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330 CHAPTER 7 TRANSPORTATION, ASSIGNMENT AND TRANSSHIPMENT PROBLEMS

Warehouse
CPUs
Plant Singapore Seattle Lisbon Sao Paulo Dubai Available
10 20 5 9 10
Shanghai 9 000

2 10 8 30 6

Changchun 4 000

1 20 7 10 4
Nanchang 8 000

CPUs
Required 3 000 5 000 4 000 6 000 3 000 21 000

a. Develop a network representation of this problem.
b. Determine the amount that should be shipped from each plant to each warehouse to
minimize the total shipping cost.
c. The Singapore warehouse has just increased its order by 1000 units, and Arnoff has
authorized the Changchun plant to increase its production by 1000 units. Will this
change lead to an increase or decrease in total shipping costs? Solve for the new
optimal solution.
6 Premier Consulting has two consultants, Avery and Baker, who can be scheduled to work
for clients up to a maximum of 160 hours each over the next four weeks. A third consultant,
Campbell, has some assignments already planned and is available for clients up to a
maximum of 140 hours over the next four weeks. The company has four clients with
projects in process. The estimated hourly requirements for each of the clients over the four-
week period are:

Client Hours
A 180
B 75
C 100
D 85

Hourly rates vary for the consultant–client combination and are based on several factors,
including project type and the consultant’s experience. The rates (dollars per hour) for
each consultant–client combination are:

Consultant Client A Client B Client C Client D
Avery 100 125 115 100
Baker 120 135 115 120
Campbell 155 150 140 130

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