SHRI V.K. PANDE COLLEGE OF SCIENCE AND MANAGEMENT HINGANGHAT

SESSIONAL EXAMINATION -2009BACHELOR OF COMPUTER APPLICATION-I

SUBJECT :OPERATION RESEARCH-3

TIME:- THREE HOURS MARKS:-40N.B 1:- All questions are compulsory and carry equal marks

2:- Draw neat diagram wherever necessary.EITHER: (4*2) 1. A) Write short note on the following:- i. Origin and Development of OR ii. Methodogies in OR iii. Nature of OR iv. OR Model.

Other Limitations:

7 5 • Make no more than 450 chairs

3Hrs 4Hrs 2400 • Make at least 100 tables

Painting 2Hrs 1Hrs 1000

OR

C) i) Write a one line Dafination on the following term:- i. Optimal solution ii. Unbounded solution iii. Infesible solution solution iv. Degenerate solution with finite vi. Unbounded solution space

EITHER: (4*2)

Factory

SourcesWahrehouse

W1 W2 W3 W4 Capacity

F1 10 30 50 10 7

F2 70 30 40 60 9

F3 40 8 70 20 18

Requirment 5 8 7 14 34 B) Explain the zero one model for assignment problem with example.

OR

C) What is Game Theory? Explain its Terminologies. D) Solve the follwing 3x5 game using dominance property:-

Player BStrategy 1 2 3 4 5

1 6 15 30 21 62 3 3 6 6 43 12 12 24 36 3

EITHER: (4*2) 3. A) Explain the various quantitive (criterion)methods which are usful for decision making un

Uncertinity and Risk. B) Given below is a payoff Table:-

Event (State of Nature) Indicate decision taken under the following appr

Action E1 E2 E3 E4 aches. i. Pessimistic ii. Optimistic iii. Laplace

A1 50 300 -150 50 iv.Suppose that the probabilites of the evnts in t

A2 400 0 100 0 are ; P(E1)=0.15 P(E2)=0.45; P(E3)=0.25; P(E4)

A3 -50 200 0 100 Calculate EMV AND EOL

A4 0 300 300 0

OR

B) Formulate the LPP Model and Solve By Graphical Method.

Tables (Per table)

Chairs

(PerChair)

Hours AvailableProfit

Contribution

Carpentry

ii) Formulation of Duality Problem and Explain it application.

D) Solve by simplex method Consider Z = 3x + 5y Subject to x < 40, y < 30, x + y < 60, x, y > 0.

Player A

C) The details of a project consisting of activities A to K are summarized in Table.

Activity Duration (Weeks)

to tm tpA - 6 7 8 1. Construct the project diagram B - 1 2 9 2. Find the Expected duration andC - 1 4 7 the variance of each activity D A 1 2 3 3. Find the critical path and ProjecE A,B 1 2 9 expected completion time.F C 1 5 9G C 2 2 8H E,F 4 4 4I E,F 4 4 10J D,H 2 5 14K I,G 2 2 8

D) Explain the following term: i. Basic conept of network ii. Time cost Trade OFF aspects in Network iii. Constraints in Network iv. Advantage in Network

EITHER: (4*2) 4 A) Name and Types of models of inventory system and explain tham in detail.

the unit cost if the unit cost is Rs.15 per unit,the cost of making one purchases is Rs.600, the holding cost

for 1 unit is Rs.20 per year and the cost of one shortage is Rs. 100 per year determine.

OR

Demand 0 1 2 3 4 5 6 or moreProbabiltiy 0.4 0.24 0.20 0.10 0.05 0.01 0.00

the holding cost of an old truck in stock for one month is Rs.100 and the penalty for a truck if not supplied on demand is Rs.1000.00. Determine the optimal size of the stock of the contractor? EITHER: (4*2)

gate is 45 seconds. The arrival rate and service rate follows possion distribution there is a complaint that

time to pass through the toll gate to 35 seconds of the idle time of the tol gate is less then 9% and the

average queue length at the gate is more than 8 vehicles check whether the installation of the second

gate is justified. OR

C) List and explain the terminologies used in queueing system.

The average time taken by a cashier to lost and calculate the customer is 2.5 minutes following

exponential distribution. What is the probability that the queue length excceds 6 ? What is the expected

time spent by a customer in the system?

Immediate

Predecessor(s)

B) i)The demand for a purchased item is 1000 units per month and the shrotage are allowed if

a. Economic order quantity b. The optimum number of Shortage c. The time between orders

d. The number of orders per year e. The optimum annual cost.

ii) if the items can be manufactured at a rate of 4000 per month. If all the costs are the same. Determine f. The optimum quantity of manufactures g. The optimum number of shortage h. The optimal annual cost i. The time of shortage j. The time between setup

k.The time to manufacture optimum quantity

C) Write short note on:- 1. Inventory control 2. Inventory Costs 3. Types of Inventory 4. Inventory Objective.

D) A contractor of second hand motor trucks maintains a stock of trucks. Every month demand of the trucks

occurs at a relatively constant rate but not in a constant size. The demand is show in the following

probability distribution:-

5 A) Write a short note on:- 1. Queueing system 2. Transient and steady state B) Vehicles are passing through a toll gate at the rate of 70 per hour. The average time to pass through the

the vehicles wait for long duration the authorites are willing to instal one more gate to reduce the average

D) In a supermarket the average arrival rate of customer is 10 every 30 minutes follwing possion process