(An) algorithm for the assignment problem with a specially structured cost function

Abstract

This thesis examines a special case of the assignment problem where two different types of facilities are paired to process a set of jobs. Each job consists of two operations characterized by the type of facilities employed, and the importance of one type facilities dominates that of the other in determining the performance of each job. Given two sets of each type facilities, we attempt to find a mapping from one set to the other which maximizes the performance of this system. Some assumptions and definitions are made to reduce the complexity of our problem. Our mathematical formulation takes a form of LP (linear programming) problem, but the cost coefficients are not known. Since the estimation of the cost coefficients entails difficult problems, the solution of this problem using available LP algorithms is not efficient. We settle such a difficulty by breaking our problem up into a set of subproblems and by assuming the hierarchically leveled structure of cost function. On the basis of this reasoning, we develop a systematic algorithm and show some applicable areas of it. A numerical example is provided to illustrate the solution process of our algorithm. Finally we make some comments on both the algorithm and its extensions.