M.B.A. DEGREE EXAMINATION, JUNE 2010

Second Semester

BA 9226 — APPLIED OPERATIONS RESEARCH FOR MANAGEMENT

(Regulation 2009)

Time : Three hours Maximum : 100 Marks

Answer ALL Questions

PART A — (10 × 2 = 20 Marks)

1. Write down the standard form of a LP problem.

2. List the applications of operation research model.

3. Distinguish between a transportation problem and assignment problem.

4. What do you understand by ‘Travelling Salesman Problem’?

5. Define ‘Mixed strategy’ in a game.

6. What is meant by mixed integer programming problem?

7. Name the inventory control systems adopted in practice.

8. Define simulation.

9. What is meant by group replacement policy?

10. List the components of a queueing system.

PART B — (5 × 16 = 80 Marks)

11. (a) A firm produces three products. These products are processors on three

different machines. The time required to manufacture one of each three

products and the daily capacity of the three machines are given below :

Machine Time per

(minutes)

Product Machine Capacity

1 2 3 Minutes/day

M1 4 5 4 460

M2 5 - 4 480

M3 4 6 - 450

It is required to determine the daily number of units to be manufactured

for each product. The profit per unit for product 1, 2 and 3 is Rs. 50

Rs. 40 and Rs. 70 respectively. It is assumed that all the products

produced are consumed in the market. Formulate a LP model maximize

the daily profit also determine the optimum production. (16)

Or

(b) (i) Find the maximum value of (12)

2 1 3 2 x x z + =

Subject to :

. y graphicall solve , 20 0

0

12

3

30

1

2 1

2

2

2 1

≤ ≤

≥ −

≤

≥

≤ +

x

x x

x

x

x x

(ii) Write the dual for the problem (4)

Minimize 4 3 2 1 3 2 x x x x z − + + =

Subject to :

0 , , ,

10 2

20 3 2

15 3 2

4 3 2 1

4 3 2 1

3 2 1

3 2 1

≥

≤ + + +

= + +

≥ + +

x x x x

and x x x x

x x x

x x x

132 132 132

J6513 3

12. (a) Find the basic feasible solution of the following transportation problem

by VAM. Also find the optimal transportation plan (16)

1 2 3 4 5 Available

A 4 3 1 2 6 80

B 5 2 3 4 5 60

C 3 5 6 3 2 40

D 2 4 4 5 3 20

Required 60 60 30 40 10 200 Total

Or

(b) (i) Explain transshipment model. (6)

(ii) A company has surplus truck in each of the cities A,B,C,D and E

and one deficit truck in each of the cities 1,2,3,4,5 and 6. The

distance between the cities in kilometers in shown in matrix below.

Find the assignment to trucks from cities in surplus to cities in

deficit so that the total distance covered by vehicle is minimum. (10)

1 2 3 4 5 6

A 12 10 15 22 18 8

B 10 18 25 15 16 12

C 11 10 3 8 5 9

D 6 14 10 13 13 12

E 8 12 11 7 13 10

13. (a) (i) Solve the following 2 × n game by method of sub - game (8)

Player B

B1 B2 B3

Player A

A1 1 3 11

A2 8 5 2

(ii) Reduce the following game by dominance property and solve it (8)

Player B

1 2 3 4 5

I 1 3 2 7 4

Player A II 3 4 1 5 6

III 6 5 7 6 5

IV 2 1 6 3 1

Or

(b) Explain the branch and bound and cutting plane algorithms for pure and

mixed integer programming problem. (16)

132 132 132

J6513 4

14. (a) (i) Explain decision making under uncertainty. (4)

(ii) A company has a demand of 12,000 unit / year for an item and it

can product 2000 such items per month. The cost of one setup is

Rs. 400 and the holding cost /unit/ month is Rs. 50. Find the

optimal lot size and the total cost per year, assuming cost of one

unit as Rs.5. Also find the maximum inventory, manufacturing time

and total time.

(12)

Or

(b) (i) Discuss the application of simulation techniques for decision

making. (4)

(ii) The demand for an item uniform at a rate of 50 units per month.

The fixed cost is Rs. 80 each time a production is made. The

production cost is Rs. 5 per item and the inventory carrying cost is

Rs. 0.50 per item per month. If the shortage cost is Rs. 2.5 per item

per month, determine how often to make a production run and of

what size it should be? (12)

15. (a) Ships arrive at a port at the rate of one in every 4 hours with exponential

distribution of inter arrival times. The time as ship occupies a berth for

unloading has exponential distribution with an average of 10 hours. If

the average delay of ships waiting for berths is to be kept below 14 hours,

how many berths should be provided at the port? (16)

Or

(b) The cost of machine is Rs. 16,100 and its scrap value is Rs. 1,100 the

maintenance costs found from experience are as follows

Year : 1 2 3 4 5 6 7 8

Maintenance : 300 450 600 800 100 1200 1500 2000

When should the machine, be replaced. (16)

Second Semester

BA 9226 — APPLIED OPERATIONS RESEARCH FOR MANAGEMENT

(Regulation 2009)

Time : Three hours Maximum : 100 Marks

Answer ALL Questions

PART A — (10 × 2 = 20 Marks)

1. Write down the standard form of a LP problem.

2. List the applications of operation research model.

3. Distinguish between a transportation problem and assignment problem.

4. What do you understand by ‘Travelling Salesman Problem’?

5. Define ‘Mixed strategy’ in a game.

6. What is meant by mixed integer programming problem?

7. Name the inventory control systems adopted in practice.

8. Define simulation.

9. What is meant by group replacement policy?

10. List the components of a queueing system.

PART B — (5 × 16 = 80 Marks)

11. (a) A firm produces three products. These products are processors on three

different machines. The time required to manufacture one of each three

products and the daily capacity of the three machines are given below :

Machine Time per

(minutes)

Product Machine Capacity

1 2 3 Minutes/day

M1 4 5 4 460

M2 5 - 4 480

M3 4 6 - 450

It is required to determine the daily number of units to be manufactured

for each product. The profit per unit for product 1, 2 and 3 is Rs. 50

Rs. 40 and Rs. 70 respectively. It is assumed that all the products

produced are consumed in the market. Formulate a LP model maximize

the daily profit also determine the optimum production. (16)

Or

(b) (i) Find the maximum value of (12)

2 1 3 2 x x z + =

Subject to :

. y graphicall solve , 20 0

0

12

3

30

1

2 1

2

2

2 1

≤ ≤

≥ −

≤

≥

≤ +

x

x x

x

x

x x

(ii) Write the dual for the problem (4)

Minimize 4 3 2 1 3 2 x x x x z − + + =

Subject to :

0 , , ,

10 2

20 3 2

15 3 2

4 3 2 1

4 3 2 1

3 2 1

3 2 1

≥

≤ + + +

= + +

≥ + +

x x x x

and x x x x

x x x

x x x

132 132 132

J6513 3

12. (a) Find the basic feasible solution of the following transportation problem

by VAM. Also find the optimal transportation plan (16)

1 2 3 4 5 Available

A 4 3 1 2 6 80

B 5 2 3 4 5 60

C 3 5 6 3 2 40

D 2 4 4 5 3 20

Required 60 60 30 40 10 200 Total

Or

(b) (i) Explain transshipment model. (6)

(ii) A company has surplus truck in each of the cities A,B,C,D and E

and one deficit truck in each of the cities 1,2,3,4,5 and 6. The

distance between the cities in kilometers in shown in matrix below.

Find the assignment to trucks from cities in surplus to cities in

deficit so that the total distance covered by vehicle is minimum. (10)

1 2 3 4 5 6

A 12 10 15 22 18 8

B 10 18 25 15 16 12

C 11 10 3 8 5 9

D 6 14 10 13 13 12

E 8 12 11 7 13 10

13. (a) (i) Solve the following 2 × n game by method of sub - game (8)

Player B

B1 B2 B3

Player A

A1 1 3 11

A2 8 5 2

(ii) Reduce the following game by dominance property and solve it (8)

Player B

1 2 3 4 5

I 1 3 2 7 4

Player A II 3 4 1 5 6

III 6 5 7 6 5

IV 2 1 6 3 1

Or

(b) Explain the branch and bound and cutting plane algorithms for pure and

mixed integer programming problem. (16)

132 132 132

J6513 4

14. (a) (i) Explain decision making under uncertainty. (4)

(ii) A company has a demand of 12,000 unit / year for an item and it

can product 2000 such items per month. The cost of one setup is

Rs. 400 and the holding cost /unit/ month is Rs. 50. Find the

optimal lot size and the total cost per year, assuming cost of one

unit as Rs.5. Also find the maximum inventory, manufacturing time

and total time.

(12)

Or

(b) (i) Discuss the application of simulation techniques for decision

making. (4)

(ii) The demand for an item uniform at a rate of 50 units per month.

The fixed cost is Rs. 80 each time a production is made. The

production cost is Rs. 5 per item and the inventory carrying cost is

Rs. 0.50 per item per month. If the shortage cost is Rs. 2.5 per item

per month, determine how often to make a production run and of

what size it should be? (12)

15. (a) Ships arrive at a port at the rate of one in every 4 hours with exponential

distribution of inter arrival times. The time as ship occupies a berth for

unloading has exponential distribution with an average of 10 hours. If

the average delay of ships waiting for berths is to be kept below 14 hours,

how many berths should be provided at the port? (16)

Or

(b) The cost of machine is Rs. 16,100 and its scrap value is Rs. 1,100 the

maintenance costs found from experience are as follows

Year : 1 2 3 4 5 6 7 8

Maintenance : 300 450 600 800 100 1200 1500 2000

When should the machine, be replaced. (16)

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