A Territory-based Approach for the Facility Assignment Problem with a Minimum Cost Formulation

This document proposes a solution process for the Online Facility Assignment problem applied to Logistics. Given a number of Expedition Centers capable of delivering packages to the final customers, the goal is to devise a policy for assigning each package to a center in order to reduce the total distance between them while respecting possible volume and exclusivity regions.
Also, the assignment must happen in an online manner. Here we propose a two-phase approach. First, we construct demand regions for each EC via a mixed linear programming formulation. Afterwards they are employed for the online package assignment. The algorithm is further improved with a minimum cost flow version. We show how the network flow approach can improve a lot on the processing time while keeping the same quality on objective value. Finally, a full walk-through
illustrates the applicability of the method in a real-world scenario.