Case Problems


[Page 217 ( continued )]

The Tennessee Pterodactyls

The Tennessee Pterodactyls is a new professional basketball franchise in Nashville. The team's general manager, Jerry East, and coach, Phil Riley, are trying to develop a roster of players. They drafted seven players from a pool to which the other teams in the league each contributed two players. However, the general manager and coach perceive these acquisitions to be no more than role players. They believe that the nucleus of their new team must come from the free agents who are currently available on the market. The team is well under the salary cap, and the owner has made $50 million per year available to them to sign players. The coach and general manager have put together the following list of 12 free agents , with important statistics for each, including their rumored asking price in terms of annual salary:

   

Per-Game Averages

Projected Annual Salary ($1,000,000s)

Player

Position

Points

Rebounds

Assists

Minutes

1. Mack Madonna

Backcourt

14.7

4.4

9.3

40.3

$ 8.2

2. Darrell Boards

Frontcourt

12.6

10.6

2.1

34.5

6.5

3. Silk Curry

Backcourt

13.5

8.7

1.7

29.3

5.2

4. Ramon Dion

Backcourt

27.1

7.1

4.5

42.5

16.4

5. Joe Eastcoast

Backcourt

18.1

7.5

5.1

41.0

14.3

6. Abdul Famous

Frontcourt

22.8

9.5

2.4

38.5

23.5

7. Hiram Grant

Frontcourt

9.3

12.2

3.5

31.5

4.7

8. Antoine Roadman

Front court

10.2

12.6

1.8

44.4

7.1

9. Fred Westcoast

Frontcourt

16.9

2.5

11.4

42.7

15.8

10. Magic Jordan

Backcourt

28.5

6.5

1.3

38.1

26.4

11. Barry Bird

Front court

24.8

8.6

6.9

42.6

19.5

12. Grant Hall

Frontcourt

11.3

12.5

3.2

39.5

8.6



[Page 218]

Jerry and Phil want to sign five free agents. They would like the group they sign to average at least 80 points per game (16 points per player), pull down an average of 40 rebounds per game (8 per player), dish out an average of 25 assists, and have averaged 190 minutes (38 minutes per player) per game in the past. Furthermore, they do not want to sign more than two front court and three back court players. Their immediate objective is to identify the players who as a group would meet their objectives at the minimum cost.

  1. Formulate an integer linear programming model to help the general manager and coach determine which players they should sign and solve it by using the computer.

  2. Is the money provided by the owner sufficient to sign the group of players identified in (A)? If not, reformulate the model so that the available funds are a constraint and the objective is to maximize the average points of the group.




Introduction to Management Science
Introduction to Management Science (10th Edition)
ISBN: 0136064361
EAN: 2147483647
Year: 2006
Pages: 358

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