LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034.

M.A. DEGREE EXAMINATION – ECONOMICS

SECOND SEMESTER – APRIL 2003

ST 2900 / s 872  –  OPERATIONS RESEARCH

 

30.04.2003

1.00 – 4.00                                                                                                       Max : 100 Marks

                                                                PART – A                                         (5´ 4=20 marks)

      Answer any FIVE questions.

 

1. Define Operations Research and highlight any four significant features.
2. How will you define basic solution to a system of ‘m’ simultaneous linear equations in ‘n’ unknowns (m < n)?
3. State the transportation problem mathematically as a linear programming problem.
4. Define : (i) Game  (ii)  Fair game (iii)  Strictly determinable game  (iv)  Saddle point.
5. Using dominance method solve the game:

Player B

Player A

6. Write a note on (i) CPM  (ii)
7. Define : (i) Setup cost  (ii)  Holding cost (iii)  Shortage cost  (iv)  Lead time.

 

 

                                                                PART – B                                       (4´ 10=40 marks)

      Answer any FOUR questions.

 

8. Find all the basic feasible solutions of the equations:.
9. Use graphical method to solve the following:

Maximize

Subject to the constraints :

10. Write the simplex algorithm used in finding an optimum solution to a linear programming problem.
11. Explain the ABC Inventory system.

 

 

 

 

 

12. Four professors are each capable of teaching any one of four different courses. Class preparation time in hours for different topics varies from professor to professor and is given in the table below. Each professor is assigned only one course. Determine an assignment schedule so as to minimize the total course preparation time for all courses:

 

Professor	Linear Programmes	Queueing Theory	Dynamic Programme	Regression Analysis
A	2	10	9	7
B	15	4	14	8
C	13	14	16	11
D	4	15	13	9

13. A small maintenance project consists of the following ten jobs whose precedence relations are identified by their node number:

Job (i, j)	(1, 2)	(2, 3)	(2, 4)	(3, 5)	(3, 6)
Duration (days)	2	3	5	4	1
Job (i, j)	(4, 6)	(4, 7)	(5, 8)	(6, 8)	(7,8)
Duration (days)	6	2	8	7	4

• Draw an arrow diagram.
• Find the critical path.

14. Explain multiple item static model with storage limitation.

 

                                                               PART – C                                         (2´20=40 marks)

Answer any TWO questions.

 

15. Use Big M method to

Minimize

Subject to the constraints :

 

16. Consider the following transportation table showing production and transportation costs along with the supply and demand positions of factories/distribution centres:

 

	M1	M2	M3	M4	Supply
F1	4	6	8	13	500
F2	13	11	10	8	700
F3	14	4	10	13	300
F4	9	11	13	3	500
Demand	250	350	1050	200

Find an initial basic feasible solution by using VAM.

• Find an optimal solution for the above problem.

17. Solve the game graphically :

Player B

Player  A

18. Explain single item static model with one price break with the necessary diagram in detail.

 

 

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