Operation Ressearch

1. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

End Semester Examinations – April 2013

MIB – II SEMESTER

Operation Ressearch

Duration: 3 Hrs                                                                         Max. Marks: 100

Section – A

1. Answer any SEVEN questions (out of TEN)     (7 x 5  = 35)

 

1. Define Operation Research. Support or refute that the following problems are suited for operations research by giving reasons in defense briefly-
2. a) Stockpiling of crackers prior to Diwali
3. b) A scooter, its driver and his companion towards office.
4. c) Opening another payment counter by a commercial bank.
5. d) A newspaper boy estimating how many copies of the Times Of India he should procure every day.
6. e) Reinforcing the strength of the unloading equipment and facilities by the port authorities of Madras.

 

2. Let us assume that you have inherited Rs1,00,000 from your father-in-law that can be invested in a combination of only two stock portfolios, with maximum investment allowed in either portfolios at Rs 75,000. The first portfolio has an average rate of return of 10% whereas the second has 20%. In terms of the risk factors associated with these portfolios, the firm has a risk rating of 4 (on a scale 0 to 10) and second has 9. Since you wish to maximize your return, you will not accept on average rate of return below 12% or a risk factor above 6. Hence you then face an important question. How much should you invest in each portfolio? Formulate the LP model and solve by graphical method.

 

3. XYZ Company wants to undertake an order for a customer. The order involves four tasks A, B, C and D. Four workers W_1, W₂, W₃ and W₄ are available for doing the tasks. Each worker will be uniquely assigned to only one of the four tasks. The company manager wants to minimize the total estimated labour hours required o complete the order. The supervisor has estimated the times required for each worker to complete each task. These times are shown in the table below:

 

	Labour Time(*hours)
Worker/job	A	B	C	D
W1	5	3	1	5
W2	6	6	2	7
W3	5	5	3	8
W4	8	2	4	3

 

Assume that any of the tasks may be done concurrently with the others. How would the manager assign workers to tasks so that the total time for completion of all four tasks is minimized?

 

 

4. Draw a network diagram and ascertain critical path

Activities	A	B	C	D	E	F	G
Predecessor	–	–	–	A	B	C	D,E,F
Duration(days)	7	10	8	5	6	4	5

Also calculate total float.

 

5. At Dr Ashok’s clinic patients arrive at an average of 6 patients per hour. The clinic is attended to by Dr Ashok himself. Some patients require only the required prescription. Some come for minor checkup while some others require thorough inspection for the diagnosis. This takes the doctor six minutes per patient on an average. It can be assumed that arrivals follow a Poisson distribution and Doctor’s inspection time follows an exponential distribution. Determine :
6. i) the percentage of time can walk to the doctor without having to wait
7. ii) the average number of patients in the system

iii) the average number of patients in the queue

 

6. Differentiate between pure strategy and mixed strategy.

Solve the game whose pay-off matrix is given by

Player A	Player B
	15	2	3
	6	5	7
	-7	4	0

 

7. a) What is a trans-shipment problem?
8. b) Describe the steps involved in solving a transportation model by MODI

method.

 

8. A confectioner sells confectionery items. Past data of demand per week in hundred kilograms with frequency is given below:

Demand/week	0	5	10	15	20	25
Frequency	2	11	8	21	5	3

Using the following sequence of random numbers, generate the demand for the next 10 weeks. Also find the average demand per week.

R.No

35

52

90

13

23

73

34

57

35

83

 

9. Give in brief the methodology of Operation Research.

 

10. What do you understand by the term duality? Write the dual for the following primal LP problem.

 

Minimize Z =20X₁ + 15X₂ +18X₃ + 10X₄

Subject to

4X₁ -3X₂ + 10X₃+ 4X₄ < 60

X₁ +  X₂+   X₃ = 27

-X₂ +4X₂+ 7X₃ > 35

Non negativity X_1, X_2, X_3, X₄ > 0

 

 

 

 

 

 Section – B

1. Answer any THREE out of FIVE.                            (3 x 15   = 45)

 

11. A diet conscious housewife wishes to ensure certain minimum intake of vitamins A,B and C for the family. The minimum daily (quantity) needs of the vitamins A,B and C for the family are respectively 30,20 and 16 units. For the supply of this minimum vitamin requirement, the housewife depends on two fresh foods. The first one provides 7,5, 2 units of three vitamin per gram respectively and the second one provides 2,4, 8 units of the same three vitamins per gram of the food stuff respectively. The first food stuff costs Rs 3 per gram and the second Rs 2 per gram. The problem is how many grams of each food stuff should the housewife buy everyday to keep her food bill as low as possible?
12. a) formulate the underlying L.P problem.
13. b) write the dual problem
14. c) solve the dual problem by using the simplex method.

 

12. The marketing manager of a company faced with the problem of assigning 5 regional managers to six zones. From past experience he knows that the efficiency percentage judged by the sales, market share, operating cost etc depends a lot on Regional Manager Zone combination given below:

	Regional Manager Zones
Managers	I	II	III	IV	V	VI
A	71	89	85	80	76	78
B	79	83	67	74	72	83
C	73	70	81	82	76	89
D	91	94	84	89	81	80
E	88	89	77	87	67	74

You are to advise the marketing manager which zone should be managed by a junior manager due to the non-availability of a regional manager, so that overall efficiency is maximized.

 

13. A company has four terminals u, v, w and x. at the start of a particular day 10, 4, 6 and 5 trailers respectively are available at these terminals. During the previous night 13, 10, 6 and 6 trailers respectively were loaded at plants A, B, C and D. the company dispatcher has come up with the costs between the terminals and plants as follows:

TERMINAL	PLANTS
		A	B	C	D
	U	20	36	10	28
	V	40	20	45	20
	W	75	35	45	50
	X	30	35	40	25

Find the allocation of loaded trailer from plants to terminals in order to minimize transportation cost.

 

14. A book store wishes to carry a particular book in stock. Demand is probabilistic and replenishment of stock takes two days (i.e if an order is placed on 1^st March, it will be delivered at the end of the day on March 3). The probabilities of demand are given below:

Demand(daily)	0	1	2	3	4
Probability	0.05	0.10	0.30	0.45	0.10

Each time an order is placed, the store incurs an ordering cost of Rs 10 per order. The store also incurs a carrying cost of Rs 0.05 per book per day. The inventory carrying cost is calculated on the basis of stock at the end of each day. The manager of the book store wishes to compare two options for his inventory decision:

A ) order 5 books when the inventory at the beginning of the day plus orders outstanding is less than 8 books.

8. B) order 8 books when the inventory at the beginning of the day plus orders outstanding is less than 8.

Currently (beginning of 1^st day) the store has a stock of 8 books plus 6 ordered two days ago and expected to arrive next day. Using Monte Carlo simulation for 10 cycles, recommend which option the manager should choose.

The two digit random numbers are: 89, 34, 78, 61, 39, 16, 13, 73.

 

15. Discuss the various techniques used in Operation Research.

 

Section – C

• ONE Compulsory Case study (No choice) (1 x 20 = 20)                     

16. Project consists of eight activities with the following time estimates:

ACTIVITY	IMMEDIATE PREDECESSOR	OPTIMISTIC TIME(DAYS)	MOST LIKELY TIME(DAYS)	PESSIMISTIC TIME(DAYS)
A	–	1	1	7
B	–	1	4	7
C	–	2	2	8
D	A	1	1	1
E	B	2	5	14
F	C	2	5	8
G	D,E	3	6	15
H	F,G	1	2	3

1. Draw PERT network.
2. Find expected time for each activity
3. Determine the earliest event time and latest allowable time.
4. Determine critical path.
5. Determine the total float for each activity
6. what is the probability that the project will be completed in
7. a) 22days b) 18 days and          c)19days.