Static pickup and delivery problems: a classification scheme and survey

Abstract Pickup and delivery problems constitute an important class of vehicle routing problems in which objects or people have to be collected and distributed. This paper introduces a general framework to model a large collection of pickup and delivery problems, as well as a three-field classification scheme for these problems. It surveys the methods used for solving them.

[1]  Giovanni Rinaldi,et al.  A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems , 1991, SIAM Rev..

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

[3]  H. Psaraftis.  An Exact Algorithm for the Single Vehicle Many-to-Many Dial-A-Ride Problem with Time Windows , 1983 .

[4]  Harilaos N. Psaraftis,et al.  A Dynamic Programming Solution to the Single Vehicle Many-to-Many Immediate Request Dial-a-Ride Problem , 1980 .

[5]  J. Mageean,et al.  The evaluation of demand responsive transport services in Europe , 2003 .

[6]  Greg N. Frederickson,et al.  Nonpreemptive Ensemble Motion Planning on a Tree , 1993, J. Algorithms.

[7]  Richard M. Karp,et al.  Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane , 1977, Math. Oper. Res..

[8]  Said Salhi,et al.  Improvements to Vehicle Routeing Heuristics , 1987 .

[9]  Fred W. Glover,et al.  Tabu Thresholding: Improved Search by Nonmonotonic Trajectories , 1995, INFORMS J. Comput..

[10]  Hoong Chuin Lau,et al.  Pickup and Delivery with Time Windows: Algorithms and Test Case Generation , 2002, Int. J. Artif. Intell. Tools.

[11]  L. V. Wassenhove,et al.  Quantitative approaches to distribution logistics and supply chain management , 2002 .

[12]  Said Salhi,et al.  An investigation into a new class of vehicle routing problem with backhauls , 2002 .

[13]  Roberto Battiti,et al.  The Reactive Tabu Search , 1994, INFORMS J. Comput..

[14]  Michel Gendreau,et al.  An Approximation Algorithm for the Traveling Salesman Problem with Backhauls , 1997, Oper. Res..

[15]  Paolo Toth,et al.  VRP with Backhauls , 2002, The Vehicle Routing Problem.

[16]  Saïd Salhi,et al.  Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries , 2005, Eur. J. Oper. Res..

[17]  Warren B. Powell,et al.  Stochastic and dynamic networks and routing , 1995 .

[18]  Haldun Süral,et al.  The single‐vehicle routing problem with unrestricted backhauls , 2003, Networks.

[19]  Michel Gendreau,et al.  The Swapping Problem on a Line , 1999, SIAM J. Comput..

[20]  Gilbert Laporte,et al.  The Dial-a-Ride Problem (DARP): Variants, modeling issues and algorithms , 2003, 4OR.

[21]  Gilbert Laporte,et al.  A Tabu Search Heuristic for the Static Multi-Vehicle Dial-a-Ride Problem , 2002 .

[22]  Hokey Min,et al.  The multiple vehicle routing problem with simultaneous delivery and pick-up points , 1989 .

[23]  Jacques Desrosiers,et al.  A Request Clustering Algorithm for Door-to-Door Handicapped Transportation , 1991, Transp. Sci..

[24]  Mikio Kubo,et al.  HEURISTIC ALGORITHMS FOR THE SINGLE VEHICLE DIAL-A-RIDE PROBLEM , 1990 .

[25]  Giovanni Righini,et al.  A Branch-and-Price Approach to the Vehicle Routing Problem with Simultaneous Distribution and Collection , 2006, Transp. Sci..

[26]  Gilbert Laporte,et al.  New Insertion and Postoptimization Procedures for the Traveling Salesman Problem , 1992, Oper. Res..

[27]  Shoshana Anily,et al.  Approximation algorithms for the capacitated traveling salesman problem with pickups and deliveries , 1999 .

[28]  George L. Nemhauser,et al.  Handbooks in operations research and management science , 1989 .

[29]  Gur Mosheiov,et al.  The Travelling Salesman Problem with pick-up and delivery , 1994 .

[30]  Arthur V. Hill,et al.  An algorithm for the traveling salesman problem with pickup and delivery customers , 1985 .

[31]  Roberto Baldacci,et al.  An exact algorithm for the Traveling Salesman Problem with Deliveries and Collections , 2003, Networks.

[32]  Teuvo Kohonen,et al.  Self-organized formation of topologically correct feature maps , 2004, Biological Cybernetics.

[33]  M. Savelsbergh.  An efficient implementation of local search algorithms for constrained routing problems , 1990 .

[34]  Jean-Yves Potvin,et al.  Heuristic approaches to vehicle routing with backhauls and time windows , 1996, Comput. Oper. Res..

[35]  P. Healy,et al.  A new extension of local search applied to the Dial-A-Ride Problem , 1995 .

[36]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[37]  Matteo Fischetti,et al.  An Additive Bounding Procedure for Combinatorial Optimization Problems , 1989, Oper. Res..

[38]  Jean-François Cordeau,et al.  A Branch-and-Cut Algorithm for the Dial-a-Ride Problem , 2006, Oper. Res..

[39]  Jacques Desrosiers,et al.  A Dynamic Programming Solution of the Large-Scale Single-Vehicle Dial-A-Ride Problem with Time Windows , 1984 .

[40]  Gilbert Laporte,et al.  Waiting strategies for the dynamic pickup and delivery problem with time windows , 2004 .

[41]  Niaz A. Wassan,et al.  A reactive tabu search meta-heuristic for the vehicle routing problem with back-hauls , 2002 .

[42]  Joaquín A. Pacheco Bonrostro.  Heurístico para los problemas de rutas con carga y descarga en sistemas LIFO , 1997 .

[43]  K. Ruland,et al.  The pickup and delivery problem: Faces and branch-and-cut algorithm , 1997 .

[44]  Gilbert Laporte,et al.  Double-horizon based heuristics for the dynamic pickup and delivery problem with time windows , 2004 .

[45]  Zhi-Long Chen,et al.  Solving a Practical Pickup and Delivery Problem , 2003, Transp. Sci..

[46]  Greg N. Frederickson,et al.  Preemptive Ensemble Motion Planning on a Tree , 1992, SIAM J. Comput..

[47]  Daniele Vigo,et al.  Heuristics for the traveling salesman problem with pickup and delivery , 1999, Comput. Oper. Res..

[48]  Gilbert Laporte,et al.  A unified tabu search heuristic for vehicle routing problems with time windows , 2001, J. Oper. Res. Soc..

[49]  Lawrence Bodin,et al.  Optimizing Single Vehicle Many-to-Many Operations with Desired Delivery Times: I. Scheduling , 1985, Transp. Sci..

[50]  Arne Løkketangen,et al.  Creating lasso-solutions for the traveling salesman problem with pickup and delivery by Tabu search , 2006, Central Eur. J. Oper. Res..

[51]  Gilbert Laporte,et al.  Variable Neighborhood Search for the Pickup and Delivery Traveling Salesman Problem with LIFO Loading , 2007, INFORMS J. Comput..

[52]  Juan José Salazar González,et al.  A branch-and-cut algorithm for a traveling salesman problem with pickup and delivery , 2004, Discret. Appl. Math..

[53]  David Pisinger,et al.  A unified heuristic for a large class of Vehicle Routing Problems with Backhauls , 2006, Eur. J. Oper. Res..

[54]  R. Dekker,et al.  Reverse logistics : quantitative models for closed-loop supply chains , 2004 .

[55]  Candace Arai Yano,et al.  Vehicle Routing at Quality Stores , 1987 .

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

[57]  Paolo Toth,et al.  A heuristic algorithm for the symmetric and asymmetric vehicle routing problems with backhauls , 1999, Eur. J. Oper. Res..

[58]  Nigel H. M. Wilson,et al.  A heuristic algorithm for the multi-vehicle advance request dial-a-ride problem with time windows , 1986 .

[59]  L. N. Wassenhove,et al.  Collection and Vehicle Routing Issues in Reverse Logistics , 2004 .

[60]  Shoshana Anily,et al.  The vehicle-routing problem with delivery and back-haul options , 1996 .

[61]  Martin Grötschel,et al.  Telebus Berlin: Vehicle Scheduling in a Dial-a-Ride System , 1999 .

[62]  J. Beardwood,et al.  The shortest path through many points , 1959, Mathematical Proceedings of the Cambridge Philosophical Society.

[63]  Jean-François Cordeau,et al.  Branch and Cut and Price for the Pickup and Delivery Problem with Time Windows , 2009, Transp. Sci..

[64]  L. B. Fu,et al.  Expected Shortest Paths in Dynamic and Stochastic Traf c Networks , 1998 .

[65]  Martin W. P. Savelsbergh,et al.  Local search in routing problems with time windows , 1984 .

[66]  Naoki Katoh,et al.  An approximation algorithm for the pickup and delivery vehicle routing problem on trees , 2006, Discret. Appl. Math..

[67]  J. A. Pacheco.  Heurístico para los problemas de rutas con carga y descarga en sistemas LIFO , 1997 .

[68]  Martin W. P. Savelsbergh,et al.  Drive: Dynamic Routing of Independent Vehicles , 1998, Oper. Res..

[69]  Lawrence Bodin,et al.  Approximate Traveling Salesman Algorithms , 1980, Oper. Res..

[70]  T. Kohonen.  Self-organized formation of topographically correct feature maps , 1982 .

[71]  Jacques Desrosiers,et al.  The Pickup and Delivery Problem with Time Windows , 1989 .

[72]  José Brandão.  A new tabu search algorithm for the vehicle routing problem with backhauls , 2006, Eur. J. Oper. Res..

[73]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[74]  Harilaos N. Psaraftis.  Analysis of an O(N2) heuristic for the single vehicle many-to-many Euclidean dial-a-ride problem , 1983 .

[75]  Russell Bent,et al.  A two-stage hybrid algorithm for pickup and delivery vehicle routing problems with time windows , 2006, Comput. Oper. Res..

[76]  Jean-Yves Potvin,et al.  A genetic algorithm for vehicle routing with backhauling , 1996, Applied Intelligence.

[77]  Rajeev Motwani,et al.  Approximating Capacitated Routing and Delivery Problems , 1999, SIAM J. Comput..

[78]  J-F Chen,et al.  Vehicle routing problem with simultaneous deliveries and pickups , 2006, J. Oper. Res. Soc..

[79]  Michel Gendreau,et al.  The Traveling Salesman Problem with Backhauls , 1996, Comput. Oper. Res..

[80]  Kamlesh Mathur,et al.  Reverse logistics: simultaneous design of delivery routes and returns strategies , 2007, Comput. Oper. Res..

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

[82]  H. D. Ratliff,et al.  Set partitioning based heuristics for interactive routing , 1981, Networks.

[83]  Kjetil Fagerholt,et al.  A multi-start local search heuristic for ship scheduling - a computational study , 2007, Comput. Oper. Res..

[84]  Juan José Salazar González,et al.  Heuristics for the One-Commodity Pickup-and-Delivery Traveling Salesman Problem , 2004, Transp. Sci..

[85]  Michael R. Anderberg,et al.  Cluster Analysis for Applications , 1973 .

[86]  David Pisinger,et al.  An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows , 2006, Transp. Sci..

[87]  Refael Hassin,et al.  The swapping problem , 1992, Networks.

[88]  M. Goetschalckx,et al.  The vehicle routing problem with backhauls , 1989 .

[89]  Said Salhi,et al.  Improvements to Vehicle Routing Heuristics , 1987 .

[90]  Moshe Dror,et al.  Savings by Split Delivery Routing , 1989, Transp. Sci..

[91]  Gilbert Laporte,et al.  A tabu search heuristic for a routing problem arising in servicing of offshore oil and gas platforms , 2008, J. Oper. Res. Soc..

[92]  Giovanni Righini,et al.  Heuristic algorithms for the vehicle routing problem with simultaneous pick-up and delivery , 2007, Comput. Oper. Res..

[93]  James A. Chisman,et al.  The clustered traveling salesman problem , 1975, Comput. Oper. Res..

[94]  Jürgen Branke,et al.  Waiting Strategies for Dynamic Vehicle Routing , 2005, Transp. Sci..

[95]  Raphael M. Robinson,et al.  Recursion and double recursion , 1948 .

[96]  Edward P. K. Tsang,et al.  Guided local search and its application to the traveling salesman problem , 1999, Eur. J. Oper. Res..

[97]  G. Dueck.  New optimization heuristics , 1993 .

[98]  David M. Stein,et al.  An Asymptotic, Probabilistic Analysis of a Routing Problem , 1978, Math. Oper. Res..

[99]  Nicos Christofides.  Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem , 1976, Operations Research Forum.

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

[101]  Jean-Yves Potvin,et al.  Constraint-Directed Search for the Advanced Request Dial-a-Ride Problem with Service Quality Constraints , 1992, Computer Science and Operations Research.

[102]  Jan Karel Lenstra,et al.  Variable-Depth Search for the Single-Vehicle Pickup and Delivery Problem with Time Windows , 1993, Transp. Sci..

[103]  Sylvie Gélinas,et al.  A new branching strategy for time constrained routing problems with application to backhauling , 1992, Ann. Oper. Res..

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

[105]  Michael H. Cole,et al.  A VEHICLE ROUTING PROBLEM WITH BACKHAULS AND TIME WINDOWS: A GUIDED LOCAL SEARCH SOLUTION , 2005 .

[106]  Jonathan F. Bard,et al.  A GRASP for the Vehicle Routing Problem with Time Windows , 1995, INFORMS J. Comput..

[107]  Jacques Desrosiers,et al.  An Algorithm for Mini-Clustering in Handicapped Transport , 1991 .

[108]  Shen Lin.  Computer solutions of the traveling salesman problem , 1965 .

[109]  Mikhail J. Atallah,et al.  Efficient Solutions to Some Transportation Problems with Applications to Minimizing Robot Arm Travel , 1988, SIAM J. Comput..

[110]  Jan Dethloff,et al.  Vehicle routing and reverse logistics: The vehicle routing problem with simultaneous delivery and pick-up , 2001, OR Spectr..

[111]  Fermín Alfredo Tang Montané,et al.  A tabu search algorithm for the vehicle routing problem with simultaneous pick-up and delivery service , 2006, Comput. Oper. Res..

[112]  Oli B. G. Madsen,et al.  A heuristic algorithm for a dial-a-ride problem with time windows, multiple capacities, and multiple objectives , 1995, Ann. Oper. Res..

[113]  Maciek A. Nowak,et al.  The Pickup and Delivery Problem with Split Loads , 2005 .

[114]  A. Lim,et al.  The one-commodity pickup and delivery travelling salesman problem on a path or a tree , 2006 .

[115]  Paolo Toth,et al.  Fast Local Search Algorithms for the Handicapped Persons Transportation Problem , 1996 .

[116]  Paolo Toth,et al.  Heuristic Algorithms for the Handicapped Persons Transportation Problem , 1997, Transp. Sci..

[117]  I H Osman,et al.  Meta-Heuristics Theory and Applications , 2011 .

[118]  Gilbert Laporte,et al.  The Pickup And Delivery Problem With Time Windows And Transshipment , 2006 .

[119]  Gilbert Laporte,et al.  Solving a vehicle-routing problem arising in soft-drink distribution , 2006, J. Oper. Res. Soc..

[120]  J. Wesley Barnes,et al.  Solving the Pickup and Delivery Problem with Time Windows Using Reactive Tabu Search Transportation , 2000 .

[121]  Enrico Angelelli,et al.  The Vehicle Routing Problem with Time Windows and Simultaneous Pick-up and Delivery , 2002 .

[122]  Gilbert Laporte,et al.  General solutions to the single vehicle routing problem with pickups and deliveries , 2007, Eur. J. Oper. Res..

[123]  Gur Mosheiov,et al.  The traveling salesman problem with delivery and backhauls , 1994, Oper. Res. Lett..

[124]  J. Kruskal.  On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[125]  E. Balas,et al.  Set Partitioning: A survey , 1976 .

[126]  Gilbert Laporte,et al.  Étude comparative de divers modèles pour le problème de transport à la demande , 2007, INFOR Inf. Syst. Oper. Res..

[127]  Chul E. Kim,et al.  Approximation Algorithms for Some Routing Problems , 1978, SIAM J. Comput..

[128]  Jacques Desrosiers,et al.  Large Scale Multi-Vehicle Dial-a-Ride Problems , 1989 .

[129]  David S. Johnson,et al.  The Traveling Salesman Problem: A Case Study in Local Optimization , 2008 .

[130]  Gilbert Laporte,et al.  Models and branch-and-cut algorithms for pickup and delivery problems with time windows , 2007 .

[131]  Bruce L. Golden,et al.  VEHICLE ROUTING: METHODS AND STUDIES , 1988 .

[132]  B. Golden,et al.  A multifaceted heuristic for the orienteering problem , 1988 .

[133]  Wansoo T. Rhee.  Convergence of optimal stochastic bin packing , 1985 .

[134]  I. Osman,et al.  A neural network algorithm for the traveling salesman problem with backhauls , 2003 .

[135]  Loren K. Platzman,et al.  An O(N log N) planar travelling salesman heuristic based on spacefilling curves , 1982, Oper. Res. Lett..

[136]  Martin W. P. Savelsbergh,et al.  The General Pickup and Delivery Problem , 1995, Transp. Sci..

[137]  Ibrahim H. Osman,et al.  Self-organizing feature maps for the vehicle routing problem with backhauls , 2006, J. Sched..

[138]  Roberto Baldacci,et al.  An Exact Method for the Vehicle Routing Problem with Backhauls , 1999, Transp. Sci..

[139]  Hussain Aziz Saleh,et al.  Handicapped Person Transportation: An application of the Grouping Genetic Algorithm , 2006, Eng. Appl. Artif. Intell..

[140]  Said Salhi,et al.  A cluster insertion heuristic for single and multiple depot vehicle routing problems with backhauling , 1999, J. Oper. Res. Soc..

[141]  R. A. Zemlin,et al.  Integer Programming Formulation of Traveling Salesman Problems , 1960, JACM.

[142]  Jean-Yves Potvin,et al.  A Tabu Search Heuristic for the Vehicle Routing Problem with Backhauls and Time Windows , 1997, Transp. Sci..

[143]  G. Peano.  Sur une courbe, qui remplit toute une aire plane , 1890 .