Multi-facility location problems in the presence of a probabilistic line barrier: a mixed integer quadratic programming model (original) (raw)
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Journal of the Operations Research Society of Japan
A general approach to optimally solve multiple facility location problems based on the t`Big [friangle Small [briangle" approach te solving single facility problems is proposed, The proposed procedure is especially effective when the solution is constrained to a given polygon such as the convex hull of demand points. The procedure is tested on the two facilities Weber problem with attraetien and repulsion (WAR) with excellent eomputational results.
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2010
Locating a semi-obnoxious facility, like an airport or correctional center is typically a bi-criterion problem combining a convex objective function representing minimum transportation cost with a multi-extremal objective function representing the non-desirable part of the facility. Generic one or bi-objective heuristic methods can be applied to generate efficient locations for the problem. We consider the location of one facility in the plane and show that a simple random or grid search with filtering already provides a very good picture of the trade-off between the two objectives. Moreover, we argue that instead of using bi-criterion meta-heuristics, one could better exploit the convex-nonconvex structure of the problem applying the constraint method. We show how to evaluate the methods systematically using several heuristics from literature.
We consider a generalized version of the rooted Connected Facility Location problem (ConFL) which occurs when extending existing communication networks in order to increase the available bandwidth for customers. In addition to choosing facilities to open and connecting them by a Steiner tree as in the classic ConFL, we have to select a subset of all potential customers and assign them to open facilities respecting given capacity constraints in order to maximize profit. We present two exact mixed integer programming formulations and a Lagrangian decomposition (LD) based approach which uses the volume algorithm. Feasible solutions are derived using a Lagrangian heuristic. Furthermore, we present two hybrid variants combining LD with local search and a very large scale neighborhood search. By applying those improvement methods only to the most promising solutions, we are able to compute much better solutions without increasing the necessary runtime too much. As documented by our computational results, our hybrid approaches compute high quality solutions with tight optimality gaps in relatively short time.
Two meta-heuristics for a multi-period minisum location–relocation problem with line restriction
The International Journal of Advanced Manufacturing Technology, 2014
This paper investigates a multiperiod rectilinear distance minisum location problem, as a mixed-integer nonlinear programming (MINLP) model with a line-shaped barrier restriction, in which the starting point of the barrier uniformly distributed in the plane. The objective function of this model is to minimize the sum of the costs associated with the expected weighted barrier distance of the new facility from the existing facilities and the costs incurred by locationdependent relocation during the planning horizon. Then, a lower bound based on the forbidden region is presented. To show the validation of the presented model, a number of numerical examples are illustrated. The associated results show that the optimization software is effective for small-sized problems. However, the optimization software is unable to find an optimum solution for large-sized problems in a reasonable time. Thus, two meta-heuristics, namely genetic algorithm (GA) and imperialist competitive algorithm (ICA), are proposed. Finally, the associated results are compared and discussed.
An Exact Algorithm for Large-scale Non-convex Quadratic Facility Location
arXiv (Cornell University), 2021
We study a general class of quadratic capacitated p-location problems facility location problems with single assignment where a non-separable, non-convex, quadratic term is introduced in the objective function to account for the interaction cost between facilities and customer assignments. This problem has many applications in the field of transportation and logistics where its most well-known special case is the single-allocation hub location problem and its many variants. The non-convex, binary quadratic program is linearized by applying a reformulation-linearization technique and the resulting continuous auxiliary variables are projected out using Benders decomposition. The obtained Benders reformulation is then solved using an exact branch-and-cut algorithm that exploits the underlying network flow structure of the decomposed separation subproblems to efficiently generate strong Pareto-optimal Benders cuts. Additional enhancements such as a matheuristic, a partial enumeration procedure, and variable elimination tests are also embedded in the proposed algorithmic framework. Extensive computational experiments on benchmark instances (with up to 500 nodes) and on a new set of instances (with up to 1,000 nodes) of four variants of single-allocation hub location problems confirm the algorithm's ability to scale to large-scale instances.
The Multi-Objective Uncapacitated Facility Location Problem
2009
Traditionally, the uncapacitated facility location problem (UFLP) is solved as a single-objective optimization exercise, and focusses on minimizing the cost of operating a distribution network. This paper presents an exploratory study in which the environmental impact is modelled as a separate objective to the economic cost. We assume that the environmental cost of transport is large in comparison to the impact involved in operating distribution centres or warehouses (in terms of CO2 emissions, for example). We further conjecture that the full impact on the environment is not fully reflected in the costs incurred by logistics operators. Based on these ideas, we investigate a number of "what if?" scenarios, using a Fast Nondominated Sorting Genetic Algorithm (NSGA-II), to provide sets of nondominated solutions to some test instances. The analysis is conducted on both two-objective (economic cost versus environmental impact) and three objective (economic cost, environmental impact and uncovered demand) models. Initial results are promising, indicating that this approach could indeed be used to provide informed choices to a human decision maker.
OPSEARCH, 1998
The paper presents the methodology to obtain the optimum location of a new facility in relation to the existing locations in the presence of two circular forbidden regions. The algorithms to compute the shortest constrained Euclidean distance in the presence of single and two-circular forbidden regions are presented. In case of constrained situations, the proposed method chooses the least path directly without computing all possible paths and thus minimizes the computation time. The programming system is interactive so that the user can opt the optimization criteria as (i) mini-sum criteria, (ii) mini-max criteria and/or (iii) bicriteria with or without the presence of forbidden regions.
A general model for the undesirable single facility location problem
2006
In this paper, a finite set in which an optimal solution for a general Euclidean problem of locating an undesirable facility in a polygonal region, is determined and can be found in polynomial time. The general problem we propose leads us, among others, to several well-known problems such as the maxisum, maximin, anticentdian or r-anticentrum problem.
Naval Research Logistics, 2010
We study a stochastic scenario-based facility location problem arising in situations when facilities must first be located, then activated in a particular scenario before they can be used to satisfy scenario demands. Unlike typical facility location problems, fixed charges arise in the initial location of the facilities, and then in the activation of located facilities. The first-stage variables in our problem are the traditional binary facility-location variables, whereas the second-stage variables involve a mix of binary facility-activation variables and continuous flow variables. Benders decomposition is not applicable for these problems due to the presence of the second-stage integer activation variables. Instead, we derive cutting planes tailored to the problem under investigation from recourse solution data. These cutting planes are derived by solving a series of specialized shortest path problems based on a modified residual graph from the recourse solution, and are tighter than the general cuts established by Laporte and Louveaux for two-stage binary programming problems. We demonstrate the computational efficacy of our approach on a variety of randomly generated test problems.