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Lifted Flow Cover Inequalities for Mixed 01 Integer Programs
 Mathematical Programming
, 1996
"... We investigate strong inequalities for mixed 01 integer programs derived from flow cover inequalities. Flow cover inequalities are usually not facet defining and need to be lifted to obtain stronger inequalities. However, because of the sequential nature of the standard lifting techniques and the c ..."
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Cited by 34 (8 self)
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We investigate strong inequalities for mixed 01 integer programs derived from flow cover inequalities. Flow cover inequalities are usually not facet defining and need to be lifted to obtain stronger inequalities. However, because of the sequential nature of the standard lifting techniques and the complexity of the optimization problems that have to be solved to obtain lifting coefficients, lifting of flow cover inequalities is computationally very demanding. We present a computationally efficient way to lift flow cover inequalities based on sequence independent lifting techniques and computational results that justify the effectiveness of our lifting procedures. 1 Introduction A mixed integer program (MIP) with binary integer variables (BMIP) is the appropriate mathematical model for many practical optimization problems. This model is used, for example, for facility location problems, distribution problems, network design problems and more generally when fixed or concave costs are re...
Facility location models for distribution system design
, 2004
"... The design of the distribution system is a strategic issue for almost every company. The problem of locating facilities and allocating customers covers the core topics of distribution system design. Model formulations and solution algorithms which address the issue vary widely in terms of fundamenta ..."
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Cited by 33 (0 self)
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The design of the distribution system is a strategic issue for almost every company. The problem of locating facilities and allocating customers covers the core topics of distribution system design. Model formulations and solution algorithms which address the issue vary widely in terms of fundamental assumptions, mathematical complexity and computational performance. This paper reviews some of the contributions to the current stateoftheart. In particular, continuous location models, network location models, mixedinteger programming models, and applications are summarized.
Capacitated facility location: separation algorithms and computational experience
 Mathematical Programming
, 1998
"... We consider the polyhedral approach to solving the capacitated facility location problem. The valid inequalities considered are the knapsack, flow cover, effective capacity, single depot, and combinatorial inequalities. The flow cover, effective capacity, and single depot inequalities form subfamili ..."
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Cited by 20 (2 self)
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We consider the polyhedral approach to solving the capacitated facility location problem. The valid inequalities considered are the knapsack, flow cover, effective capacity, single depot, and combinatorial inequalities. The flow cover, effective capacity, and single depot inequalities form subfamilies of the general family of submodular inequalities. The separation problem based on the family of submodular inequalities is NPhard in general. For the wellknown subclass of flow cover inequalities, however, we show that if the client set is fixed, and if all capacities are equal, then the separation problem can be solved in polynomial time. For the flow cover inequalities based on an arbitrary client set, and for the effective capacity and single depot inequalities we develop separation heuristics. An important part of all these heuristic is based on constructive proofs that two specific conditions are necessary for the effective capacity inequalities to be facet defining. The proofs show precisely how structures that violate the two conditions can be modified to produce stronger inequalities. The family of combinatorial inequalities was originally developed for the uncapacitated facility location problem, but is also valid for the capacitated problem. No computational experience using the combinatorial inequalities has been reported so far. Here we suggest how partial output from the heuristic identifying violated submodular inequalities can be used as input to a heuristic identifying violated combinatorial inequalities. We report on computational results from solving 60 small and medium size problems.
Planning Models for LongHaul Operations of Postal and Express Shipment Companies
, 1999
"... Postal and express shipment companies face the task to provide service between a ..."
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Cited by 11 (0 self)
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Postal and express shipment companies face the task to provide service between a
Stochastic pRobust Location Problems
, 2004
"... Many objectives have been proposed for optimization under uncertainty. The typical stochastic programming objective of minimizing expected cost may yield solutions that are inexpensive in the long run but perform poorly under certain realizations of the random data. On the other hand, the typical ro ..."
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Cited by 8 (3 self)
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Many objectives have been proposed for optimization under uncertainty. The typical stochastic programming objective of minimizing expected cost may yield solutions that are inexpensive in the long run but perform poorly under certain realizations of the random data. On the other hand, the typical robust optimization objective of minimizing maximum cost or regret tends to be overly conservative, planning against a disastrous but unlikely scenario. In this paper, we present facility location models that combine the two objectives by minimizing the expected cost while bounding the relative regret in each scenario. In particular, the models seek the minimumexpectedcost solution that is probust; i.e., whose relative regret is no more than 100p% in each scenario.
A Survey of Optimization Models for LongHaul Freight Transportation
, 1998
"... We present the main freight transportation planning and management issues, briefly review the associated literature, describe a number of major developments, and identify trends and challenges. In order to keep the length of the paper within reasonable limits, we focus on longhaul, intercity, freig ..."
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Cited by 4 (0 self)
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We present the main freight transportation planning and management issues, briefly review the associated literature, describe a number of major developments, and identify trends and challenges. In order to keep the length of the paper within reasonable limits, we focus on longhaul, intercity, freight transportation. Optimizationbased operations research methodologies are privileged. The paper starts with an overview of freight transportation systems and planning issues and continues with models which attempt to analyze multimodal, multicommodity transportation systems at the regional, national or global level. We then review location and network design formulations which are often associated with the longterm evolution of transportation systems and also appear prominently when service design issues are considered as described later on. Operational models and methods, particularly those aimed at the allocation and repositioning of resources such as empty vehicles, are then described....
Reformulation of Capacitated Facility Location Problems: How Redundant Information Can Help
 Annals of Operations Research
, 1996
"... Most facility location problems are computationally hard to solve. The standard technique for solving these problems is branchandbound. To keep the size of the branchandbound tree as small as possible it is important to obtain a good lower bound on the optimal solution by deriving strong linear ..."
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Cited by 4 (0 self)
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Most facility location problems are computationally hard to solve. The standard technique for solving these problems is branchandbound. To keep the size of the branchandbound tree as small as possible it is important to obtain a good lower bound on the optimal solution by deriving strong linear relaxations. One way of strengthening the linear relaxation is by adding inequalities that define facets of the convex hull of feasible solutions. Here we describe some simple, but computationally very useful classes of inequalities that were originally developed for relaxations of the facility location problems. Algorithms for generating violated inequalities belonging to the described classes have been implemented as system features in various branchand bound software packages, so as long as the software can recognize the relaxations for which the inequalities are developed, the inequalities will be generated "automatically". Here we explicitly add the variables and constraints that are n...
Improving traditional subgradient scheme for Lagrangean relaxation: an application to location problems
 International Journal of Mathematical Algorithms
, 1999
"... Lagrangean relaxation is largely used to solve combinatorial optimization problems. A known problem for Lagrangean relaxation application is the definition of convenient step size control in subgradient like methods. Even preserving theoretical convergence properties, a wrong defined control can ref ..."
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Cited by 2 (2 self)
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Lagrangean relaxation is largely used to solve combinatorial optimization problems. A known problem for Lagrangean relaxation application is the definition of convenient step size control in subgradient like methods. Even preserving theoretical convergence properties, a wrong defined control can reflect in performance and increase computational times, a critical point in large scale instances. We show in this work how to accelerate a classical subgradient method, using the local information of the surrogate constraints relaxed in the Lagrangean relaxation. It results in a onedimensional search that corrects the step size and is independent of the step size control used. The application to Capacitated and Uncapacitated Facility Location problems is shown. Several computational tests confirm the superiority of this scheme. Key words: Location problems, Lagrangean relaxation, Subgradient method. 1. Introduction Facility location is the problem of locating a number of facilities from a s...
Surviving in a Competitive Spatial Market: The Threshold Capture Model
, 1999
"... Most facility location decision models ignore the fact that for a facility to survive it needs a minimum demand level to cover costs. In this paper we present a decision model for a #rm that wishes to enter a spatial market where there are several competitors already located. This market is such tha ..."
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Most facility location decision models ignore the fact that for a facility to survive it needs a minimum demand level to cover costs. In this paper we present a decision model for a #rm that wishes to enter a spatial market where there are several competitors already located. This market is such that for each outlet there is a demand threshold level that has to be achieved in order to survive. The #rm wishes to know where to locate its outlets so as to maximize its market share taking into account the threshold level. It may happen that due to this new entrance, some competitors will not be able to meet the threshold and therefore will disappear. A formulation is presented together with a heuristic solution method and computational experience. jel: C61,R12,R53 keywords: discrete facility location, threshold, competitive location. # This research has been partially #nanced by DCYGIT grant PB950980, Ministry of Education #Spain#. Please do not quote without the author's permission. y ...