A Capacitated Bottleneck Facility Location Problem

This paper considers the problem of locating capacitated facilities to meet customer demands. The objective of the problem considers both a bottleneck transportation cost and a total cost of opening facilities. The structure of the problem is similar to that of the total cost capacitated facility location problem. Problems with a bottleneck objective function are solved via a Lagrangean relaxation.

An implicit enumeration algorithm is developed to solve the relaxed problem. After a feasible facility configuration is selected, the resulting allocation problem is a bottleneck transportation problem. Special attention is given to the dual of the bottleneck transportation problem to aid the branching and fathoming steps of the solution procedure. Computation results are presented for several test problems.