Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints

This paper considers the design and analysis of algorithms for vehicle routing and scheduling problems with time window constraints. Given the intrinsic difficulty of this problem class, approximation methods seem to offer the most promise for practical size problems. After describing a variety of heuristics, we conduct an extensive computational study of their performance. The problem set includes routing and scheduling environments that differ in terms of the type of data used to generate the problems, the percentage of customers with time windows, their tightness and positioning, and the scheduling horizon. We found that several heuristics performed well in different problem environments; in particular an insertion-type heuristic consistently gave very good results.

[1]  H. G. M. Pullen,et al.  A computer application to a transport scheduling problem , 1967, Comput. J..

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

[3]  Linus Schrage,et al.  Formulation and structure of more complex/realistic routing and scheduling problems , 1981, Networks.

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

[5]  K. W. Knight,et al.  Vehicle Scheduling with Timed and Connected Calls: A Case Study , 1968 .

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

[7]  Lawrence Bodin,et al.  Optimizing Single Vehicle Many-to-Many Operations with Desired Delivery Times: II. Routing , 1985, Transp. Sci..

[8]  R. H. Mole,et al.  A Sequential Route-building Algorithm Employing a Generalised Savings Criterion , 1976 .

[9]  Paolo Toth,et al.  State-space relaxation procedures for the computation of bounds to routing problems , 1981, Networks.

[10]  Jacques Desrosiers,et al.  Routing with Time Windows: Synthesis , 1983 .

[11]  Billy E. Gillett,et al.  A Heuristic Algorithm for the Vehicle-Dispatch Problem , 1974, Oper. Res..

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

[13]  Edward K. Baker,et al.  LARGE SCALE IMPLEMENTATION OF A TIME ORIENTED VEHICLE SCHEDULING MODEL , 1982 .

[14]  N. S. Barnett,et al.  Private communication , 1969 .

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

[16]  Edward K. Baker,et al.  Technical Note - An Exact Algorithm for the Time-Constrained Traveling Salesman Problem , 1983, Oper. Res..

[17]  Thomas L. Magnanti,et al.  Implementing vehicle routing algorithms , 1977, Networks.

[18]  B. J. Lageweg,et al.  Hierarchical distribution modelling with routing costs : (preprint) , 1980 .

[19]  Thomas M. Cook,et al.  A SIMULATION AND STATISTICAL ANALYSIS OF STOCHASTIC VEHICLE ROUTING WITH TIMING CONSTRAINTS , 1978 .

[20]  Arthur J. Swersey,et al.  Scheduling School Buses , 1984 .

[21]  Nicos Christofides,et al.  The vehicle routing problem , 1976, Revue française d'automatique, informatique, recherche opérationnelle. Recherche opérationnelle.

[22]  Samuel J. Raff,et al.  Routing and scheduling of vehicles and crews : The state of the art , 1983, Comput. Oper. Res..

[23]  Robert A. Russell,et al.  Technical Note - An Effective Heuristic for the M-Tour Traveling Salesman Problem with Some Side Conditions , 1977, Oper. Res..

[24]  Marshall L. Fisher,et al.  A generalized assignment heuristic for vehicle routing , 1981, Networks.

[25]  Clifford S. Orloff,et al.  Route Constrained Fleet Scheduling , 1976 .

[26]  Jacques Desrosiers,et al.  Routing with time windows by column generation , 1983, Networks.

[27]  Marius Mihai Solomon,et al.  VEHICLE ROUTING AND SCHEDULING WITH TIME WINDOW CONSTRAINTS: MODELS AND ALGORITHMS (HEURISTICS) , 1984 .

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