Lagrangean relaxation and decomposition in an uncapacitated 2-hierarchal location-allocation problem

Abstract

We consider an uncapacitated 2-hierarchal location-allocation problem where p1 level 1 facilities and p2 level 2 facilities are to be located among n(≥p1 + p2) potential locations so as to minimize the total weighted travel distance to the facilities when θ, (0 ≤ θ ≤ 1) fraction of the demand from a level 1 facility is referred to a level 2 facility. At most one facility may be located at any location. In this model, a level 2 facility provides services in addition to services provided by a level 1 facility. The problem is formulated as a mathematical programming problem, relaxed and solved by a subgradient optimization procedure. The proposed procedure is illustrated with an example. © 1985.