# Accession Number:

## AD0602672

# Title:

## A MULTIPLE-ASSIGNMENT PROBLEM

# Descriptive Note:

## Mathematical note

# Corporate Author:

## BOEING SCIENTIFIC RESEARCH LABS SEATTLEWA

# Personal Author(s):

# Report Date:

## 1964-04-01

# Pagination or Media Count:

## 18.0

# Abstract:

A generalization of Kuhns simple assignment problem is considered There are m men and n tasks given with each man qualified for certain of the tasks. The output from each task is given as a concave function of the number of qualified men assigned to it. Find an assignment of men to task, perhaps more than one man to a task, so as to maximize total output. An algorithm for solving this general problem is given in which transfers like those used by Kuhn on the simple problem are selected using a node-labeling procedure on a related network. The algorithm yields for every k, 1 k m, an optimal assignment of the first k men only, employing a single transfer to increase k by one. Several special forms of the generalized problem are considered including a target assignment problem which A. S. Manne has formulated as a linear program.

# Descriptors:

# Subject Categories:

- Operations Research
- Safety Engineering