The period routing problem

Christofides, Nicos; Beasley, John E.

doi:10.1002/net.3230140205

Cited by 283 publications

(201 citation statements)

References 10 publications

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“…Of course, simulated annealing was used for solving vehicle routing problems in the past. In particular, Chiang and Russell (1996) describe a simulated annealing where the neighborhood is defined by the -interchange mechanism of Osman (1993) and the k-node interchange mechanism of Christofides and Beasley (1984). The algorithm in Chiang and Russell (1996) makes use of a tabu list within the simulated annealing process and uses a weighted objective function incorporating total time along with number of vehicles and travel cost.…”

Section: Discussion and Related Workmentioning

confidence: 99%

A Two-Stage Hybrid Local Search for the Vehicle Routing Problem with Time Windows

Bent

Hentenryck

2004

Transportation Science

270

148

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pvh@csbrown.edu} T he vehicle routing problem with time windows is a hard combinatorial optimization problem that has received considerable attention in the last decades. This paper proposes a two-stage hybrid algorithm for this transportation problem. The algorithm first minimizes the number of vehicles, using simulated annealing. It then minimizes travel cost by using a large neighborhood search that may relocate a large number of customers. Experimental results demonstrate the effectiveness of the algorithm, which has improved 10 (17%) of the 56 best published solutions to the Solomon benchmarks, while matching or improving the best solutions in 46 problems (82%). More important perhaps, the algorithm is shown to be very robust. With a fixed configuration of its parameters, it returns either the best published solutions (or improvements thereof) or solutions very close in quality on all Solomon benchmarks. Very preliminary results on the extended Solomon benchmarks are also given. IntroductionVehicle routing problems are important components of many distribution and transportation systems, including such examples as bank deliveries, postal deliveries, school bus routing, and security patrol services. They have received considerable attention in the past decades. This paper considers the vehicle routing problem with time windows (VRPTW). Given a number of customers with known demands and a fleet of identical vehicles with known capacities, the problem consists of finding a set of routes originating and terminating at a central depot and servicing all the customers exactly once. The routes cannot violate the capacity constraints on the vehicles and, in addition, must meet the time windows of the customers, which specify the earliest and latest times for the start of service at a customer site. A standard objective of the VRPTW problem consists of minimizing the number of routes or vehicles (primary criterion) and the total travel cost (secondary criterion). Other objective functions have been considered in various papers; for example, optimality results often focus only on the second criterion. The VRPTW problem is NP-complete (Lenstra and Rinnooy Kan 1981), and instances involving 100 customers or more are very hard to solve optimally. Indeed, very few of the Solomon benchmarks (Solomon 1987) involving 100 customers have been solved optimally (see Fisher et al. 1997 andKohl et al. 1999 for some recent results). As a consequence, local search techniques are often used to find good solutions in reasonable time.Early work in local search on the VRPTW often utilized simple heuristics or metaheuristics, and an excellent summary can be found in Gendreau et al. (1997). In recent years, the focus of local search has shifted to more complicated metaheuristics to increase the power of the earlier techniques. These include simulated annealing (Chiang and Russell 1996), tabu search (Chiang and Russell 1997, Cordeau et al. 2001, De Backer et al. 2000, Rochat and Taillard 1995, Taillard et al. 1997, genetic/evolutionary al...

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Section: Discussion and Related Workmentioning

confidence: 99%

A Two-Stage Hybrid Local Search for the Vehicle Routing Problem with Time Windows

Bent

Hentenryck

2004

Transportation Science

270

148

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“…Other heuristics are developed by Christofides and Beasley (1984), Tan and Beasley (1984) and Russel and Gribbin (1991). Gaudioso and Paletta (1992) present a heuristic for the PVRP with the objective to minimize the number of vehicles.…”

Section: Introductionmentioning

confidence: 99%

A variable neighborhood search heuristic for periodic routing problems

Hemmelmayr

Doerner

Hartl

2009

European Journal of Operational Research

247

119

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The aim of this paper is to propose a new heuristic for the Periodic Vehicle Routing Problem (PVRP) without time windows. The PVRP extends the classical Vehicle Routing Problem to a planning horizon of several days. Each customer requires a certain number of visits within this time horizon while there is some flexibility on the exact days of the visits. Hence, one has to choose the visit days for each customer and to solve a VRP for each day. Our method is based on Variable Neighborhood Search (VNS). Computational results are presented, that show that our approach is competitive and even outperforms existing solution procedures proposed in the literature. Also considered is the special case of a single vehicle, i.e. the Periodic Traveling Salesman Problem (PTSP). It is shown that slight changes of the proposed VNS procedure is also competitive for the PTSP.

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“…However, unlike in the classical PVRP the visit frequency is not fixed, but is a decision of the model. The problem was solved through a heuristic based on the method proposed by Christofides and Beasley (1984): First initial frequencies and visit day-combinations are assigned to the points, followed by an interchange procedure that tries to find better visit day-combinations. These concepts are further developed by Francis et al (2006) who proposed an extension of the PVRP, called PVRP with Service Choice (PVRP-SC) motivated by an applications arising in interlibrary loan delivery services.…”

Section: Related Workmentioning

confidence: 99%

Models and Algorithms for the Integrated Planning of Bin Allocation and Vehicle Routing in Solid Waste Management

Hemmelmayr

Doerner

Hartl

et al. 2014

Transportation Science

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The efficient organization of waste collection systems based on bins located along the streets involves the solution of several tactical optimization problems. In particular, the bin configuration and sizing at each collection site as well as the service frequency over a given planning horizon have to be decided. In this context, a higher service frequency leads to higher routing costs, but at the same time less or smaller bins are required which lead to lower bin allocation investment costs. The bins used have different types and different costs and there is a limit on the space at each collection site as well as a limit on the total number of bins of each type that can be used. In this paper we consider the problem of designing a collection system consisting in the combination of a vehicle routing and a bin allocation problem in which the trade-off between the associated costs has to be considered. The solution approach combines an effective VNS metaheuristic for the routing part with a MILP-based exact method for the solution of the bin allocation part. We propose hierarchical solution procedures in which the two decision problems are solved in sequence, as well as an integrated approach where the two problems are considered simultaneously. Extensive computational testing on synthetic and real-world instances with hundreds of collection sites show the benefit of the integrated approaches with respect to the hierarchical ones.

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The period routing problem

Cited by 283 publications

References 10 publications

A Two-Stage Hybrid Local Search for the Vehicle Routing Problem with Time Windows

A Two-Stage Hybrid Local Search for the Vehicle Routing Problem with Time Windows

A variable neighborhood search heuristic for periodic routing problems

Models and Algorithms for the Integrated Planning of Bin Allocation and Vehicle Routing in Solid Waste Management

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