Chapter 10: Vehicle Routing Problems with Profits

Abstract

The key characteristic of the class of Vehicle Routing Problems with Profits (VRPPs) is that, contrary to what happens for the most classical vehicle routing problems, the set of customers to serve is not given. Therefore, two different decisions have to be taken: (i) which customers to serve, and (ii) how to cluster the customers to be served in different routes (if more than one) and order the visits in each route. In general, a profit is associated with each customer that makes such a customer more or less attractive. Thus, any route or set of routes, starting and ending at a given depot, can be measured both in terms of cost and in terms of profit. The difference between route profit and cost may be maximized, or the profit or the cost optimized with the other measure bounded in a constraint.There are several types of applications that can be modeled by means of a problem of this class:• scheduling of the daily operations of a steel rolling mill (see, e.g., Balas [13, 16]);• design of tourist trips to maximize the value of the visited attractions in a limited period (see, e.g., Vansteenwegen and Van Oudheusden [109]);• identification of suppliers to visit to maximize the recovered claims with a limited number of auditors (see Ilhan, Iravani, and Daskin [61]);• recruiting of athletes from high schools for a college team (see Butt and Cavalier [24]);• planning of the visits of a salesperson (see, e.g., Ramesh and Brown [89]);• routing of oil tankers to serve ships at different locations (see Golden, Levy, and Vohra [57]);

The multi-vehicle profitable pickup and delivery problem

“…Much fewer studies can be found on the PTP (Archetti et al 2014). An approximation algorithm for the asymmetric PTP is presented by Nguyen and Nguyen (2010).…”

“…A classification of traveling salesman problems with profits is given in Feillet et al (2005). While in the TOP, the objective is to maximize the total collected profit, other problems, like the prize-collecting VRP, minimize the total traveling cost (Feillet et al 2005;Tang and Wang 2006;Archetti et al 2014). If a carrier can either visit a customer with one of his vehicles or assign the customer to a common carrier, the problem is referred to as VRP with private fleet and common carrier which is investigated by, e.g., Chu (2005), Bolduc et al (2008), Stenger et al (2013).…”

“…In a recent book, Archetti et al (2014) claim that an important application of VRP with profits arises in the context of the small packaging industry. Large companies in this branch outsource last-mile deliveries of unprofitable areas to subcontractors .…”

Dynamic Vehicle Routing Problems with Enhanced Ant Colony Optimization

“…This is because shortening vehicles running distances will promote the efficiency of vehicles and drivers. In addition, the algorithm can improve customers service quality, reduce exhaust emissions, and promote vehicles dispatch efficiency [3]. Consequently, the research of vehicle routing problem, which is a significate topic, has grabbed the scholars' attentions during the past few decades [4].…”

Solving a bi-objective vehicle routing problem under uncertainty by a revised multi-choice goal programming approach

“…Moreover, in the recent years, some issues (e.g., global warming, resource scarcity, traffic congestion and pollution) are causing companies and governments to design logistic systems effectively (Archetti et al, 2014). The VRP is a complex problem in the field of operations research.…”