Algorithms for the Assignment and Transportation Problems

In this paper we presen algorithms for the solution of the general assignment and transportation problems. In Section 1, a statement of the algorithm for the assignment problem appears, along with a proof for the correctness of the algorithm. The remarks which constitute the proof are incorporated parenthetically into the statement of the algorithm. Following this appears a discussion of certain theoretical aspects of the problem. In Section 2, the algorithm is generalized to one for the transportation problem. The algorithm of that section is stated as concisely as possible, with theoretical remarks omitted. 1. THE ASSIGNMENT PROBLEM. The personnel-assignment problem is the problem of choosing an optimal assignment of n men to n jobs, assuming that numerical ratings are given for each man’s performance on each job. An optimal assignment is one which makes the sum of the men’s ratings for their assigned jobs a maximum. There are n! possible assignments (of which several may be optimal), so that it is physically impossible, except