Star p-hub median problem with modular arc capacities

Cataloged from PDF version of article.We consider the hub location problem, where p hubs are chosen from a given set of nodes, each nonhub node is connected to exactly one hub and each hub is connected to a central hub. Links are installed on the arcs of the resulting network to route the traffic. The aim is to find the hub locations and the connections to minimize the link installation cost.We propose two formulations and a heuristic algorithm to solve this problem. The heuristic is based on Lagrangian relaxation and local search.We present computational results where formulations are compared and the quality of the heuristic solutions are tested. 2007 Elsevier Ltd. All rights reserved

Park-and-Ride Facilities Design for Special Events Using Space-Time Network Models

abstract: Given that more and more planned special events are hosted in urban areas, during which travel demand is considerably higher than usual, it is one of the most effective strategies opening public rapid transit lines and building park-and-ride facilities to allow visitors to park their cars and take buses to the event sites. In the meantime, special event workforce often needs to make balances among the limitations of construction budget, land use and targeted travel time budgets for visitors. As such, optimizing the park-and-ride locations and capacities is critical in this process of transportation management during planned special event. It is also known as park-and-ride facility design problem. This thesis formulates and solves the park-and-ride facility design problem for special events based on space-time network models. The general network design process with park-and-ride facilities location design is first elaborated and then mathematical programming formulation is established for special events. Meanwhile with the purpose of relax some certain hard constraints in this problem, a transformed network model which the hard park-and-ride constraints are pre-built into the new network is constructed and solved with the similar solution algorithm. In doing so, the number of hard constraints and level of complexity of the studied problem can be considerable reduced in some cases. Through two case studies, it is proven that the proposed formulation and solution algorithms can provide effective decision supports in selecting the locations and capabilities of park-and-ride facilities for special events.Dissertation/ThesisMasters Thesis Civil and Environmental Engineering 201

Comparison of Formulations for the Two-Level Uncapacitated Facility Location Problem with Single Assignment Constraints

International audienceWe consider the two-level uncapacitated facility location problem with single assignment constraints (TUFLP-S), an extension of the uncapacitated facility location problem. We present six mixed-integer programming models for the TUFLP-S based on reformulation techniques and on the relaxation of the integrality of some of the variables associated with location decisions. We compare the models by carrying out extensive computational experiments on large, hard, artificial instances, as well as on instances derived from an industrial application in freight transportation

Multi-level Facility Location Problems

We conduct a comprehensive review on multi-level facility location problems which extend several classical facility location problems and can be regarded as a subclass within the well-established field of hierarchical facility location. We first present the main characteristics of these problems and discuss some similarities and differences with related areas. Based on the types of decisions involved in the optimization process, we identify three different categories of multi-level facility location problems. We present overviews of formulations, algorithms and applications, and we trace the historical development of the field

Valid Inequalities and Facets of the Capacitated Plant Location Problem

Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems.In this paper, we investigate the polyhedral structure of the capacitated plant location problem. Our purpose is to identify facets and valid inequalities for a wide range of capacitated fixed charge problems that contain this prototype problem as a substructure.The first part of the paper introduces a family of facets for a version of the capacitated plant location problem with constant capacity K for all plants. These facet inequalities depend on K and thus differ fundamentally from the valid inequalities for the uncapacitated version of the problem. We also introduce a second formulation for a model with indivisible customer demand and show that it is equivalent to a vertex packing problem on a derived graph. We identify facets and valid inequalities for this version of the problem by applying known results for the vertex packing polytope

A New Dantzig-Wolfe Reformulation And Branch-And-Price Algorithm For The Capacitated Lot Sizing Problem With Set Up Times

The textbook Dantzig-Wolfe decomposition for the Capacitated LotSizing Problem (CLSP),as already proposed by Manne in 1958, has animportant structural deficiency. Imposingintegrality constraints onthe variables in the full blown master will not necessarily givetheoptimal IP solution as only production plans which satisfy theWagner-Whitin condition canbe selected. It is well known that theoptimal solution to a capacitated lot sizing problem willnotnecessarily have this Wagner-Whitin property. The columns of thetraditionaldecomposition model include both the integer set up andcontinuous production quantitydecisions. Choosing a specific set upschedule implies also taking the associated Wagner-Whitin productionquantities. We propose the correct Dantzig-Wolfedecompositionreformulation separating the set up and productiondecisions. This formulation gives the samelower bound as Manne'sreformulation and allows for branch-and-price. We use theCapacitatedLot Sizing Problem with Set Up Times to illustrate our approach.Computationalexperiments are presented on data sets available from theliterature. Column generation isspeeded up by a combination of simplexand subgradient optimization for finding the dualprices. The resultsshow that branch-and-price is computationally tractable andcompetitivewith other approaches. Finally, we briefly discuss how thisnew Dantzig-Wolfe reformulationcan be generalized to other mixedinteger programming problems, whereas in theliterature,branch-and-price algorithms are almost exclusivelydeveloped for pure integer programmingproblems.branch-and-price;Lagrange relaxation;Dantzig-Wolfe decomposition;lot sizing;mixed-integer programming

Lagrangian Relaxation for q-Hub Arc Location Problems

The topic of this Master thesis is an in-depth research study on a specific type of network systems known as hub-and-spoke networks. In particular, we study q-Hub Arc Location Problems that consist, at a strategical level, of selecting q hub arcs and at most p hub nodes, and of the routing of commodities through the so called hub level network. We propose strong formulations to two variants of the problem, namely the q-hub arc location problem and the $q$-hub arc location problem with isolated hub nodes. We present a Lagrangian relaxation that exploits the structure of these problems by decomposing them into |K|+2 independent easy-to-solve subproblems and develop Lagrangian heuristics that yield high quality feasible solutions to both models. We, further, provide some insights on the structure of the optimal solutions to both models and investigate the cost benefit of incomplete hub networks with and without isolated hub nodes. Finally, computational results on a set of benchmark instances with up to 100 nodes are reported to assess the performance of the proposed MIP formulations and of our algorithmic approach

Location models in the public sector

The past four decades have witnessed an explosive growth in the field of networkbased facility location modeling. This is not at all surprising since location policy is one of the most profitable areas of applied systems analysis in regional science and ample theoretical and applied challenges are offered. Location-allocation models seek the location of facilities and/or services (e.g., schools, hospitals, and warehouses) so as to optimize one or several objectives generally related to the efficiency of the system or to the allocation of resources. This paper concerns the location of facilities or services in discrete space or networks, that are related to the public sector, such as emergency services (ambulances, fire stations, and police units), school systems and postal facilities. The paper is structured as follows: first, we will focus on public facility location models that use some type of coverage criterion, with special emphasis in emergency services. The second section will examine models based on the P-Median problem and some of the issues faced by planners when implementing this formulation in real world locational decisions. Finally, the last section will examine new trends in public sector facility location modeling.Location analysis, public facilities, covering models

An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging

This paper proposes two new mixed integer programming models for capacitated multi-level lot-sizing problems with backlogging, whose linear programming relaxations provide good lower bounds on the optimal solution value. We show that both of these strong formulations yield the same lower bounds. In addition to these theoretical results, we propose a new, effective optimization framework that achieves high quality solutions in reasonable computational time. Computational results show that the proposed optimization framework is superior to other well-known approaches on several important performance dimensions

Primal-dual variable neighborhood search for the simple plant-location problem

Copyright @ 2007 INFORMSThe variable neighborhood search metaheuristic is applied to the primal simple plant-location problem and to a reduced dual obtained by exploiting the complementary slackness conditions. This leads to (i) heuristic resolution of (metric) instances with uniform fixed costs, up to n = 15,000 users, and m = n potential locations for facilities with an error not exceeding 0.04%; (ii) exact solution of such instances with up to m = n = 7,000; and (iii) exact solutions of instances with variable fixed costs and up to m = n = 15, 000.This work is supported by NSERC Grant 105574-02; NSERC Grant OGP205041; and partly by the Serbian Ministry of Science, Project 1583