Search results for "Branch-and-cut algorithm"

showing 4 items of 4 documents

The stacker crane problem and the directed general routing problem

2015

[EN] This article deals with the polyhedral description and the resolution of the directed general routing problem (DGRP) and the stacker crane problem (SCP). The DGRP contains a large number of important arc and node routing problems as special cases, including the SCP. Large families of facet-defining inequalities for the DGRP are described and a branch-and-cut algorithm for these problems is presented. Extensive computational experiments over different sets of DGRP and SCP instances are included.

Mathematical optimizationDirected general routing problemStacker crane problemComputer Networks and CommunicationsStackerNode (networking)Branch-and-cut algorithmDirected graphResolution (logic)Directed rural postman problemHardware and ArchitectureRouting (electronic design automation)MATEMATICA APLICADASoftwareInformation SystemsMathematics
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A branch-and-cut algorithm for the Team Orienteering Problem

2017

The Team Orienteering Problem aims at maximizing the total amount of profit collected by a fleet of vehicles while not exceeding a predefined travel time limit on each vehicle. In the last years, several exact methods based on different mathematical formulations were proposed. In this paper, we present a new two-index formulation with a polynomial number of variables and constraints. This compact formulation, reinforced by connectivity constraints, was solved by means of a branch-and-cut algorithm. The total number of instances solved to optimality is 327 of 387 benchmark instances, 26 more than any previous method. Moreover, 24 not previously solved instances were closed to optimality.

branch-and-cut algorithm; Team Orienteering Problem; two-index mathematical formulation; Computer Science Applications1707 Management Science and Operations Research;0209 industrial biotechnologyMathematical optimization021103 operations researchStrategy and Management0211 other engineering and technologiesOrienteering02 engineering and technologyManagement Science and Operations ResearchComputer Science Applicationstwo-index mathematical formulationTravel timeComputer Science Applications1707 Management Science and Operations Research020901 industrial engineering & automationManagement of Technology and InnovationBenchmark (computing)Limit (mathematics)branch-and-cut algorithmTeam Orienteering ProblemBusiness and International ManagementBranch and cutAlgorithmPolynomial numberMathematics
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Formulations for an inventory routing problem

2014

In this paper, we present and compare formulations for the inventory routing problem (IRP) where the demand of customers has to be served, over a discrete time horizon, by capacitated vehicles starting and ending their routes at a depot. The objective of the IRP is the minimization of the sum of inventory and transportation costs. The formulations include known and new mathematical programming formulations. Valid inequalities are also presented. The formulations are tested on a large set of benchmark instances. One of the most significant conclusions is that the formulations that use vehicle-indexed variables are superior to the more compact, aggregate formulations.

Inventory routing problemMathematical optimizationSupply chain managementRouting problemsComputer scienceStrategy and ManagementAggregate (data warehouse)Branch-and-cut algorithmInteger programmingManagement Science and Operations ResearchComputer Science ApplicationsDiscrete time and continuous timeManagement of Technology and InnovationBenchmark (computing)MinificationBusiness and International ManagementInteger programmingSupply chain managementInternational Transactions in Operational Research
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A branch-and-cut algorithm for the Profitable Windy Rural Postman Problem

2016

[EN] In this paper we study the profitable windy rural postman problem. This is an arc routing problem with profits defined on a windy graph in which there is a profit associated with some of the edges of the graph, consisting of finding a route maximizing the difference between the total profit collected and the total cost. This problem generalizes the rural postman problem and other well-known arc routing problems and has real-life applications, mainly in snow removal operations. We propose here a formulation for the problem and study its associated polyhedron. Several families of facet-inducing inequalities are described and used in the design of a branch-and-cut procedure. The algorithm…

Arc routingMathematical optimizationInformation Systems and ManagementGeneral Computer ScienceTotal costSnow removal0211 other engineering and technologies02 engineering and technologyManagement Science and Operations ResearchIndustrial and Manufacturing EngineeringProfit (economics)Polyhedron0502 economics and businessWindy rural postman problemMathematics050210 logistics & transportation021103 operations research05 social sciencesBranch-and-cut algorithmModeling and SimulationMATEMATICA APLICADAArc routingAlgorithmBranch and cutPolyhedronProfits
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