Solving Assignment Problems
Using the Hungarian Method
1. The management of a market research firm
wants to assign project leaders to clients, one leader to each client. There are three project leaders
available. The estimated project
completion times in days are given below.
Find the optimal assignment. What
is the total time?
Client
|
Project Leader |
1 |
2 |
3 |
4 |
|
|
6 |
3 |
8 |
12 |
|
Barkin |
10 |
2 |
10 |
14 |
|
Cramer |
9 |
5 |
7 |
13 |
2. An accounting firm has four accountants
available for assignments to three clients.
The estimated completion times in days are given in the following
table. Find the assignment of
accountants to clients that will minimize the total time to complete all projects. If there are tying optimal solutions,
indicate all. What is the total time?
Client
|
Accountant |
A |
B |
C |
|
Goldman |
8 |
13 |
7 |
|
Wise |
7 |
16 |
3 |
|
Brown |
4 |
12 |
1 |
|
Spears |
6 |
14 |
4 |
3. SBB Cable, Inc., has four sales territories. Each sales territory will be assigned a sales
representative. The sales manager estimated
the annual sales volume (in thousands of dollars) for each sales representative
in each sales territory as given in the table below. Find the sales representative territory
assignments that will maximize sales.
What is the total sales in dollars?
|
Sales Representative |
1 |
2 |
3 |
4 |
|
Smith |
54 |
85 |
57 |
70 |
|
Johnson |
70 |
61 |
45 |
82 |
|
|
46 |
65 |
53 |
58 |
|
Baker |
62 |
81 |
41 |
50 |
Answers:
1. 15 days
2. 20 days
3. $282,000