This thesis deals with product allocation problem in which a number of agencies are controlled and supplied by a central firm. To develop the model a method for evaluating overall performance of agency considering various factors related to the operation of agency is derived.
With the nonlinear profit function of agency developed, a set of optimal allocation quantity to each agency which maximizes the total profit of the central firm is obtained by the Lagrange multiplier method.
We consider the above problem in two cases depending on the number of manufacturing plants (supplying sources) the Central firm operates. For the case of multiple manufacturing plants. An algorithm for solving the products Allocation-transportation problem is developed.
This algorithm that utilizes the special structure of the Allocation-transportation problem is more efficient than the general method for solving convex nonlinear programming problems. Also this thesis presents a method for obtaining optimal purchasing (producing) quantity of product in the central firm using the economic interpretation of Lagrange multiplier.
