Showing papers on "Assignment problem published in 1970"

A Sequential Stochastic Assignment Problem

Abstract: Suppose there are n men available to perform n jobs. The n jobs occur in sequential order with the value of each job being a random variable X. Associated with each man is a probability p. If a “p” man is assigned to an “X = x” job, the (expected) reward is assumed to be given by px. After a man is assigned to a job, he is unavailable for future assignments. The paper is concerned with the optimal assignment of the n men to the n jobs, so as to maximize the total expected reward. The optimal policy is characterized, and a recursive equation is presented for obtaining the necessary constants of this optimal policy. In particular, if p1 ≦ p2 ≦ ⋯ ≦ pn the optimal choice in the initial stage of an n stage assignment problem is to use pi if x falls into an ith nonoverlapping interval comprising the real line. These intervals depend on n and the CDF of X, but are independent of the p's. The optimal policy is also presented for the generalized assignment problem, i.e., the assignment problem where the (expected)...

An Algorithm for the Quadratic Assignment Problem

Abstract: The paper presents a new approach to solving a class of combinatorial economic allocation problems. One member of this class is known as the quadratic assignment problem. Besides presenting an algorithm to solve this problem, we will discuss in general terms the techniques for treating combinatorial problems. A novel feature of the paper is the development of the statistical properties of the criterion function. These statistical properties are used in conjunction with a general enumerative procedure to form the main parts of the algorithm. Using the idea of confidence level enumeration, an extension of the algorithm is proposed which should allow for the effective treatment of large scale combinatorial problems. Finally we present some computational results in order to illustrate the effectiveness of the general approach.

The personnel assignment problem - A specific application to the assignment of scientific and engineering officers in the United States Air Force

Abstract: Mathematical model for optimal assignment of scientific and engineering personnel in Armed Forces

The assignment problem and a suboptimal solution technique

Abstract: A technique is presented which finds a fast suboptimal solution to the assignment problem. This same technique is then applied to two large dynamic programming problems for which the optimal solution is not known. These examples illustrate how easily this technique can be applied and that it is better than most optimizing techniques because it is fast, cheap and only minor hand calculations are needed. The effect of different initial solutions and their value are compared and it is found that the initial solution is not as significant in a suboptimal technique as in an optimizing technique. The initial solution is significant enough, however, to warrant some care in choosing it.

A linear programming method for detecting negative circuits with special application to the assignment problem

Abstract: A new method for detecting negative cycles in a graph is proposed. This method is based upon the primal dual relationships of a linear program formulated from an assignment problem type network. A computer program is developed for this new method to include the complete solution of the assignment problem. Results are given on program efficiency

Comment on "Delay-Free Asynchronous Circuits with Constrained Line Delays"

Abstract: A method for applying Tracey's procedure to the state assignment problem of nonnormal mode flow tables is proposed.