Industrial Vehicle Routing

Solving the Vehicle Routing Problem (VRP) is a key to efficiency in transportation and supply chain management. The VRP is an NP-hard problem that comes in many guises. The VRP literature contains thousands of papers, and VRP research is regarded as one of the great successes of OR. Vehicle routing decision support tools provide substantial savings in society every day, and an industry of routing tool vendors has emerged. Exact methods of today cannot consistently solve VRP instances with more than 50–100 customers in reasonable time, which is generally a small number in real-life applications. For industrial problem sizes, and if one aims at solving a variety of VRP variants, approximation methods is the only viable approach. There is still a need for VRP research, particularly for large-scale instances and complex, rich VRP variants. In this chapter, we give a brief general introduction to the VRP. We then describe how industrial requirements motivate extensions to the basic, rather idealized VRP models that have received most attention in the research community, and how such extensions can be made. At SINTEF Applied Mathematics, industrial variants of the VRP have been studied since 1995. Our efforts have led to the development of a generic VRP solver that has been commercialized through a spin-off company. We give a description of the underlying, rich VRP model and the selected uniform algorithmic approach, which is based on metaheuristics. Finally, results from computational experiments are presented. In conclusion, we point to important issues in further VRP research.

[1]  George B. Dantzig,et al.  The Truck Dispatching Problem , 1959 .

[2]  G. Nemhauser,et al.  Integer Programming , 2020 .

[3]  Russell Bent,et al.  A two-stage hybrid algorithm for pickup and delivery vehicle routing problems with time windows , 2003, Comput. Oper. Res..

[4]  Jean-Yves Potvin,et al.  A parallel route building algorithm for the vehicle routing and scheduling problem with time windows , 1993 .

[5]  Kjetil Fagerholt,et al.  Ship Routing and Scheduling: Status and Perspectives , 2004, Transp. Sci..

[6]  Michel Gendreau,et al.  A Survey of Heuristics for the Vehicle Routing Problem Part I: Basic Problems and Supply Side Extensions , 2008 .

[7]  Mandell Bellmore,et al.  Transformation of Multisalesman Problem to the Standard Traveling Salesman Problem , 1974, JACM.

[8]  F. Glover,et al.  Handbook of Metaheuristics , 2019, International Series in Operations Research & Management Science.

[9]  Nicos Christofides,et al.  An Algorithm for the Vehicle-dispatching Problem , 1969 .

[10]  J. K. Lenstra,et al.  Local Search in Combinatorial Optimisation. , 1997 .

[11]  Nenad Mladenović,et al.  An Introduction to Variable Neighborhood Search , 1997 .

[12]  Martin W. P. Savelsbergh,et al.  Efficient Insertion Heuristics for Vehicle Routing and Scheduling Problems , 2004, Transp. Sci..

[13]  Paolo Toth,et al.  The Vehicle Routing Problem , 2002, SIAM monographs on discrete mathematics and applications.

[14]  Jacques Desrosiers,et al.  Technical Note - Optimizing the Schedule for a Fixed Vehicle Path with Convex Inconvenience Costs , 1989, Transp. Sci..

[15]  Les R. Foulds,et al.  Construction properties of combinatorial deltahedra , 1979, Discret. Appl. Math..

[16]  Silvano Martello,et al.  Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization , 2012 .

[17]  Marius M. Solomon,et al.  Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints , 1987, Oper. Res..

[18]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[19]  Abraham P. Punnen,et al.  A survey of very large-scale neighborhood search techniques , 2002, Discret. Appl. Math..

[20]  M. R. Rao,et al.  Technical Note - A Note on the Multiple Traveling Salesmen Problem , 1980, Oper. Res..

[21]  Gerrit K. Janssens,et al.  New heuristics for the Fleet Size and Mix Vehicle Routing Problem with Time Windows , 2002, J. Oper. Res. Soc..

[22]  Jean-François Cordeau,et al.  VRP with Time Windows , 1999, The Vehicle Routing Problem.

[23]  M. Dror Arc Routing : Theory, Solutions and Applications , 2000 .

[24]  Tore Grünert,et al.  Sequential search and its application to vehicle-routing problems , 2006, Comput. Oper. Res..

[25]  Jacques Desrosiers,et al.  A Unified Framework for Deterministic Time Constrained Vehicle Routing and Crew Scheduling Problems , 1998 .

[26]  Michel Gendreau,et al.  Vehicle Routing Problem with Time Windows, Part I: Route Construction and Local Search Algorithms , 2005, Transp. Sci..

[27]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[28]  Atle Riise,et al.  Dynamic And Stochastic Vehicle Routing In Practice , 2007 .

[29]  Jörg Homberger,et al.  Two Evolutionary Metaheuristics For The Vehicle Routing Problem With Time Windows , 1999 .

[30]  Martin W. P. Savelsbergh,et al.  Branch-and-Price: Column Generation for Solving Huge Integer Programs , 1998, Oper. Res..

[31]  Michel Gendreau,et al.  A Survey of Heuristics for the Vehicle Routing Problem Part II: Demand Side Extensions , 2008 .

[32]  Michel Gendreau,et al.  New Heuristics for the Vehicle Routing Problem , 2005 .

[33]  Thomas Stützle,et al.  Stochastic Local Search: Foundations & Applications , 2004 .

[34]  Michel Gendreau,et al.  Vehicle Routing Problem with Time Windows, Part II: Metaheuristics , 2005, Transp. Sci..

[35]  David Pisinger,et al.  A general heuristic for vehicle routing problems , 2007, Comput. Oper. Res..

[36]  G. Clarke,et al.  Scheduling of Vehicles from a Central Depot to a Number of Delivery Points , 1964 .

[37]  Martin Stølevik,et al.  Solving the Long-Term Forest Treatment Scheduling Problem , 2007, Geometric Modelling, Numerical Simulation, and Optimization.

[38]  Paolo Toth,et al.  The Granular Tabu Search and Its Application to the Vehicle-Routing Problem , 2003, INFORMS J. Comput..

[39]  B. Gillett,et al.  Multi-terminal vehicle-dispatch algorithm , 1976 .

[40]  G. Dueck,et al.  Record Breaking Optimization Results Using the Ruin and Recreate Principle , 2000 .

[41]  Ángel Corberán,et al.  Separating capacity constraints in the CVRP using tabu search , 1998, Eur. J. Oper. Res..

[42]  Michel Gendreau,et al.  A Tabu Search Algorithm for a Routing and Container Loading Problem , 2006, Transp. Sci..

[43]  Helena Ramalhinho Dias Lourenço,et al.  Iterated Local Search , 2001, Handbook of Metaheuristics.

[44]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[45]  Andrew Lim,et al.  A metaheuristic for the pickup and delivery problem with time windows , 2001, Proceedings 13th IEEE International Conference on Tools with Artificial Intelligence. ICTAI 2001.