(A) B & B algorithm for locating both capaitated plants and warehouses in the two-stage facility location problem

Abstract

This thesis deals with the problems of locating both plants and warehouses simultaneously for a two-stage distribution system where commodities are delivered from plants to customers via intermediate warehouses, under the following assumptions : (i) Demand requirement for each customer is given fixed. (ii) Locations and capacities for all the potential plants and warehouses are given. With the cost elements of (a) Linear transportation costs between plants, warehouses and customers. (b) Fixed costs associated with opening capacitated plants and warehouses. Our objective is to determine the optimum set of plants and warehouses to open, and the corresponding transportation policy which satisfy all the customers`` demand requirements at minimum total cost. To obtain the optimal solution of this problem, modelled as the mixed integer linear programming problem, an efficient branch & bound algorithm is developed which successfully generalizes the work by Akinc & Khumawala for the single stage case to the two stage case, just as kaufman et al. did, for the uncapacitated problem, on the work by Efroymson & Ray. Our algorithm is explained in comparison with the work by Akinc & Khumawala and some limited results are given.