Optimizing Collection Center Location on a Heatmap Using the Weiszfeld Algorithm for the Fermat-Weber Problem

Abstract

Facility location problems play an important role in logistics, particularly in the design of collection and distribution centers. This study presents a novel approach to determining the optimal location of a collection center based on existing collection tasks, represented by coordinates and associated quantities. The proposed method models the entire area using a heatmap, capturing the spatial distribution of goods to be collected. Based on this heatmap, the optimal location of the collection point is identified by solving the Fermat-Weber Problem (FWP) using the Weiszfeld Algorithm (WA), ensuring minimal materials handling costs. The study demonstrates how the heatmap representation enables a more flexible and dynamic facility location strategy compared to traditional point-based optimization approach. Numerical example shows that the locations derived from the heatmap closely approximate those computed directly from discrete collection points, making this approach suitable for collection tasks with dynamic and continuously changing demand patterns.