan for the following:Task: Determine a set of vehicle routes to perform all (or some) transportation requests with the given vehicle fleet at minimum cost; in particular, decide which vehicle handles which requests in which sequence so that all vehicle routes can be feasibly executed.In this type of problem, subsumed under the term Vehicle Routing Problem (VRP), the transportation requests to be served are generally concentrated in specific points of a road network as opposed to the Arc Routing Problems (ARP; see the companion book by Corberán and Laporte [35]), where the requests are dispersed along the arcs, i.e., street segments of the underlying road network. The following sections will shed light on the basic VRP components, which are the transportation requests and how they can be performed, the fleet of vehicles, the related costs and profits (if relevant), and the feasibility of routes.Before going into the details, however, we discuss the economic relevance of computersupported vehicle routing. Indeed, the large number of real-world applications have widely shown that the use of computerized solution methods for the solution of VRP, both at the planning and the operational levels, yields substantial savings in the global transportation costs. The success of the utilization of optimization techniques is due not only to the power of the current computer systems and to the full integration of the information systems into the operations and commercial processes, but it can also be attributed to the development of rigorous mathematical models, which are able to take into account al-1 Downloaded 12/15/14 to 132.236.27.111. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php 2 Chapter 1. The Family of Vehicle Routing Problems most all the characteristics of the VRP arising in real-world applications. Furthermore, the corresponding algorithms and their computer implementations (software tools) play an essential role in finding high-quality feasible solutions for real-world instances within acceptable computing times. Compared to procedures not based on optimization techniques, significant cost savings and a better utilization of the vehicle fleet can be achieved. In addition, by means of such planning software it is possible to improve the automation, standardization, and integration into the organizations' overall planning processes, leading to less time-consuming and more cost-efficient planning processes with respect to manual planning. Moreover, computerized planning allows planners to compare several different planning scenarios, and herewith to choose a best one through a careful and fast evaluation of cost and service-related performance indicators.In the last years, software tools integrating telematics services (electronic data transmission between vehicles and planners) have b...

Shared Capacity Routing Problem − An omni-channel retail study

“…The appendix provides a mixed integer linear programming (MILP) formulation for the SCRP based on a two-index formulation for the capacitated VRP [12]. In preliminary experiments, we could solve only very small instances with this MILP using the GUROBI solver.…”

“…We use a standard branch-and-cut procedure to solve the VRP, in which we make use of a 2-index flow formulation including the well known rounded capacity constraints [12]. We relax the rounded capacity constraints, identify violated rounded capacity constraints when a feasible integer solution is found and add these to the formulation.…”

A three-step scheduling based on geographic information system for workforce-planning problem

“…The workforce planning problem can be referred as the VRP with time windows (VRPTW). The conventional objective mainly aims minimising the travel distance and the transportation cost [7] and service time consisting of the total travel time, waiting time, and total travel distance are defined as hard constraints of the problems. To solve the VRPTW, the Travelling Salesman Problem (TSP) is employed to represent the form of the VRPTW [8].…”

Logistics Management

“…Other objectives could be to minimize the total length of all routes or the number of vehicles employed, a balancing of routes as well as the maximization of profit. Furthermore, a combination of different goals is possible and therefore the implementation of a hierarchical objective system or the usage of multi-criteria optimization methods is necessary (Irnich et al 2014). Nevertheless, cost minimization is still the most important objective and as it is the single aim of the underlying real-world issue, it will be further examined.…”

“…Likewise, the decision variables may be connected in a non-linear way. As a result, real-world objective functions are much more complex than the one shown in (1) (Irnich et al 2014). This also applies to the cost function present in the business case described above, which will be further studied in the following.…”