Uncapacitated and Capacitated Facility Location Problems

Abstract

The uncapacitated facility location problem (UFLP) involves locating an undetermined number of facilities to minimize the sum of the (annualized) fixed setup costs and the variable costs of serving the market demand from these facilities. UFLP is also known as the “simple” facility location problem SFLP, where both the alternative facility locations and the customer zones are considered discrete points on a plane or a road network. This assumes that the alternative sites have been predetermined and the demand in each customer zone is concentrated at the point representing that region. UFLP focuses on the production and distribution of a single commodity over a single time period (e.g., one year that is representative of the firm’s long-run demand and cost structure), during which the demand is assumed to be known with certainty. The distinguishing feature of this basic discrete location problem, however, is the decision maker’s ability to determine the size of each facility without any budgetary, technological, or physical restrictions. Krarup and Pruzan (1983) provided a comprehensive survey of the early literature on UFLP, including its solution properties. By demonstrating the relationships between UFLP and the set packing-covering-partitioning problems, they established its NP-completeness.