Cumulative Vehicle Routing Problems

Kadri, Muhammad Bilal

doi:10.5772/5812

Cited by 43 publications

(41 citation statements)

References 33 publications

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“…Recently, with an increasing concern for the environment, new vehicle routing models started being considered, where the objective was not only to take into account the travel costs or distances but also energy consumption and greenhouse gas emissions; see, for instance, Kara, Kara, and Yetiş (2008); Bektaş and Laporte (2011); Lysgaard and Wøhlk (2014) and a recent survey by Demir, Bektaş, and Laporte (2014).…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, the existing approach for solving the EMVRP exactly was based on an MILP model that was able to solve only small-size instances with up to 31 customers (Kara, Kara, and Yetiş 2008). A constant-factor approximation algorithm was developed in Gaur, Mudgal, and Singh (2013), and local search algorithms and metaheuristics (Kramer et al 2015;Zachariadis, Tarantilis, and Kiranoudis 2015) were also applied to solve the EMVRP.…”

Section: Introductionmentioning

confidence: 99%

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A Branch-Cut-and-Price Algorithm for the Energy Minimization Vehicle Routing Problem

Fukasawa

Song

2016

Transportation Science

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W e study a variant of the capacitated vehicle routing problem where the cost over each arc is defined as the product of the arc length and the weight of the vehicle when it traverses that arc. We propose two new mixed-integer linear programming formulations for the problem: an arc-load formulation and a set partitioning formulation based on q-routes with additional constraints. A family of cycle elimination constraints are derived for the arc-load formulation. We then compare the linear programming (LP) relaxations of these formulations with the two-index one-commodity flow formulation proposed in the literature. In particular, we show that the arc-load formulation with the new cycle elimination constraints gives the same LP bound as the set partitioning formulation based on 2-cycle-free q-routes, which is stronger than the LP bound given by the two-index one-commodity flow formulation. We propose a branch-and-cut algorithm for the arc-load formulation, and a branch-cut-and-price algorithm for the set partitioning formulation strengthened by additional constraints. Computational results on instances from the literature demonstrate that a significant improvement can be achieved by the branch-cut-and-price algorithm over other methods.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Branch-Cut-and-Price Algorithm for the Energy Minimization Vehicle Routing Problem

Fukasawa

Song

2016

Transportation Science

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“…Kara et al [42] tackle another vehicle routing problem that they call cumulative VRP. They explain that the cost of a route is not adequately represented by the distance between nodes.…”

Section: Context and Problems Related To The Mt-ccvrpmentioning

confidence: 99%

A multistart iterated local search for the multitrip cumulative capacitated vehicle routing problem

2014

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The multitrip cumulative capacitated vehicle routing problem (mt-CCVRP) is a non-trivial extension of the classical CVRP: the goal is to minimize the sum of arrival times at demand nodes and each vehicle may perform several trips. Applications of this NP-hard problem can be found in disaster logistics and maintenance operations. Contrary to the CVRP, the cost of a solution varies if a trip is reversed or if its rank in a multitrip is changed. Moreover, evaluating local search moves in constant time is not obvious. This article presents a mixed integer linear program (MILP), a dominance rule, and a hybrid metaheuristic: a multi-start iterated local search (MS-ILS) calling a variable neighborhood descent with O(1) move evaluations. On three sets of instances, MS-ILS obtains good solutions, not only on the mt-CCVRP, but also on the cumulative CVRP where it competes with four existing algorithms. Moreover, the metaheuristic retrieves the optimal solutions of the MILP, which can be computed for small instances using a commercial solver.

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“…Therefore, the minimum latency VRP is the minimization of the sum of the latency of each request. This problem is classified as cumulative, because the request's cost accumulates until it is serviced [8]. It is typically called the TRP, because the repairman needs to minimize the time to service all of the requests (which is dependent on how long until he gets to the location).…”

Section: B Minimum Latency Vrpmentioning

confidence: 99%

VRP with Minimum Delivery Latency Using Linear Programming

Sabo

Kumar

Cohen

et al. 2012

Infotech@Aerospace 2012

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Vehicle Routing Problems (VRPs) concern allocating multiple vehicles to service requests with routes that start and end at a depot, visit all requests, and minimize some operational cost. Many UAV situations can be modeled in a manner that represents tasks to be accomplished by service requests and UAVs as agents that fulfill these requests. Often, communications are restricted by available power, data rate, noise margins, and cost. These constraints cause information gathered at request locations to be delivered only when the UAV returns to the "depot." In other words, UAVs must be allocated to services requests and then deliver information gathered at the request location to a communication range to be able to transmit information back to a command and control HQ. Because of limited communication ranges which result from limited power onboard small UAVs, information is not delivered until the UAV returns to the depot. Research on similar problems show some related work on minimizing the latency of the pickup of requests but not the delivery. This work attempts to study the VRP with minimum delivery latency and formulate a Linear Programming (LP) solution. The objective function is shown to be nonlinear, but it can belinearized at a cost: many new variables are added to linearize it. This in turn, makes the problem intractable, and only solutions to small problems are obtained. Nomenclature N = Number of Requests M = Number of Vehicles R = Number of Tours i, j = Request Indices r = Trip Index k = Vehicle Index = Arrival time of request i = Pickup time of request i = Delivery time of request i

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Cumulative Vehicle Routing Problems

Cited by 43 publications

References 33 publications

A Branch-Cut-and-Price Algorithm for the Energy Minimization Vehicle Routing Problem

A Branch-Cut-and-Price Algorithm for the Energy Minimization Vehicle Routing Problem

A multistart iterated local search for the multitrip cumulative capacitated vehicle routing problem

VRP with Minimum Delivery Latency Using Linear Programming

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