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its first edition, the class was composed of 18 students from 11 different nationalities. Most of these stu- dents had some working experience. 3.2 Course Contents One of the OR tools studied in the course are heuristic methods and their applications to business prob- lems. One such a problem is the vehicle routing problem (VRP), which is a logistics problem faced by many companies in numerous industries. All tangible products raw materials, components, manufactured goods, etc. must be transported and distributed to other factories, warehouses, distribution centers, stores, or customers’ homes. Therefore, companies must design routes to deliver all these products. Typi- cally, there is a central depot that delivers goods to a set of geographically dispersed customers that have placed orders. A fleet of vehicles based at the depot is available to serve these orders. The VRP aims at finding a sequence of deliveries (routes) for each vehicle so that all customers are served and the total dis- tance traveled by the fleet is minimized. This problem has been studied for over 50 years (Laporte 2009) 3611
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Grasas, Juan, and Ramalhinho and has dozens of variants that incorporate additional constraints faced in real life. Solving a VRP opti- mally is very difficult as the problem size increases. Since exact methods can handle up to 50 or 75 cus- tomers only, one must resort to heuristic methods for relatively large problems. One of the most funda- mental and commonly used heuristic is the Clarke and Wright (1964) savings (CWS) heuristic. This method uses the concept of savings associated to merging two different routes. At each step, all savings resulting from feasibly merging pairs of routes are computed. The algorithm takes the link with the great- est savings and joins the two routes as long as the new merged route is feasible. The merging procedure continues until no more routes can be merged. There exist many more heuristics that build on this savings heuristic to enhance its performance or to solve variations of the standard VRP. 3.3 Application and Insights The simulation of the VRP is played over two consecutive lectures. Grasas and Ramalhinho (2013) offer a complete and detailed description of this application and its supporting material. In this simulation game, students will be responsible for route planning in a fictitious company. They will be competing to each other to see which group can find the best results. To complement this exercise, an open web-based tool was developed. Figure 1 shows a screenshot of the webpage, which can be found at . In the first lecture, there is a brief discussion on logistics and the importance of vehicle routing problems for companies. At this point, no solution method or heuristic has been introduced yet. Students are then presented a small case in which a manufacturer needs to distribute its products to a net- work of 20 stores located at different shopping malls in the Northeast of Spain. The case contains the postal addresses of each mall, the demand for each store, and the capacity of the available trucks. The
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