Facility location problems determine optimal positions for supply points to serve customer demand. The P-median problem minimizes distance-based transportation cost by selecting p median points; the Fixed Charge problem adds location costs and capacity constraints. Both formulations balance service accessibility with infrastructure investment. Table of Contents: • P-median problem: select p facilities from n candidate locations to minimize customer-to-facility distances • Binary integer formulation: median indicator variables, assignment variables for non-median-to-median links • Constraints: exactly p medians chosen, each non-median assigned to exactly one median, non-medians assigned only to medians • Computational complexity: enumeration of nCp combinations; solved optimally via binary programming or heuristics • Thumb rule heuristics: choose geographically dispersed medians (farthest-distance principle) for better clustering • Fixed Charge problem: adds location cost fi per facility and capacity Ci constraints • Variants: allow multiple suppliers per customer (transportation problem) or single-supplier-per-customer assignment models
Facility location problems determine optimal positions for supply points to serve customer demand. The P-median problem minimizes distance-based transportation cost by selecting p median points; the …