A Facility Location Model With Partial Demand Satisfaction: Minimizing Total Cost In Logistics Networks

Facility location optimization plays a pivotal role across both public and private sectores, with critical application in telecommunication, urban planning, industrial layout, and most notably for logistics and supply chain management. The main objective of a Facility Location Problem (FLP) is to determine the optimal placement of a set of facilities (Regional Distribution Centers) within defined geographical space based on spatial distribution of customer demand points. This strategic decision directly influences operational efficiency, service levels, and overall system cost. In the model presented, key factors such as the proximity of facilities to demand nodes, the volume of products required, transportation expenses, and dissastisfaction cost (i.e., penalties for unmet demand) are explicitly incorporated into the optimization framework. The goal is not only to identify the best facility locations but also to decide which transportation links to activate and how much flow to allocate across them, therefore minimizing total system cost while satisfying demand requirements as effectively as possible. The computational results demonstrate crucial insight. Dissatisfaction costs are increased reflecting higher penalties for failing to meet costumer demand. The model responds by fully satisfying all destinations, even if it entails higher dissatisfaction expenditures and reducing the total cost.