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Journal Article•DOI•

Vehicle routing problem with time windows and a limited number of vehicles

Hoong Chuin Lau1, Melvyn Sim2, Kwong Meng Teo•
National University of Singapore1, Massachusetts Institute of Technology2
01 Aug 2003-European Journal of Operational Research (North-Holland)-Vol. 148, Iss: 3, pp 559-569
TL;DR: This paper proposes a tabu search approach characterized by a holding list and a mechanism to force dense packing within a route that allows time windows to be relaxed by introducing the notion of penalty for lateness.
About: This article is published in European Journal of Operational Research.The article was published on 2003-08-01. It has received 258 citations till now. The article focuses on the topics: Vehicle routing problem & Combinatorial optimization.
Citations
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Journal Article•DOI•
Vehicle Routing Problem with Time Windows, Part II: Metaheuristics

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Olli Bräysy1, Michel Gendreau2•
University of Jyväskylä1, Université de Montréal2
01 Feb 2005-Transportation Science
TL;DR: This paper surveys the research on the metaheuristics for the Vehicle Routing Problem with Time Windows and describes basic features of each method, and experimental results for Solomon's benchmark test problems are presented and analyzed.
Abstract: This paper surveys the research on the metaheuristics for the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval; all routes start and end at the depot, and the total demands of all points on one particular route must not exceed the capacity of the vehicle. Metaheuristics are general solution procedures that explore the solution space to identify good solutions and often embed some of the standard route construction and improvement heuristics described in the first part of this article. In addition to describing basic features of each method, experimental results for Solomon's benchmark test problems are presented and analyzed.

845 citations

Cites background from "Vehicle routing problem with time w..."

  • ...In addition, Le Bouthillier and Crainic (2005) con sider waiting and residual time at each customer....

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  • ...…et al. 2001 Insertion heuristic Exchange, relocate No Constraint-based diversification Cordeau et al. 2001 Modification of sweep heuristics Relocate, GENI No — Lau et al. 2003 Relocation from a holding list Exchange, relocate Yes Holding list for unrouted nodes, limit for number of routes Table…...

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  • ...In Lau et al. (2003) a limit is set for the number of routes that cannot be exceeded during the search....

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  • ...…63 4 25 464 1 211 54 960 43 832 13 612 25 1 385 05 1 232 65 58 432 Cordeau et al. (2001) 12 08 2 73 10 00 3 00 11 50 3 25 407 1 210 14 969 57 828 38 589 86 1 389 78 1 134 52 57 556 Lau et al. (2003) 12 17 3 00 10 00 3 00 12 25 3 38 418 1 211 55 1 001 12 832 13 589 86 1 418 77 1 170 93 58 477 Note....

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  • ...Notes Garcia et al. 1994 Solomon’s I1 heuristic 2-opt∗, Or-opt Yes Neighborhood restricted to arcs close in distance Rochat and Taillard 1995 Modification of Solomon’s I1, 2-opt, relocate No Adaptive memory 2-opt Carlton 1995 Insertion heuristic Relocate No Reactive tabu search Potvin and Bengio 1996 Solomon’s I1 heuristic 2-opt*, Or-opt Yes Neighborhood restricted to arcs close in distance Taillard et al. 1997 Solomon’s I1 heuristic CROSS No Soft time windows, adaptive memory Badeau et al. 1997 Solomon’s I1 heuristic CROSS No Soft time windows, adaptive memory Chiang et al. 1997 Modification of Russell (1995) -interchange No Reactive tabu search De Backer and Furnon 1997 Savings heuristic Exchange, relocate, 2-opt∗, No Constraint programming used 2-opt, Or-opt to check feasibility of moves Brandão 1999 Insertion heuristics Relocate, exchange, GENI No Neighborhoods restricted to arcs close in distance Schulze and Fahle 1999 Solomon’s I1, parallel I1 Ejection chains, Or-opt Yes Generated routes stored in a pool and savings heuristics Tan et al. 2000 Insertion heuristic of -interchange, 2-opt∗ No — Thangiah et al. (1994) Lau et al. 2001 Insertion heuristic Exchange, relocate No Constraint-based diversification Cordeau et al. 2001 Modification of sweep heuristics Relocate, GENI No — Lau et al. 2003 Relocation from a holding list Exchange, relocate Yes Holding list for unrouted nodes, limit for number of routes Table 2 Comparison of Tabu Search Algorithms Authors R1 R2 C1 C2 RC1 RC2 CNV/CTD Garcia et al. (1994) 12 92 3 09 10 00 3 00 12 88 3 75 436 1 317 7 1 222 6 877 1 602 3 1 473 5 1 527 0 65 977 Rochat and Taillard (1995) 12 25 2 91 10 00 3 00 11 88 3 38 415 1 208 50 961 72 828 38 589 86 1 377 39 1 119 59 57 231 Potvin and Bengio (1996) 12 50 3 09 10 00 3 00 12 63 3 38 426 1 294 5 1 154 4 850 2 594 6 1 456 3 1 404 8 63 530 Taillard et al. (1997) 12 17 2 82 10 00 3 00 11 50 3 38 410 1 209 35 980 27 828 38 589 86 1389 22 1 117 44 57 523 Chiang and Russell (1997) 12 17 2 73 10 00 3 00 11 88 3 25 411 1 204 19 986 32 828 38 591 42 1 397 44 1 229 54 58 502 De Backer and Furnon (1997) 14 17 5 27 10 00 3 25 14 25 6 25 508 1 214 86 930 18 829 77 604 84 1 385 12 1 099 96 56 998 Brandão (1999) 12 58 3 18 10 00 3 00 12 13 3 50 425 1 205 995 829 591 1 371 1 250 58 562 Schulze and Fahle (1999) 12 25 2 82 10 00 3 00 11 75 3 38 414 1 239 15 1 066 68 828 94 589 93 1 409 26 1 286 05 60 346 Tan et al. (2000) 13 83 3 82 10 00 3 25 13 63 4 25 467 1 266 37 1 080 24 870 87 634 85 1 458 16 1 293 38 62 008 Lau et al. (2001) 14 00 3 55 10 00 3 00 13 63 4 25 464 1 211 54 960 43 832 13 612 25 1 385 05 1 232 65 58 432 Cordeau et al. (2001) 12 08 2 73 10 00 3 00 11 50 3 25 407 1 210 14 969 57 828 38 589 86 1 389 78 1 134 52 57 556 Lau et al. (2003) 12 17 3 00 10 00 3 00 12 25 3 38 418 1 211 55 1 001 12 832 13 589 86 1 418 77 1 170 93 58 477 Note....

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Journal Article•DOI•
A Survey on the Vehicle Routing Problem and Its Variants

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Suresh Nanda Kumar, Ramasamy Panneerselvam
25 May 2012-Intelligent Information Management
TL;DR: The various exact methods and the heuristics and meta-heuristics used to solve the VRP and its variants are discussed.
Abstract: In this paper, we have conducted a literature review on the recent developments and publications involving the vehicle routing problem and its variants, namely vehicle routing problem with time windows (VRPTW) and the capacitated vehicle routing problem (CVRP) and also their variants. The VRP is classified as an NP-hard problem. Hence, the use of exact optimization methods may be difficult to solve these problems in acceptable CPU times, when the problem involves real-world data sets that are very large. The vehicle routing problem comes under combinatorial problem. Hence, to get solutions in determining routes which are realistic and very close to the optimal solution, we use heuristics and meta-heuristics. In this paper we discuss the various exact methods and the heuristics and meta-heuristics used to solve the VRP and its variants.

332 citations

Cites background from "Vehicle routing problem with time w..."

  • ...The authors [46] have considered a variant of VRPTW constrained by a limited vehicle fleet, which is a more realistic problem in logistics....

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Journal Article•DOI•
Improved route planning and scheduling of waste collection and transport

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Teemu Nuortio1, Jari Kytöjoki2, Harri Niska1, Olli Bräysy2•
University of Eastern Finland1, University of Jyväskylä2
01 Feb 2006-Expert Systems With Applications
TL;DR: The optimization of vehicle routes and schedules for collecting municipal solid waste in Eastern Finland is described by a recently developed guided variable neighborhood thresholding metaheuristic that is adapted to solve real-life waste collection problems.
Abstract: The collection of waste is a highly visible and important municipal service that involves large expenditures. Waste collection problems are, however, one of the most difficult operational problems to solve. This paper describes the optimization of vehicle routes and schedules for collecting municipal solid waste in Eastern Finland. The solutions are generated by a recently developed guided variable neighborhood thresholding metaheuristic that is adapted to solve real-life waste collection problems. Several implementation approaches to speed up the method and cut down the memory usage are discussed. A case study on the waste collection in two regions of Eastern Finland demonstrates that significant cost reductions can be obtained compared with the current practice.

284 citations

Cites background from "Vehicle routing problem with time w..."

  • ...The interested reader is referred to Lau, Sim, and Teo (2003)....

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Journal Article•DOI•
Vehicle routing scheduling for cross-docking in the supply chain

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Young Hae Lee1, Jung Woo Jung1, Kyong Min Lee2•
Hanyang University1, Philips2
01 Oct 2006-Computers & Industrial Engineering
TL;DR: An integrated model considering both cross-docking and vehicle routing scheduling is treated and a heuristic algorithm based on a tabu search algorithm is proposed to find the optimal vehicle routing schedule.

266 citations

Journal Article•DOI•
A multiobjective evolutionary algorithm for solving vehicle routing problem with time windows

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Kay Chen Tan1, Tong Heng Lee1, Yong Huat Chew1, Loo Hay Lee1•
National University of Singapore1
10 Nov 2003
TL;DR: A hybrid multiobjective evolutionary algorithm (HMOEA) that incorporates various heuristics for local exploitation in the evolutionary search and the concept of Pareto's optimality for solving multiobjectives optimization in VRPTW is proposed.
Abstract: Vehicle routing problem with time windows (VRPTW) involves the routing of a set of vehicles with limited capacity from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. This paper proposes a hybrid multiobjective evolutionary algorithm (HMOEA) that incorporates various heuristics for local exploitation in the evolutionary search and the concept of Pareto's optimality for solving multiobjective optimization in VRPTW problems. The proposed HMOEA optimizes all routing constraints and objectives simultaneously, which improves the routing solutions in many aspects, such as lower routing cost, wider scattering area and better convergence trace.

251 citations

References
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Journal Article•DOI•
Algorithms for the vehicle routing and scheduling problems with time window constraints

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Marius M. Solomon1•
Northeastern University1
01 Apr 1987-Operations Research
TL;DR: This paper considers the design and analysis of algorithms for vehicle routing and scheduling problems with time window constraints and finds that several heuristics performed well in different problem environments; in particular an insertion-type heuristic consistently gave very good results.
Abstract: 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.

3,211 citations

Book Chapter•DOI•
Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems

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Paul Shaw1•
ILOG1
26 Oct 1998
TL;DR: In this paper, a local search method called Large Neighbourhood Search (LNS) is used to solve vehicle routing problems, analogous to the shuffling technique of job shop scheduling.
Abstract: We use a local search method we term Large Neighbourhood Search (LNS) to solve vehicle routing problems. LNS is analogous to the shuffling technique of job-shop scheduling, and so meshes well with constraint programming technology. LNS explores a large neighbourhood of the current solution by selecting a number of "related" customer visits to remove from the set of planned routes, and re-inserting these visits using a constraint-based tree search. Unlike similar methods, we use Limited Discrepancy Search during the tree search to re-insert visits. We analyse the performance of our method on benchmark problems. We demonstrate that results produced are competitive with Operations Research meta-heuristic methods, indicating that constraint-based technology is directly applicable to vehicle routing problems.

1,207 citations

Journal Article•
Using constraint programming and local Search methods to solve vehicle routing problems

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Paul Shaw
01 Jan 1998-Lecture Notes in Computer Science
TL;DR: This work uses a local search method that is analogous to the shuffling technique of job-shop scheduling, and so meshes well with constraint programming technology, to solve vehicle routing problems.
Abstract: We use a local search method we term Large Neighbourhood Search (LNS) to solve vehicle routing problems. LNS is analogous to the shuffling technique of job-shop scheduling, and so meshes well with constraint programming technology. LNS explores a large neighbourhood of the current solution by selecting a number of related customer visits to remove from the set of planned routes, and re-inserting these visits using a constraint-based tree search. Unlike similar methods, we use Limited Discrepancy Search during the tree search to re-insert visits. We analyse the performance of our method on benchmark problems. We demonstrate that results produced are competitive with Operations Research meta-heuristic methods, indicating that constraint-based technology is directly applicable to vehicle routing problems.

1,172 citations

Journal Article•DOI•
A new optimization algorithm for the vehicle routing problem with time windows

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Martin Desrochers1, Jacques Desrosiers2, Marius M. Solomon3•
École Polytechnique de Montréal1, École Normale Supérieure2, Northeastern University3
01 Apr 1992-Operations Research
TL;DR: This paper presents a new optimization algorithm capable of optimally solving 100-customer problems of the vehicle routing problem with time windows VRPTW and indicates that this algorithm proved to be successful on a variety of practical sized benchmark VRPTw test problems.
Abstract: The vehicle routing problem with time windows VRPTW is a generalization of the vehicle routing problem where the service of a customer can begin within the time window defined by the earliest and the latest times when the customer will permit the start of service. In this paper, we present the development of a new optimization algorithm for its solution. The LP relaxation of the set partitioning formulation of the VRPTW is solved by column generation. Feasible columns are added as needed by solving a shortest path problem with time windows and capacity constraints using dynamic programming. The LP solution obtained generally provides an excellent lower bound that is used in a branch-and-bound algorithm to solve the integer set partitioning formulation. Our results indicate that this algorithm proved to be successful on a variety of practical sized benchmark VRPTW test problems. The algorithm was capable of optimally solving 100-customer problems. This problem size is six times larger than any reported to date by other published research.

1,085 citations

A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows

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Martin Desrochers1, Jacques Desrosiers2, Marius M. Solomon3•
École Polytechnique de Montréal1, École Normale Supérieure2, Northeastern University3
01 Jun 1990
TL;DR: In this paper, the authors present an LP relaxation of the set partitioning formulation of the VRPTW problem, which is solved by column generation, where feasible columns are added as needed by solving a shortest path problem with time windows and capacity constraints using dynamic programming.
Abstract: The vehicle routing problem with time windows VRPTW is a generalization of the vehicle routing problem where the service of a customer can begin within the time window defined by the earliest and the latest times when the customer will permit the start of service. In this paper, we present the development of a new optimization algorithm for its solution. The LP relaxation of the set partitioning formulation of the VRPTW is solved by column generation. Feasible columns are added as needed by solving a shortest path problem with time windows and capacity constraints using dynamic programming. The LP solution obtained generally provides an excellent lower bound that is used in a branch-and-bound algorithm to solve the integer set partitioning formulation. Our results indicate that this algorithm proved to be successful on a variety of practical sized benchmark VRPTW test problems. The algorithm was capable of optimally solving 100-customer problems. This problem size is six times larger than any reported to date by other published research.

992 citations

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Algorithms for the vehicle routing and scheduling problems with time window constraints

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01 Apr 1987-Operations Research
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The Truck Dispatching Problem

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01 Oct 1959-Management Science
George B. Dantzig, J. H. Ramser
A Tabu Search Heuristic for the Vehicle Routing Problem with Soft Time Windows

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01 May 1997-Transportation Science
Éric D. Taillard, Philippe Badeau, Michel Gendreau, François Guertin, Jean-Yves Potvin 
The vehicle routing problem

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01 Jan 2001
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Scheduling of Vehicles from a Central Depot to a Number of Delivery Points

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