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Logistics is an essential part of management and responsible for planning and controlling all processes required for an effective and efficient delivery of goods and services from the point of production to the point of consumption. A key activity within Logistics is transportation planning, and a major concern of the latter one is the routing and scheduling of vehicles. Aiming at an efficient use of a fleet of vehicles for the purpose of meeting customer demands, vehicle routing has been since many years an important field of application of Operations Research methods, especially integer programming and combinatorial optimization. Due to the complexity of vehicle routing problems, it is required to distinguish and use a wide range of models and mostly heuristic but also exact solution techniques. This course tries to impart knowledge on the most fundamental vehicle routing models and methods and their application.
Introduction to the field of vehicle routing; the travelling salesman problem (TSP): problem formulation and solution construction methods, improvement heuristics, the Lin-Kernighan heuristic, valid inequalities; classicle vehicle routing heuristics: route first-cluster second, generalized assignment and location-based heuristic, sweep procedure, petal method and set partitioning based heuristics, savings procedures, insertion procedures; improvement heuristics; sequential local search for the VRP; recent meta-heuristic solution methods for the VRP; k-center tree relaxation; k-tree relaxation; resource-constraint shortest path problems; column generation and branch-and-price techniques for the VRP.
At the end of this course, the students should be able to (a) apply and possibly also combine standard tools and techniques to the standard vehicle routing problem, (b) see the conflict between the necessity of exploiting specific problem structure and the objective of having generally applicable methods, (c) recognize the limitations and assumptions of vehicle routing models regarding real-world vehicle routing applications, (d) get an idea which methods can be used and combined to address practical vehicle routing problems, (e) to build the insight about fundamental models and techniques required for deeper studies and investigations in this field of Operations Research and Logistics.
Mathematical Programming.
Andreas Klose.
2 x 2 hours of lecture per week.
English.
Toth P, Vigo D (2002) The Vehicle Routing Problem. SIAM Monograph on Discrete Mathematics and Applications.
Examination: 2nd quarter. Re-examination: Contact the teacher.
Department of Mathematical Sciences.
Information Office, Department of Mathematical Sciences.
The evaluation is divided into two parts. The first part is written assignments after the 1st and after the 2nd quarter with a workload of approximately 20 hours for each of the two assignments. The second part is an oral examination of about 20 minutes with an external examiner. The oral examination will be without preparation. The mark after the Danish 7-grade scale is given based on the written assignments and the oral examintion.
