Integer programming formulations of vehicle routing problems

Kulkarni, R.V.; Bhave, Pramod R.

doi:10.1016/0377-2217(85)90284-x

Cited by 162 publications

(63 citation statements)

References 22 publications

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“…(i) every vehicle starts and ends its trip in the same depot, (ii) every client is attended by a single one vehicle once only, (iii) the total demand of every route does not exceed the vehicle capacity and (iv) the routes traveled are minimized (Montoya et al, 2015). Kulkarni and Bhave (1985) propose a three-index mathematical model that requires the definition of a binary decision variable xijk that takes the value of "1" when two nodes i and j are in the vehicle route k and take the "0" value otherwise. The model is formulated as a generalized TSP problem.…”

Section: Momdvrp Proposed Modelmentioning

confidence: 99%

See 1 more Smart Citation

Multi-objective MDVRP solution considering route balance and cost using the ILS metaheuristic

Galindres-Guancha¹,

Toro-Ocampo²,

Rendón³

2018

10.5267/j.ijiec

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The multi-objective problem of multi-depot vehicle routing (MOMDVRP) is proposed by considering the minimization of the traveled arc costs and the balance of routes. Seven mathematical models were reviewed to determine the route balance equation and the bestperforming model is selected for this purpose. The solution methodology consists of three stages; in the first one, beginning solutions are built up by means of a constructive heuristic. In the second stage, fronts are constructed from each starting solution using the iterated local search multi-objective metaheuristics (ILSMO). In the third stage, we obtain a single front by using concepts of dominance, taking as a base the fronts of the previous stage. Thus, the first two fronts are taken and a single front is formed that corresponds to the current solution of the problem; next the third front is added to the current Pareto front of the problem, the procedure is repeated until exhaustion of the list of the fronts initially obtained. The resulting front is the solution to the problem. To validate the methodology we use instances from the specialized literature, which have been used for the multi-depot routing problem (MDVRP). The results obtained provide very good quality. Finally, decision criteria are used to select the most appropriate solution for the front, both from the point of view of the balance and the route cost.

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Section: Momdvrp Proposed Modelmentioning

confidence: 99%

“…In the case of the exact-technique approach, the MDVRP is formulated as a Mixed-Integer Linear Programming (MILP) problem, as described by Kulkarni and Bhave (1985) and Montoya et al (2015). However, these techniques converge into optimal solutions for small-size problems (less than 50 clients).…”

Section: Introductionmentioning

confidence: 99%

Multi-objective MDVRP solution considering route balance and cost using the ILS metaheuristic

Galindres-Guancha¹,

Toro-Ocampo²,

Rendón³

2018

10.5267/j.ijiec

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show abstract

“…Constraints (7d) ensure that the duration of a tour doesn't exceed a predefined amount. Separate sub-tour elimination constraints are not necessary since the calculation of arrival times (constraints 7a-d) provide comparable functionality as node-potential-based sub-tour elimination constraints, initially proposed by [30] for the Traveling Salesman Problem and used by [22] for the Multi-Depot Vehicle Routing Problem. Constraints (8) impose binary values for the flow variables ‫ݔ‬ ௧ .…”

Section: The Field Service Scheduling With Priorities Problemmentioning

confidence: 99%

On the impact of real-time information on field service scheduling

Petrakis

Hass

Bichler

2012

Decision Support Systems

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Mobile phone operators need to plan and schedule field force personnel for maintenance and repair tasks on mobile phone base stations across the country on a daily basis. In this paper, we will introduce the field force scheduling problem with priorities. Motivated by the rising popularity of mobile field force management solutions, we compare online and offline heuristics as well as hybrids to solve the problem. The results help understand the benefits of dynamic scheduling based on realtime position information as compared to traditional daily offline planning.

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“…CVRP formulations are the formulation of Kara and Bektas (2005), two formulations of Baldacci et al (2004) (one is multi-commodity flow formulation and the other is two-commodity flow formulation), and the formulation of Waters (1988). DCVRP formulations are the two formulations of Kara and Derya (2011) (one is node-based and the other is arc-based formulation), and the formulation of Kulkarni and Bhave (1985). Since we are interested in the formulations of the CVRP, we ignored the distance constraints and used only the capacity constraints in the DCVRP formulations.…”

Section: The Numerical Application Of the Proposed Modelmentioning

confidence: 99%

“…Since we are interested in the formulations of the CVRP, we ignored the distance constraints and used only the capacity constraints in the DCVRP formulations. In this study, considered formulations are given with their abbreviations in the following: The Formulation of Kulkarni and Bhave (1985) Kara and Bektaş (2005): KABE.…”

Section: The Numerical Application Of the Proposed Modelmentioning

confidence: 99%

A Comparative Study of the Capability of Alternative Mixed Integer Programming Formulations

Keçeci

Derya

Dinler

et al. 2017

Technological and Economic Development of Economy

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Abstract. In selecting the best mixed integer linear programming (MILP) formulation the important issue is to figure out how to evaluate the performance of each candidate formulation in terms of selected criteria. The main objective of this study is to propose a systematic approach to guide the selection of the best MILP formulation among the alternatives according to the needs of the decision maker. For this reason we consider the problem of "selecting the most appropriate MILP formulation for a certain type of decision maker" as a multi-criteria decision making problem and present an integrated AHP-TOPSIS decision making methodology to select the most appropriate formulation. As an example the proposed decision making methodology is implemented on the selection of the MILP formulations of the Capacitated Vehicle Routing Problem (CVRP). A numerical example is provided for illustrative purposes. As a result, the proposed decision model can be a tool for the decision makers (here they are the scientists, engineers and practitioners) who intend to choose the appropriate mathematical model(s) among the alternatives according to their needs on their studies. The integrated AHP-TOPSIS approach can simply be incorporated into a computer-based decision support system since it has simplicity in both computation and application.

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Integer programming formulations of vehicle routing problems

Cited by 162 publications

References 22 publications

Multi-objective MDVRP solution considering route balance and cost using the ILS metaheuristic

Multi-objective MDVRP solution considering route balance and cost using the ILS metaheuristic

On the impact of real-time information on field service scheduling

A Comparative Study of the Capability of Alternative Mixed Integer Programming Formulations

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