Simple Plant Location Problem Research Articles

Simple plant location under uniform delivered pricing

Given a geographical system of demand functions, the simple-plant location problem under uniform delivered pricing consists in determining the delivered price taken as uniform for all customers, the number, the locations, the sizes and the market areas of the plants which supply these customers, in order to maximize the profit of the firm. A model is proposed, which allows, moreover, to integrate some aspects of the commercial policy of the firm, i.e., its decision to satisfy all markets with positive demands or profitable markets only, or to allow a maximum unit loss or require a minimum unit gain on each served market. An efficient algorithm is presented and illustrated by an example. Computational results with a code using recursively Erlenkotter's DUALOC program as a subroutine are summarized.

A Canonical Representation of Simple Plant Location Problems and Its Applications

We consider a location problem whose mathematical formulation is $\max_S \{ v( S ): S \subseteq N,|S| = K \}$ where $v ( S ) = v ( \emptyset ) + \sum_{i \in I} \max_{j \in S} c_{ij}, C = ( c_{ij} )$ is a real matrix with row index set $I = \{ 1, \cdots ,m \}$ and column index set $N = \{ 1, \cdots ,n \}$ and $K\leqq n$ is a positive integer. A set function of the form $v ( S )$ is called a simple location function. We give a constructive proof that a set function w is a simple location function if and only if it can be represented in the canonical form $w ( S ) = r_\emptyset + \Sigma _{T \cap S \ne \emptyset } r_T $ with $r_T \geqq 0$ for all $\emptyset \subset T \subset N$. The proof is also a polynomial algorithm for reducing the matrix C to the canonical form. We give two applications of this canonical representation. The first is that a large class of algorithms for the location problem need to enumerate all but l of the feasible solutions in order to find one of the lth best solutions. The second application is the derivation of new integer programming formulations of the location problem. Some of these formulations seem to be easier to solve than the standard one. We conclude the paper with two alternate representations of set functions and, in each case, characterize the nondecreasing, submodular and simple location functions.

The simple plant location problem

The simple plant location problem

Plant Location with Generalized Search Origin

There exists computational experience to the effect that search algorithms of the type introduced by Balas are frequently ineffective because of being tied to a rigid “natural” search origin. In this paper the dynamic relocation of the search origin to possibly more appropriate points is advocated. Details of such a procedure are given for the Simple Plant Location Problem. Computational improvements of, sometimes, a striking nature are presented.

Algorithms for the Simple Plant-Location Problem with Some Side Conditions

The algorithms of this paper belong to the direct-search or implicit-enumeration type. They compare to the recently proposed algorithm of Efroymson and Ray, as does the mixed integer algorithm proposed by C. E. Lemke and the author to that of Land and Doig. The general plan of procedure is expected to be equally valid for the capacitated plant-location problem and for transshipment problems with fixed charges; with some of the proposed devices more important for these difficult problems than for the simple plant location problem. Considerable computational experience has been accumulated and is discussed at some length. It suggests that additional work on the construction of “adaptive” programs, matching algorithm to data structure, is desirable.