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332 CHAPTER 7 TRANSPORTATION, ASSIGNMENT AND TRANSSHIPMENT PROBLEMS

Three machines are available for the manufacturing operations. All three machines can
produce all the products at the same production rate. However, due to varying defect
percentages of each product on each machine, the unit costs of the products vary
depending on the machine used. Machine capacities for the next week, and the unit costs,
are as follows:

Product
Machine Capacity (units) Machine A B C

1 1 500 1 E1.00 E1.20 E0.90
2 1 500 2 E1.30 E1.40 E1.20
3 1 000 3 E1.10 E1.00 E1.20

Formulate and solve a linear programming model that can be used to develop the
minimum cost production schedule for the products and machines.

9 Scott and Associates, Inc., is an accounting firm that has three new clients. Project leaders will be
assigned to the three clients. Based on the different backgrounds and experiences of the
leaders, the various leader–client assignments differ in terms of projected completion times. The
possible assignments and the estimated completion times in days are:

Client

Project Leader 1 2 3
Jackson 10 16 32
Ellis 14 22 40
Smith 22 24 34

a. Develop a network representation of this problem.
b. Formulate the problem and solve. What is the total time required?
10 Assume that in Problem 9 an additional employee is available for possible assignment. The
following table shows the assignment alternatives and the estimated completion times.

Client
Project Leader 1 2 3
Jackson 10 16 32
Ellis 14 22 40
Smith 22 24 34
Burton 14 18 36

a. What is the optimal assignment?
b. How did the assignment change compared to the best assignment possible in Problem
9? Were any savings associated with considering Burton as one of the possible project
leaders?
c. Which project leader remains unassigned?

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