Plant Location Problem Research Articles

Solving the simple plant location problem by genetic algorithm

The simple plant location problem (SPLP) is considered and a genetic algorithm is proposed to solve this problem. By using the developed algorithm it is possible to solve SPLP with more than 1000 facility sites and customers. Computational results are presented and compared to dual based algorithms.

On High-Speed Connections and the Location of Activities

We study the impact of a high-speed connection between two regional economies on the location of production activities, using the simple plant-location problem and toy networks. As expected, the relative value of fixed production costs to transportation costs is crucial in the determination of facility locations. Less expected is the fairly strong instability observed in the structure of the locational pattern of facilities when the relative value of the fixed costs changes. The construction of a piece of infrastructure has an impact on the regional structure of production provided that it allows for a substantial reduction in transport spending. When scale economies in production are large, one regional center swallows up the other and may eventually become the only production center within the integrated economy.

On the resolution of the single product capacitated machine siting problem

The single product capacitated machine siting problem (SPCMSP) is an extension of the simple plant location problem, in which plant production depends on installing capacitated machines. In this paper we compare, both theoretically and computationally, three heuristic algorithms for the SPCMSP based upon Lagrangean relaxation and reduction tests of a mixed-integer formulation of the problem, which is NP-hard. We test the performance of the algorithms with examples involving up to 100 potential plants, 1000 customers and six potential machines per plant, which we obtain encouraging results.

The maximum return-on-investment plant location problem

The standard plant location problem determines which plants to open from a set of potential sites in order to satisfy the demands at a set of customer vertices at a minimum total cost. However, the optimal solution may exceed a limit on investment costs imposed on the enterprise in a practical setting. This paper examines the plant location problem in an environment in which the investment in plant and equipment is also an objective to be minimised. The problem is posed as a bicriterion model which examines the tradeoff between the sum of operational and investment costs and investment cost (or total cost vs sunk cost). A weighting method is used to generate efficient solutions, one of which is shown to maximise the return on investment. The integer-friendliness of the LP relaxation is investigated.

The Maximum Return-On-Investment Plant Location Problem

The Maximum Return-On-Investment Plant Location Problem

A multiperiod two-echelon multicommodity capacitated plant location problem

In this paper we deal with a facility location problem where one desires to establish facilities at two different distribution levels by selecting the time periods. Our model intends to minimize the total cost for meeting demands for all the products specified over the planning horizon at various customer locations while satisfying the capacity requirements of the production plants and intermediate warehouses. We address this problem by means of a formulation as a mixed integer programming problem. A Lagrangean relaxation is proposed to solve the problem, together with a heuristic procedure that constructs feasible solutions of the original problem from the solutions at the lower bounds obtained by the relaxed problems. Computational tests are provided showing the good performance of this approach for a wide range of problems.

An integrated approach to dynamic plant location and capacity planning

We consider a dynamic capacitated plant location problem in which capacities of opened plants are determined by acquisition and/or disposal of multiple types of facilities. We determine the opening schedule of plants, allocations of customers' demands and plans for acquisition and/or disposal of plant capacities that minimise the sum of discounted fixed costs for opening plants, delivery costs of products, and acquisition and operation costs of facilities. The dynamic capacitated plant location problem is formulated as a mixed integer linear program and solved by a heuristic algorithm based on Lagrangian relaxation and a cut and branch algorithm which uses Gomory cuts. Several solution properties of the relaxed problem are found and used to develop efficient solution procedures for the relaxed problem. A subgradient optimisation method is employed to obtain better lower bounds. The heuristic algorithm is tested on randomly generated test problems and results show that the algorithm finds good solutions in a reasonable amount of computation time.

The Data-Correcting Algorithm for the Minimization of Supermodular Functions

The Data-Correcting (DC) Algorithm is a recursive branch-and-bound type algorithm, in which the data of a given problem instance are “heuristically corrected” at each branching in such a way that the new instance will be as close as possible to polynomially solvable and the result satisfies a prescribed accuracy (the difference between optimal and current solution). In this paper the DC algorithm is applied to determining exact or approximate global minima of supermodular functions. The working of the algorithm is illustrated by an instance of the Simple Plant Location (SPL) Problem. Computational results, obtained for the Quadratic Cost Partition Problem (QCP), show that the DC algorithm outperforms a branch-and-cut algorithm, not only for sparse graphs but also for nonsparse graphs (with density more than 40%), often with speeds 100 times faster.

Parallel Complexity of Additive Location Problems

Parallel NC-algorithms for a general class of multifacility location problems on a tree with identical facilities and the minisum objective function are presented. The class includes the p-median problem, the p-coverage problem, and the uncapacitated plant location problem.

Reactive Grasp And Tabu Search Based Heuristics For The Single Source Capacitated Plant Location Problem

This paper considers the Single Source Capacitated Plant Location Problem (SSCPLP). SSCPLP is a discrete location problem. It allows capacities on the plants to be opened and constrains each client to be served by a single open plant. The following algorithms are proposed: A Reactive GRASP heuristic; a Tabu Search heuristic; and two different hybrid approaches that combine elements of the GRASP and the Tabu Search methodologies. The elements of the proposed heuristics are presented. The Reactive GRASP algorithm is a self-tuning heuristic in which the calibration process is replaced by an automated criterion for selecting the parameter value. The Tabu Search heuristic provides the framework for the first of the hybrid approaches. It consists of two phases. The GRASP methodology is used for the first one, which can be viewed as a strong diversification mechanism. The second one consists of an intensification phase. The second hybrid algorithm follows the framework of the Reactive GRASP heuristic. It also consists of two phases and Tabu Search is used in the second phase as a mechanism to strengthen the Local Search. Computational experiments have been performed to evaluate the behavior of the proposed methods. The results on two different sets of test problems show that the proposed methods are very efficient. In particular, all of them outperform previous heuristic approaches in small computation times. Moreover, the outcome of different series of experiments carried out with CPLEX confirm the quality of all the heuristics and, in particular, of the two hybrid approaches.

Exact solution methods for uncapacitated location problems with convex transportation costs

In this paper we study exact solution methods for uncapacitated facility location problems where the transportation costs are nonlinear and convex. An exact linearization of the costs is made, enabling the formulation of the problem as an extended, linear pure zero–one location model. A branch-and-bound method based on a dual ascent and adjustment procedure is developed, and compared to application of a modified Benders decomposition method. The specific application studied is the simple plant location problem (SPLP) with spatial interaction, which is a model suitable for location of public facilities. Previously approximate solution methods have been used for this problem, while we in this paper investigate exact solution methods. Computational results are presented.

Efficient solution of large scale, single-source, capacitated plant location problems

The single-source, capacitated plant location problem is considered. This problem differs from the capacitated plant location problem by the additional requirement that each customer must be supplied with all its demand from a single plant. An efficient heuristic solution, capable of solving large problem instances, is presented. The heuristic combines Lagrangian relaxation with restricted neighbourhood search. Computational experiments on two sets of problem instances are presented.

Efficient Solution of Large Scale, Single-Source, Capacitated Plant Location Problems

Efficient Solution of Large Scale, Single-Source, Capacitated Plant Location Problems

Upper and lower bounds for the two‐level simple plant location problem

In this paper, we consider a problem relevant to the telecommunications industry. In atwo‐level concentrator access network, each terminal has to be connected to a first‐levelconcentrator, which in turn must be connected to a second‐level concentrator. If no extracomplicating constraints are taken into account, the problem, translated into the language ofdiscrete location theory, amounts to an extension to two levels of facilities of the simpleplant location problem (SPLP). A straightforward formulation can be used, but we proposea more complicated model involving more variables and constraints. We show that the linearprogramming relaxations of both formulations have the same optimal values. However, thesecond formulation can be tightened by using a family of polyhedral cuts that define facetsof the convex hull of integer solutions. We develop a Lagrangian relaxation method tocompute lower bounds on the optimal value of the linear programming formulations andfeasible solutions of the integer programming model. A simulated annealing algorithm isalso designed to improve upon some of the upper bounds returned by the Lagrangian relaxationalgorithm. Experiments show the effectiveness of the formulation incorporating poly‐hedralcuts and of an approach combining a Lagrangian relaxation method and a simulatedannealing algorithm.

The plant location problem with demand-dependent setup costs and centralized allocation

Suppose that customers are situated at the nodes of a transportation network, and a service company plans to locate a number of facilities that will serve the customers. The objective is to minimize the sum of the total setup cost and the total transportation cost. The setup cost of a facility is demand-dependent, that is, it depends on the number of customers that are served by the facility. Centralized allocation of customers to facilities is assumed, that is, the service company makes a decision about allocation of customers to facilities. In the case of a general network, the model can be formulated as a mixed integer programming problem. For the case of a tree network, we develop a polynomial-time dynamic programming algorithm.

Solving the plant location problem on a line by linear programming

This paper investigates the simple uncapacitated plant location problem on a line. We show that under general conditions the special structure of the problem allows the optimal solution to be obtained directly from a linear programming relaxation. This result may be extended to the related p-median problem on a line. Thus, the practitioner is now able to use readily available LP codes in place of specialized algorithms to solve these one-dimensional models. The findings also shed some light on the “integer friendliness” of the general problem.

Lagrangean heuristics applied to a variety of large capacitated plant location problems

A series of performance improving heuristics are developed and embedded into the procedure of Lagrangean heuristics. The principles and ideas of these heuristics are used to build a general framework with which a variety of large Capacitated Plant Location Problems (CPLP) are solved, including the multi-capacitated case. A significant improvement over the results discussed in the literature is recorded. The single-source multi-Capacitated Plant Location Problem, which has not been addressed in the literature, is also tackled with encouraging results.

Lagrangean Heuristics Applied to a Variety of Large Capacitated Plant Location Problems

Lagrangean Heuristics Applied to a Variety of Large Capacitated Plant Location Problems

Transportation Networks and the Location of Human Activities

The impact of transportation networks on the location of human activities is a surprisingly neglected topic in economic geography. Using the simple plant location problem, this paper investigates such an impact in the case of a few idealized networks. It is seen that a grid network tends to foster a dispersed pattern of activities, while the center of a radial network acts as an attractor. The case of two economies characterized by different network configurations that form a custom union is then analyzed. It is shown that the structural properties of the networks still hold, though some locations are pulled toward the common border. This suggests that no such relocation should be expected within the European Union if the state members endorse similar fiscal and social policies after the formation of the single market.

Lagrangean heuristics applied to a variety of large capacitated plant location problems

Lagrangean heuristics applied to a variety of large capacitated plant location problems