Practical aspects of applying the grid method for facility location

Abstract: In the literature, the grid method for facility location is frequently described and recommended for use due to its simplicity. However, as demonstrated in the article, the simplicity of the grid method is achieved by incorporating a series of simplifying assumptions that do not need to be considered given current computational capabilities. Furthermore, in the literature, the initial solution for the grid method is often equated with the optimal solution, which in some cases can lead to erroneous location decisions. Considering the imperfections in the description of the grid method in the literature and the progress in numerical techniques, this article proposes certain modifications to the grid method.1. INTRODUCTION
The issue of facility location in logistics, despite various approaches to its solution, continues to pose serious numerical problems to this day. Consequently, by incorporating many simplifying assumptions, approximate solutions to this problem are determined, or the issue is reduced to comparing several variant solutions. These problems already apply to single-facility decision problems, and they accumulate exponentially in multi-facility problems.
One of the oldest facility location methods is the grid method. According to this method, the location problem is solved by minimizing the sum of distances from supply and distribution points to the sought location of the facility that will serve these points. The basic assumption of the grid method is an infinitely dense network of transport connections, which in practice is unattainable in land transport and, as shown in the further part of the article, can constitute a significant limitation to the utility of this method.
Due to its “simplicity,” the grid method is still the most frequently used today. However, it should be noted that over the years, the idea of this method has been distorted many times, and therefore the solutions indicated by some researchers using this method are, objectively speaking, incorrect.
2. THE GRID METHOD IN THE LITERATURE
In the literature, the grid method also appears under the names of the distance minimization method, the gravity method, or the grid technique (compare J. J. Coyle, E. J. Bardi and C. J. Langley, M. Brzeziński, Z. Korzeń, and Cz. Skowronek and Z. Syriusz-Wolski4). (…)

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