Plant Location Problem Research Articles

The Location of Plants of the Uniform Delivered Price Manufacturer: A Case Study of Coca-Cola Ltd.

This paper discusses the locational patterns of plants for Coca-Cola Ltd., a multiplant, uniform delivered price manufacturer. The uniform delivered pricing strategy is rationalized. A nonlinear mathematical programming technique to determine optimal plant locations, sizes, and market areas through the trade-off of internal economies of scale with transportation costs incurred, due to spatial price equalization, is presented. The actual locations, sizes, and market areas of southwestern Ontario Coca Cola bottling plants are compared with the results obtained from the normative model. It appears from the results that the plant location problem is easier for the firm to solve than the plant size problem.

A Plant and Warehouse Location Problem

AbstractA model is proposed for the simultaneous location of plants and warehouses among a given set of possible locations in order to satisfy a given demand at minimum cost. The demand of each cus...

Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms

The number of days required to clear a check drawn on a bank in city j depends on the city i in which the check is cashed. Thus, to maximize its available funds, a company that pays bills to numerous clients in various locations may find it advantageous to maintain accounts in several strategically located banks. We will discuss the problem of optimally locating bank accounts to maximize clearing times. The importance of this problem depends in part on its mathematical equivalence to the well-known uncapacitated plant location problem. We present a Lagrangian dual for obtaining an upper bound and heuristics for obtaining a lower bound on the value of an optimal solution. Our main results are analytical worst-case analyses of these bounds. In particular we show that the relative error of the dual bound and a “greedy” heuristic never exceeds [(K − 1)/K]k < 1/e for a problem in which at most K locations are to be chosen. Two other heuristics are shown to have worst-case relative errors of at least (k − 1)/(2K − 1) < 1/2. Examples are given showing that all these bounds can be achieved. We present extensive computational results for these approximations.

A Plant and Warehouse Location Problem

A Plant and Warehouse Location Problem

The Simple Plant-Location Problem under Uncertainty

There is a class of simple plant-location problems under uncertainty that can be decomposed into two simpler problems that can be solved sequentially with surprising ease. The salient characteristic of this class of problems is that for any demand generating region, one plant dominates all others as a supply source. We develop and discuss the conditions required for this dominance. The risk-averse nature of the firm is incorporated into this model with a mean-variance formulation of the objective function. The general formulation is particularized to four paradigms of firms characterized by a range of behavioral and market assumptions.

Supply Source Location Involving Fixed Charges and Economics of Scale: A Heuristic Approach

This paper presents a model capable of accommodating plant location problems where 1) the long-run source or plant cost function exhibits a positive intercept (fixed charge), 2) the long-run plant cost function is discontinuous, and 3) there are economies of scale associated with increasing plant size. The model developed and presented here reverses the cost minimizing sequence of the Chern and Polopolus formulation, a model designed to include a discontinuous long-run plant cost function. For many types of plant location problems, the developed model (source location cost-sequencing model) will yield a lower cost solution than the Chern and Polopolus formulation.

A Cotton Ginning Problem

This paper examines the plant location problem of the cotton-processing industry. In recent years the industry has experienced an excess gin plant capacity. By considering the transportation requirements from the farms to the gins, the gin costs, and the gin capabilities, we develop a model to determine which gins should be used for this seasonal product. A case study is used to illustrate the analysis and emphasis is placed on alternative formulations of the model.

The simple plant location problem

The simple plant location problem

A Negative-Cost Approach to the Formulation of a Transhipment Problem

The transhipment problem formulation has been and is still being used extensively by researchers to solve spatial equilibrium and plant location problems. Hurt and Tramel, King and Logan, Rhody, and Judge et al. have all treated the subject of alternative formulations of transhipment problems. This paper (1) proposes an alternative formulation of these problems using a negative-cost technique and, (2) suggests a matrix reduction scheme which will reduce computational time for some problems.King and Logan used a three region, two-stage formulation of the transhipment model which was reformulated by Hurt and Tramel. As a point of departure, the same sample problem will be used to present the negative-cost formulation. This should enable the reader to more readily determine differences between formulations and decide which formulation best serves his particular needs.

A Modification of the Modified Stollsteimer Location Moled

The Stollsteimer plant location model is a normative tool appropriate for deterrmning least-cost number, size and location of a subindustry's marketing facilities. Several modification and extensions of the basic model have increased its value to the applied economist. Ladd and Halvorson developed a procedure to determine sensitivity of the optimal solution to variation in model parameters, i.e., the researcher may resolve how magnitude cost parameters are altered before the solution becomes non-optimal. The basic model's solution procedure prevented application where large numbers of potential plant sites were involved. A recent modification by Warrack and Fletcher effects a reduction in required computer time by approximating optimization, thus increasing size of plant location problems investigated. Polopolus extended the basic model to encompass multiple product plants and, in collaboration with Chern, modified the basic Stollsteimer model to permit substitution of a discontinuous, long-run plant cost function for the strategically assumed continuous linear form. Prior to the latter modification, the basic model accommodated only a long-run total plant cost function which was linear with a positive intercept.

The Optimal Nodal Location of Public Facilities With Price‐Sensitive Demand

AbstractThe purpose of this paper is to present some models for the location of public facilities in nodal networks that explicitly maximize social welfare by accounting for price‐elastic demand functions. The models presented here are general; yet they are mathematically equivalent to the plant location problem and are therefore amenable to solution procedures developed for the plant location problem. The models presented here distinguish between two institutional environments that reflect the degree of power of the consumer to choose which facility to patronize. If consumers can be assigned arbitrarily to facilities and can be denied service, then the environment is one of public fiat. If consumers must be served at the facility of their choice, then a “serve‐allcomers” environment exists. Separate models for each environment are specified, and the relationship between optimal assignments and pricing policies is developed.

An efficient heuristic procedure for the capacitated warehouse location problem

AbstractThis paper introduces an efficient heuristic procedure for solving a special class of mixed integer programming problem called the capacitated warehouse (plant) location problem. This procedure parallels the work reported earlier in [9] on the uncapacitated warehouse location problem. The procedure can be viewed as tracing a judiciously selected path of the branch and bound tree (from the initial node to the terminal node) to arrive at a candidate solution. A simple backtracking scheme is also incorporated in the procedure to investigate possible improvement in the solution. Computational results on problems found in the literature look quite encouraging.

A cost function property for plant location problems

A cost function property for plant location problems

The Optimal Location of Nuclear-Power Facilities in the Pacific Northwest

This paper treats the optimal location of nuclear-power plants in the Pacific Northwest with respect to capital-construction, operating, and transmission costs. It presents a mathematical formulation of this two-product (peak and energy power) plant-location problem, using the simplex method in conjunction with a branch-and-bound process, and indicates a check procedure using Vogel’s approximation method in conjunction with an algorithm for solving the transportation problem and a branch-and-bound process. The paper gives results for demand-growth rates of 4, 5, 6 and 7 percent and alternative designs and their costs. It also discusses the stability of the optimal solution.

An efficient heuristic procedure for the uncapacitated warehouse location problem

AbstractThis paper introduces an efficient heuristic procedure for a special class of mixed integer programming problems called the uncapacitated warehouse (plant) location problem. This procedure is derived from the branching decision rules proposed for the branch and bound algorithm by the author in an earlier paper. It can be viewed as tracing a single path of the branch and bound tree (from the initial node to the terminal node), the path being determined by the particular branching decision rule used. Unlike branch and bound the computational efficiency of this procedure is substantially less than linearly related to the number of potential warehouse locations (integer variables) in the problem. Its computational efficiency is tested on problems found in the literature.

Location Theory, Dominance, and Convexity

This paper explores the nature of optimal solutions to a plant-location problem on a plane under general distance measures. It develops conditions that guarantee an optimal location of a facility to lie in the convex hull of source and destination points. The effect of restricting the solution to some predetermined set is explored. The development is based on a generalization of Kuhn's characterization of a convex hull by dominance. When a “Manhattan” norm is employed, it is shown to be sufficient to consider, as optimal locations, the finite number of “intersection points” in the convex hull.

Facility Location under a Maximum Travel Restriction: An Example Using Day Care Facilities

Geographical AnalysisVolume 4, Issue 3 p. 258-266 Free Access Facility Location under a Maximum Travel Restriction: An Example Using Day Care Facilities John Holmes, John Holmes John Holmes is visiting lecturer in geography, Queen's University, Kingston, OntarioSearch for more papers by this authorForrest B. Williams, Forrest B. Williams Forrest B. Williams is a graduate student and Lawrence A. Brown is professor in the department of geography, Ohio State UniversitySearch for more papers by this authorLawrence A. Brown, Lawrence A. Brown Forrest B. Williams is a graduate student and Lawrence A. Brown is professor in the department of geography, Ohio State UniversitySearch for more papers by this author John Holmes, John Holmes John Holmes is visiting lecturer in geography, Queen's University, Kingston, OntarioSearch for more papers by this authorForrest B. Williams, Forrest B. Williams Forrest B. Williams is a graduate student and Lawrence A. Brown is professor in the department of geography, Ohio State UniversitySearch for more papers by this authorLawrence A. Brown, Lawrence A. Brown Forrest B. Williams is a graduate student and Lawrence A. Brown is professor in the department of geography, Ohio State UniversitySearch for more papers by this author First published: July 1972 https://doi.org/10.1111/j.1538-4632.1972.tb00474.xCitations: 49 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat LITERATURE CITED 1 Brown, L. A., F. B. Williams, C. Youngmann, J. Holmes, and K. Walby. Day Care Centers in Columbus: A Locational Strategy,” Ohio State University, Dept. of Geography Discussion, Paper 26, 1972. 2 Davis, P. S. and T. L. Ray. A Branch and Bound Algorithm for the Capacitated Facilities Location Problem,” Naval Research Logistics Quarterly, 16 (1969), 331– 43. 3 Ellwein, L. B. Fixed Charge Location-Allocation Problems with Capacity and Configuration Constraints,” Stanford University Department of Industrial Engineering, Technical Report Number 70–2, 1970. 4 Hagerstrand, T. The Propagation of Innovation Waves. Lund: Gleerup, Lund Studies in Geography, Number B-4, 1952. 5 Hillier, F. S. and G. J. Lieberman. Introduction to Operations Research. San Francisco: Holden-Day, 1967. 6 ReVelle, C. S. and R. W. Swain. Central Facilities Location,” Geographical Analysis, 2 (1970), 30– 42. 7 Rojeski, P. and C. S. ReVelle. Central Facilities Location Under an Investment Constraint,” Geographical Analysis, 2 (1970), 343– 60. 8 Sa, G. Branch and Bound and Approximate Solutions to the Capacitated Plant-Location Problem,” Operations Research, 17 (1969), 1005– 16. 9 Scott, A. J. Location-Allocation Systems: A Review,” Geographical Analysis, 2, (1970), 95– 119. 10 Toregas, C., R. W. Swain, C. S. ReVelle, and L. Bergman. The Location of Emergency Service Facilities,” Operations Research, 19 (1971), 1363– 73. Citing Literature Volume4, Issue3July 1972Pages 258-266 ReferencesRelatedInformation

Parametric Solutions to the Stollsteimer Model

EDITOR'S COMMENT: The three following papers on plant size and location were submitted separately and independently. All authors were advised of the other manuscripts and encouraged to condense their papers for complementary presentation as Research Notes. I have deleted the introductory section of each paper and attempted to integrate their content as follows: Stollsteimer's 1963 article, A Working Model for Plant Numbers and Locations [JFE 45:631-645, Aug. 1963], offered a concept for determining minimum cost numbers, sizes, and locations of processing plants. It was a long-run simultaneous, computable, single-product model without provision in its framework for structural change. The following year King and Logan, in Optimum Location, Number and Size of Processing Plants with Raw Product and Final Product Shipments [JFE 46:94-108, Feb. 1964], presented a transhipment-based model that included both inand out-flows. Among other papers to follow, as noted by the several authors, the most recent to be presented in this Journal was that on Sensitivity Testing and the Plant Location Problem [AJAE 52:403-410, Aug. 1970].

Plant‐Location Model Suboptimization for Large Problems

O PERATIONAL constraints of the Stollsteimer long-run spatial model have been severe. The data input requirements are large. More serious, for all but small problems the optimization tends to be computationally demanding to the point of infeasibility. The purpose of this paper is to enlarge the scope of problem for which the basic computational model can be used. Specifically, an algorithm is suggested that operationalizes the Stollsteimer model for plant location problems where a large number of plants may enter the optimum solution.

Sensitivity Testing and the Plant Location Problem

AbstractA wide range of models and and solution procedures are now available to the analyst concerned with plant or warehouse location problems. While these produce an optimal solution, no explicit statement is usually made about solution stability. One large group of models concerned with size and siting problems uses the transportation model of linear programming as a solution procedure. This paper presents a method of testing the stability of such solutions. The problem outlined here concerns a plant location study and explicitly examines processing cost variations. However, the sensitivity test used can be applied in general to any cost elements of a transportation problem matrix.