(A) cross decomposition algorithm applied to the two level simultaneous facility location problem

Abstract

The purpose of this thesis is to solve the two level simultaneous location problem with the warehouse capacity restriction. In order to produce the optimal location of both plants and warehouses, cross decomposition method will be used. Cross decomposition method, recently developed by Van Roy, unifies Benders decomposition and Lagrangean relaxation into a single framework that solves successively Benders subproblem, Lagrangean subproblem, and sometimes master problems. In our problem, Benders subproblem turns out to be a transshipment problem and Lagrangean subproblem becomes a two level uncapacitated simultaneous location problem. Solution methods to the derived sub and master problems are discussed and computational results are given for 21 test problems.