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DATA ENVELOPMENT ANALYSIS 191

Problems

Note: The following problems have been designed to give you an understanding and appreci-
ation of the broad range of problems that can be formulated as linear programmes. You should
be able to formulate a linear programming model for each of the problems. However, you will
need access to a linear programming computer package to develop the solutions and make the
requested interpretations.
1 The Uppsala Chamber of Commerce periodically sponsors public service seminars and
programmes. Currently, promotional plans are under way for this year’s programme.
Advertising alternatives include television, Internet and newspaper. Audience estimates,
costs and maximum media usage limitations are as shown.

Constraint Television Internet Newspaper
Audience per advertisement 100 000 18 000 40 000
Cost per advertisement E2 000 E300 E600
Maximum media usage 10 20 10

To ensure a balanced use of advertising media, Internet advertisements must not exceed
50 per cent of the total number of advertisements authorized. In addition, television should
account for at least 10 per cent of the total number of advertisements authorized.
a. If the promotional budget is limited to E18 200, how many commercial messages
should be run on each medium to maximize total audience contact? What is the
allocation of the budget among the three media, and what is the total audience
reached?
b. By how much would audience contact increase if an extra E100 were allocated to the
promotional budget?

2 The management of Hartman Company is trying to determine the amount of each of two
products to produce over the coming planning period. The following information concerns
labour availability, labour utilization and product profitability.

Product (hours/unit)
Department 1 2 Labour-Hours Available

A 1.00 0.35 100
B 0.30 0.20 36
C 0.20 0.50 50
Profit contribution/unit E30.00 E15.00

a. Develop a linear programming model of the Hartman Company problem. Solve the
model to determine the optimal production quantities of products 1 and 2.
b. In calculating the profit contribution per unit, management doesn’t deduct labour costs
because they are considered fixed for the upcoming planning period. However,
suppose that overtime can be scheduled in some of the departments. Which
departments would you recommend scheduling for overtime? How much would you be
willing to pay per hour of overtime in each department?

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