An Integer L-shaped Method for the Generalized Vehicle Routing Problem with Stochastic Demands

Biesinger, Benjamin; Hu, Bin; Raidl, Günther R.

doi:10.1016/j.endm.2016.03.033

Cited by 17 publications

(13 citation statements)

References 8 publications

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“…To evaluate the developed algorithm a computational study is performed. We rely on a set of 158 benchmark instances for the GVRPSD (https://www.ac.tuwien.ac.at/research/ problem-instances/#Generalized_Vehicle_Routing_Problem_with_Stochastic_Demands), which is also used by Biesinger et al (2015c) and Biesinger et al (2015b). These instances are based on (deterministic) instances for the generalized vehicle routing problem generated by Bektaş et al (2011).…”

Section: Computational Resultsmentioning

confidence: 99%

“…As the generalized vehicle routing problem with stochastic demands is a relatively new variant of a VRP, there is not much specific literature available yet. It was introduced by Biesinger et al (2015b,c) who presented an initial attempt to solve small instances of the problem with up to 40 nodes and 14 clusters exactly by using an integer L-shaped method (Biesinger et al 2015b) and a variable neighborhood search to tackle larger instances with up to 101 nodes and 34 clusters (Biesinger et al 2015c). The authors also presented a multi-level evaluation scheme which significantly reduces the time needed for the solution evaluations.…”

Section: Literature Surveymentioning

confidence: 99%

“…To the best of our knowledge there is no exact algorithm described for the VRPSD with preventive restocking. However, the L-shaped method for the GVRPSD with preventive restocking from Biesinger et al (2015b) can also be used to solve the non-generalized version. Several authors developed metaheuristics.…”

Section: Literature Surveymentioning

confidence: 99%

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A Genetic Algorithm in Combination with a Solution Archive for Solving the Generalized Vehicle Routing Problem with Stochastic Demands

Biesinger

Raidl

2018

Transportation Science

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This work presents a steady-state genetic algorithm enhanced by a complete trie-based solution archive for solving the generalized vehicle routing problem with stochastic demands using a preventive restocking strategy. As the necessary dynamic programming algorithm for the solution evaluation is very time consuming, considered candidate solutions are stored in the solution archive. It acts as complete memory of the search history, avoids re-evaluations of duplicate solution candidates and is able to efficiently transform them into guaranteed new ones. This increases the diversity of the population and reduces the risk of premature convergence. Similar to a branch-and-bound algorithm, the tree structure of the solution archive is further exploited to compute lower bounds on the nodes to cut off parts of the solution space which evidently do not contain good solutions. Since in each iteration a not yet considered solution candidate is generated and completeness can be efficiently checked, the overall method is in principle an exact enumeration algorithm, which leads to guaranteed optimal solutions for smaller instances. Computational results of this algorithm show the superiority over the so far state-of-the-art metaheuristic.

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Section: Computational Resultsmentioning

confidence: 99%

Section: Literature Surveymentioning

confidence: 99%

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A Genetic Algorithm in Combination with a Solution Archive for Solving the Generalized Vehicle Routing Problem with Stochastic Demands

Biesinger

Raidl

2018

Transportation Science

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“…Some small-scale instances (such as with no more than 60 customers) can be solved by the exact algorithms with good performance, e.g. the Branch-and-cut algorithms [20], the column generation [21], the branch and cut and price [22], the branch-and-price [23], the bidirectional labeling algorithms [24] and the L-shaped method [25]. However, exact algorithms spend too much time in solving large-sized (with more than 100 customers) and medium-sized problem (with customers ranging from 60 to 100), even cannot obtain solutions within acceptable time (within 2h).…”

Section: Literature Reviewmentioning

confidence: 99%

Last Mile Delivery With Stochastic Travel Times Considering Dual Services

Zhou

2019

IEEE Access

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Nowadays there are two prevailing delivery modes in the last mile delivery; one is the home delivery (HD) that vehicles deliver parcels to customers' homes; and the other is the customers' pickup (CP) that vehicle deliver parcels to some kind of intelligent express boxes where customers can pick up their parcels with free time. This article studies a green vehicle routing problem considering dual services (HD and CP) with stochastic travel times (GVRP-DS-STT) to provide customers with sustainable and diversified delivery services. The GVRP-DS-STT problem is formulated as a two-stage stochastic optimization model with recourse strategy. The purpose of the model is to minimize the total operational cost under stochastic environment. In addition, a two-stage heuristic algorithm integrating with a sampling strategy is developed to solve approximately the problem, the first of which is the greedy-based initial feasible solution generation, and the second of which is an improvement heuristic with late acceptance to explore the solution space. The computational results show that there are increasing benefit in terms of total operational cost, number of the vehicles used and loading rate with the increase of percentage of CP customers. The time windows have great effect on the operational cost, but more CP customers can reduce their impact. The stochastic model outperforms the deterministic model in terms of total operational cost. INDEX TERMS Green vehicle routing problem, stochastic travel times, dual services, sample average approximation sampling, hybrid heuristics.

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“…The GVRP was introduced by Ghiani and Improta (20 0 0) and it is another generalization of the VRP in which the set of delivery locations is partitioned into clusters and exactly one location from each cluster has to be visited in a solution. Despite its relatively recent introduction, the GVRP has already attracted the attention of many researchers, in part because it has many real-life applications ( Baldacci et al, 2010;Bektas et al, 2011;Kovacs et al, 2014;Afsar et al, 2014;Quttineh et al, 2015;Biesinger et al, 2016;Louati et al, 2016 ).…”

Section: Introductionmentioning

confidence: 99%

A branch-and-price algorithm for the vehicle routing problem with roaming delivery locations

Özbaygın

Karaşan

Savelsbergh

et al. 2017

Transportation Research Part B: Methodological

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We study the vehicle routing problem with roaming delivery locations in which the goal is to find a least-cost set of delivery routes for a fleet of capacitated vehicles and in which a customer order has to be delivered to the trunk of the customer's car during the time that the car is parked at one of the locations in the (known) customer's travel itinerary. We formulate the problem as a set-covering problem and develop a branch-and-price algorithm for its solution. The algorithm can also be used for solving a more general variant in which a hybrid delivery strategy is considered that allows a delivery to either a customer's home or to the trunk of the customer's car. We evaluate the effectiveness of the many algorithmic features incorporated in the algorithm in an extensive computational study and analyze the benefits of these innovative delivery strategies. The computational results show that employing the hybrid delivery strategy results in average cost savings of nearly 20% for the instances in our test set.

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An Integer L-shaped Method for the Generalized Vehicle Routing Problem with Stochastic Demands

Cited by 17 publications

References 8 publications

A Genetic Algorithm in Combination with a Solution Archive for Solving the Generalized Vehicle Routing Problem with Stochastic Demands

A Genetic Algorithm in Combination with a Solution Archive for Solving the Generalized Vehicle Routing Problem with Stochastic Demands

Last Mile Delivery With Stochastic Travel Times Considering Dual Services

A branch-and-price algorithm for the vehicle routing problem with roaming delivery locations

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