Optimizing Area Coverage for Time‐Differentiated Distribution: A Unidimensional Analysis

This article studies the problem of optimally locating storage facilities and determining their service areas for the distribution of goods within multiple distance constraints. The problem is relevant for the service systems that maintain inventories of items required for servicing at demand locations within different service time windows (e.g., the after‐sales service systems that maintain service parts for critical equipment). A location optimization model is presented that considers a continuous unidimensional coverage under two service distance constraints, demand composition, and inventory and transportation costs. The investigation primarily focuses on the tradeoff between inventory and transportation costs to provide guidelines for the appropriate distribution setups under a set of different conditions. The article adds to the under‐researched area of continuous location optimization and offers some novel insights in this area. Some of the existing optimization methods in this area rely on Voronoi partitioning. However, the analysis highlights that Voronoi regions may not be optimum when inventory costs are considered. It also highlights that different cost and demand compositions can result in significantly different optimum location patterns.