Location problems (original) (raw)

Fast bounding procedures for large instances of the Simple Plant Location Problem

Computers & Operations Research, 2012

Some new, simple and extremely fast bounding procedures are presented for large-scale instances of the Simple Plant Location Problem. The lower-bounding procedures are based on dual ascent. The fastest of them runs in Oðmn log mÞ time, where m and n are the number of locations and clients, respectively. The upper-bounding procedures are based on iteratively dropping facilities, and the fastest of them runs in Oðmðn þ log mÞÞ time. Extensive computational results show that, in practice, the procedures give very good bounds extremely quickly.

On the exact solution of large-scale simple plant location problems

NTIS, SPRINGFIELD, VA(USA), 1987, 32, 1987

The simple plant location problem deals with the selection of facility sites from a set of possible locations with the intention of serving a given set of customers from the chosen locations. The objective is to minimize the sum of the fixed charges for establishing the facilities and the transportation costs corresponding to the supply of the demands. We show how to modify a primal-dual version of Erlenkotter's exact algorithm to get an improved procedure. Computational experience with large-scale problems indicates that, compared with Erlenkotter's code, an implementation of the modified algorithm is faster by more than one order of magnitude. For real-life problems with 1500 potential facility sites the increase of computational speed may even exceed the factor of 100.

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.

Branch and peg algorithms for the simple plant location problem

2003

The simple plant location problem is a well-studied problem in combinatorial optimization. It is one of deciding where to locate a set of plants so that a set of clients can be supplied by them at the minimum cost. This problem often appears as a subproblem in other combinatorial problems. Several branch and bound techniques have been developed to solve these problems. In this paper we present two techniques that enhance the performance of branch and bound algorithms.

The heuristic concentration-integer and its application to a class of location problems

Computers & Operations Research, 2009

We propose a new metaheuristic called heuristic concentration-integer (HCI). This metaheuristic is a modified version of the heuristic concentration (HC), oriented to find good solutions for a class of integer programming problems, composed by problems in which p elements must be selected from a larger set, and each element can be selected more than once. These problems are common in location analysis. The heuristic is explained and general instructions for rewriting integer programming formulations are provided, that make the application of HCI to these problems easier. As an example, the heuristic is applied to the maximal availability location problem (MALP), and the solutions are compared to those obtained using linear programming with branch and bound (LP + B&B). For one-third of the instances of MALP, LP + B&B can be allowed to run until the computer is out of memory without termination, while HCI can find good solutions to the same instances in a reasonable time. In one such case, LP-IP was allowed to run for nearly 100 times longer than HCI and HCI still found a better solution. Furthermore, HCI found the optimal solution in 33.3% of cases and had an objective value gap of less than 1% in 76% of cases. In 18% of the cases, HCI found a solution that is better than LP+B&B. Therefore, in cases where LP + B&B is unreasonable due to time or memory constraints, HCI is a valuable tool.

Equivalent instances of the simple plant location problem

2000

Abstract In this paper we deal with a pseudo-Boolean representation of the simple plant location problem. We define instances of this problem that are equivalent, in the sense that each feasible solution has the same goal function value in all such instances. We further define a collection of polytopes whose union describes the set of instances equivalent to a given instance.

Computational Geometry and Heuristic Approaches for Location Problems

Proceedings of the 2015 International Conference on Electrical, Automation and Mechanical Engineering, 2015

In this paper we deal with two problems, whose common basis is to find the location of a service center for potential customers, but with different criterion functions, determining what we consider in these tasks as optimal. While maximizing the coverage of an area by supermarkets, we choose a new supermarket the location that minimises interaction (and thus competition) with existing supermarkets. On the contrary, if we want to provide the availability of certain services for all customers within a reasonable distance, and yet we know in advance where it would be possible to set up servicing points, the goal is to minimize their number. We show that the first type of problem can be solved in polynomial time using the Voronoi diagram, the task of the second type leads to the set covering problem, which is an NP-hard problem, and it is therefore necessary to solve larger instances of a task by heuristics. It is proposed we use a genetic algorithm approach and special attention is paid to implementation of a repair operator for infeasible solutions generated by the operations of crossover and mutation.

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.

A separation algorithm for the simple plant location problem

Operations Research Letters, 2021

The Simple Plant Location Problem (SPLP) is a well-known N Phard optimisation problem with applications in logistics. Although many families of facet-defining inequalities are known for the associated polyhedron, very little work has been done on separation algorithms. We present the first ever polynomial-time separation algorithm for the SPLP that separates exactly over an exponentially large family of facetdefining inequalities. We also present some promising computational results.