Capacitated Plant Location Problem Research Articles

A Branch-and-Price algorithm for the Single Source Capacitated Plant Location Problem

This paper considers the Single Source Capacitated Plant Location Problem (SSCPLP). We propose an exact algorithm in which a column generation procedure for finding upper and lower bounds is incorporated within a Branch-and-Price framework. The bounding procedure exploits the structure of the problem by means of an iterative approach. At each iteration, a two-level optimization problem is considered. The two levels correspond with the two decisions to be taken: first, the selection of a subset of plants to be opened and then, the allocation of clients within the subset of open plants. The second level subproblem is solved using column generation. The algorithm has been tested with different sets of test problems and the obtained results are satisfactory.

The capacitated plant location problem with multiple facilities in the same site

In this paper, we introduce the capacitated plant location problem (CPLP) with multiple facilities in the same site (CPLPM), a special case of the classical CPLP where several facilities can be opened in the same site. Applications of the CPLPM arise in a number of contexts, such as the location of polling stations. Although the CPLPM can be modelled and solved as a standard CPLP, this approach usually performs very poorly. In this paper we describe a novel Lagrangean relaxation and a tailored Lagrangean heuristic that overcome the drawbacks of classical procedures. These algorithms were used to solve a polling station location problem in Italy. Computational results show that the average deviation of the heuristic solution over the lower bound is less than 2%. Scope and purpose This paper deals with a location problem that is of utmost importance for many public and private organizations. The problem aims at determining a set of capacitated facilities (warehouses, plants, polling stations, etc.) in such a way that the sum of facility construction costs and transportation costs is minimised. Unlike previous papers we allow multiple facilities in the same site. As classical lower and upper bounding procedures perform very poorly in this case, we devised a novel Lagrangean relaxation and a tailored Lagrangean heuristic. Our study was motivated by a real-world application arising in Italian municipalities where one has to locate polling stations and to assign voters to polling stations.

A Lagrangean heuristic for the plant location problem with multiple facilities in the same site

This article addresses the Capacitated Plant Location Problem with Multiple Facilities in the Same Site (CPLPM), a special case of the classical Capacitated Plant Location Problem (CPLP) in which several facilities (possibly having different fixed costs and different capacities) can be opened in the same site. Applications of the CPLPM arise in a number of contexts, such as the location of polling stations. Although the CPLPM can be modelled and solved as a standard CPLP, this approach usually performs very poorly. In this article we describe a tailored Lagrangean heuristic that overcomes the drawbacks of classical procedures. Our algorithm was tested on a set of randomly generated instances and on a large real-world instance. Computational results indicate that our algorithm is able to provide high quality lower and upper bounds in a reasonable amount of time. In particular, our technique is able to provide good upper bounds for large-scale real-world applications, whereas general-purpose ILP solvers fail to determine even a feasible solution.

ADD/DROP PROCEDURES FOR THE CAPACITATED PLANT LOCATION PROBLEM

Abstract Abstract The capacitated plant location problem with linear transportation costs is considered. An algorithm based on ADD/DROP procedures is proposed. Exact rules are presented allowing an a priori opening or closing of facilities. Facilities left are submitted to an extension of the exact rules. Procedures are implemented with the help of lower and upper bounds using Lagrangean relaxation. Computational results are presented and comparisons with other algorithms are made.

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.

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.

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

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

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

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

The use of reduction tests and simulated annealing for the capacitated plant location problem

This paper discusses a new algorithm for the capacitated plant location problem. The first part of this algorithm consists of reduction tests to open or close facilities. Not all facilities may have their status determined this way. For the set of facilities that cannot be determined this way, we use simulated annealing (SA). Unfortunately, both reduction tests and SA imply the necessity for solving a great number of transportation problems. Therefore, the implementation may be greatly improved by using bounds based on Lagrangean relaxation. Computational results are presented for problems used by Beasley and based on Kuehn and Hamburger data.

Polyhedral analysis and decompositions for capacitated plant location-type problems

We study the polyhedral structure of two primal relaxations of a class of specially structured mixed integer programming problems. This class includes the generalized capacitated plant location problem and a production scheduling problem as special cases. We show that for this class of problems two polyhedra constructed from the constraint sets in two different primal relaxations are identical. The results have the following surprising implications; with linear or nonlinear objective functions, the bounds from two a priori quite different primal relaxations of the capacitated plant location problem are actually equal. In the linear case, this means that a simple Lagrangean substitution yields exactly the same strong bound as the computationally more expensive Lagrangean decomposition introduced in Guignard and Kim (1987) and studied in Cornuejols et al. (1991).

A Lagrangean heuristic for the facility location problem with staircase costs

In this paper we develop and compare heuristic solution methods for the capacitated facility location problem with staircase shaped production cost functions, a linear mixed integer programming problem with a large proportion of integer variables. We propose a Lagrangean heuristic, including Lagrangean relaxation and subgradient optimization as a base for an efficient primal heuristic, and using convex piecewise linearizations of the staircase shaped cost functions to get good initial upper and lower bounds as well as initial dual solutions. Based on the solution of the Lagrangean relaxation a transportation problem which yields primal feasible solutions is constructed. For comparison we have generalized the well-known ADD heuristic for the capacitated plant location problem to enable the application to the staircase cost facility location problem, and improved it by including certain priority rules. Computational results are given indicating that the Lagrangean heuristic is quite promising.

An algorithm for optimal shipments with given frequencies

This article deals with the problem of minimizing the transportation and inventory cost associated with the shipment of several products from a source to a destination, when a finite set of shipping frequencies is available. A mixed-integer programming model—shown to be NP-hard—is formulated for that problem. The computational complexity of some similar models applied to different problems is also investigated. In particular, whereas the capacitated plant location problem with operational cost in product form is NP-hard, the simple plant location problem with the same characteristics can be solved in polynomial time. A branch-and-bound algorithm is finally worked out, and some computational results are presented. © 1996 John Wiley & Sons, Inc.

A Lagrangian heuristic for the capacitated plant location problem with single source constraints

In this paper we look at the Lagrangian relaxations of the Capacitated Plant Location Problem with Single Source constraints in terms of the bounds and solution techniques. We propose a heuristic based on a lagrangian relaxation of the problem. We also show how this heuristic can be used to solve other combinatorial problems that are related to this problem, such as the concentrator location problem and the bin packing problem.

A Lagrangian Heuristic for the Capacitated Plant Location Problem with Side Constraints

A Lagrangian Heuristic for the Capacitated Plant Location Problem with Side Constraints

A Lagrangian Heuristic for the Capacitated Plant Location Problem with Side Constraints

In this paper we present a Lagrangian relaxation-based heuristic for solving the capacitated plantlocation problem with side constraints. The side constraints are upper-bound constraints on disjoint subsets of the (0-1) variables. Computational results are reported for some problems, having been obtained both on a mainframe computer and on a personal computer.

A Lagrangian Heuristic for the Capacitated Plant Location Problem with Side Constraints

A Lagrangian Heuristic for the Capacitated Plant Location Problem with Side Constraints