On the exact solution of large-scale simple plant location problems (original) (raw)
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A Comparison of Exact and Heuristic Methods for a Facility Location Problem
International journal of simulation: systems, science & technology
We formulate a facility location problem where the demand of any single client must be allocated to a single facility and a prize is obtained by allocating the demand of a client to a certain facility, i.e. a prize-based variant of the Single Source Capacitated Facility Location Problem. For this problem we pursue both an exact approach through Integer Linear Programming and a heuristic approach based on a local search algorithm. We compare both approaches by considering 500+ instances. The heuristic approach allows to obtain a reduction of the computational time by a factor larger than 10 in 92% of instances and 100 in 64% of instances. The time reduction is obtained with a small sacrifice in the value of the objective function that is achieved, smaller than 10% in nearly 70% of cases.
Primal-Dual Algorithms for Connected Facility Location Problems
2002
We consider the Connected Facility Location problem. We are given a graph G = (V, E) with costs {c e } on the edges, a set of facilities F ⊆ V , and a set of clients D ⊆ V . Facility i has a facility opening cost f i and client j has d j units of demand. We are also given a parameter M ≥ 1. A solution opens some facilities, say F , assigns each client j to an open facility i(j), and connects the open facilities by a Steiner tree T . The total cost incurred is i∈F f i + j∈D d j c i(j)j + M e∈T c e . We want a solution of minimum cost.
A heuristic method for large-scale multi-facility location problems
Computers & Operations Research, 2004
A heuristic method for solving large-scale multi-facility location problems is presented. The method is analogous to Cooper's method [3], using the authors' single facility location method [20] as a parallel subroutine, and reassigning customers to facilities using the heuristic of Nearest Center Reclassification. Numerical results are reported.
An aggressive reduction scheme for the simple plant location problem
European Journal of Operational Research, 2014
Pisinger et al. introduced the concept of 'aggressive reduction' for large-scale combinatorial optimization problems. The idea is to spend much time and effort in reducing the size of the instance, in the hope that the reduced instance will then be small enough to be solved by an exact algorithm. We present an aggressive reduction scheme for the 'Simple Plant Location Problem', which is a classical problem arising in logistics. The scheme involves four different reduction rules, along with lower-and upper-bounding procedures. The scheme turns out to be particularly effective for instances in which the facilities and clients correspond to points on the Euclidean plane.
Brazilian Journal of Operations & Production Management, 2017
The objective in terms of the facility location problem with limited distances is to minimize the sum of distance functions from the facility to its clients, but with a limit on each of these distances, from which the corresponding function becomes constant. The problem is applicable in situations where the service provided by the facility is insensitive after given threshold distances. In this paper, we propose a polynomial-time algorithm for the discrete version of the problem with capacity constraints regarding the number of served clients. These constraints are relevant for introducing quality measures in facility location decision processes as well as for justifying the facility creation.
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.
Approximation algorithms for hard capacitated k-facility location problems
European Journal of Operational Research, 2015
We study the capacitated k-facility location problem, in which we are given a set of clients with demands, a set of facilities with capacities and a constant number k. It costs f i to open facility i, and c ij for facility i to serve one unit of demand from client j. The objective is to open at most k facilities serving all the demands and satisfying the capacity constraints while minimizing the sum of service and opening costs. In this paper, we give the first fully polynomial time approximation scheme (FPTAS) for the single-sink (single-client) capacitated k-facility location problem. Then, we show that the capacitated k-facility location problem with uniform capacities is solvable in polynomial time if the number of clients is fixed by reducing it to a collection of transportation problems. Third, we analyze the structure of extreme point solutions, and examine the efficiency of this structure in designing approximation algorithms for capacitated k-facility location problems. Finally, we extend our results to obtain an improved approximation algorithm for the capacitated facility location problem with uniform opening cost.
A strengthened formulation for the simple plant location problem with order
Operations Research Letters, 2007
The Simple Plant Location Problem is well known in the literature: it consists in deciding which facilities to open among a set of potential nodes and allocating a set of customers to the open facilities in such a way that the total cost is minimum, allocation process which is carried out by the locator.
2022
Facility Location Problems with Capacities, Revenues, and Closest Assignments (FLP-CRCA) are an extension of the well known, strongly N P-complete Facility Location Problem (FLP). With this extension, we recognise that facilities have an upper capacity on the customers to be served, but also need to generate a minimum revenue to be operated economically. Furthermore, we acknowledge that customers have a strong preference towards their closest facility. We show that finding a feasible solution for FLP-CRCA is already strongly N P-complete if the underlying graph forms a star, but that the problem can be solved efficiently on paths and cycles. In the case where the number of facilities is fixed, we propose a pseudo-polynomial algorithm and show that the problem is weakly N P-complete under this condition. Our results also hold for FLPs with closest assignments and either capacities or revenues.
An effective heuristic for large-scale capacitated facility location problems
Journal of Heuristics, 2008
The Capacitated Facility Location Problem (CFLP) consists of locating a set of facilities with capacity constraints to satisfy the demands of a set of clients at the minimum cost. In this paper we propose a simple and effective heuristic for largescale instances of CFLP. The heuristic is based on a Lagrangean relaxation which is used to select a subset of "promising" variables forming the core problem and on a Branch-and-Cut algorithm that solves the core problem. Computational results on very large scale instances (up to 4 million variables) are reported.