B.E. (Production)
OPERATIONS RESEARCH (2008 Pattern) (Sem. – I)
Time :3 Hours] [Max. Marks :100
Instructions to the candidates:
1) Attempt question 1 or 2; 3 or 4 and 5 or 6 from section I.
2) Attempt question 7 or 8; 9 or 10 and 11 or 12 from section II.
3) Answers to section I and Section II be written in separate answer books.
4) Use of calculators and Normal distribution probability tables is per permitted.
SECTION – I Unit – I
Q1) a) Solve by Simplex method :

b) The postal department is considering the purchase of vehicles to pick up and deliver mail from various offices. They are considering three types of vehicles. The costs of each of these are 5, 10 and 8 lakhs per vehicles. These require crew of 2, 4 and 4 persons per day considering multiple shifts respectively. They expect those to run for 60, 100 and 80 kilometers. Based on fuel economy, the operating cost per day for these vehicles are 200, 350 and 300 Rs/day respectively. They have budget restriction of Rs. 1.6 crore and have 80 people available for crew. How many vehicles of each type to be purchase so as to minimize the operating costs?
(Only formulate LPP. Do not solve it) [5]
OR
Q2) a) Solve by Dual Simplex method :
b) Discuss Duality and its applications. Unit – II 
Q3) a) Following table represents cost of projects (lakhs) for particular bidder.
Find out optimal assignment of bidders to projects so as to minimize total cost. Find also total cost of the projects. One bidder is to be given only one project. [12]
Projects  
Bidders  I 
II 
III 
IV 
A 
10 
11 
16 
25 
B 
13 
33 
41 
60 
C 
20 
50 
83 
96 
D 
26 
71 
110 
135 
[6] 
b) Discuss Travelling Salesman Problem.
OR
Q4) a) How unbalanced Assignment problem is solved? How maximization Assignment problem is solved? [6]
b) A company has three factories F1, F2, and F3 and goods are supplied to 4 different cities D1, D2, D3 and D4. The table shows per unit cost of transportation. The supply capacities and demand are as shown in the table.
Factories  Consumption centers 
Capacity 

D1 
D2 
D3 
D4 

F1 
3 
1 
7 
4 
300 
F2 
2 
6 
5 
9 
400 
F3 
8 
3 
3 
2 
500 
Demand 
250 
350 
400 
200 
i) Find BFS by VAM. [6]
ii) Test if VAM solution optimal? [6]
Unit – III
Q5) a) Discuss Integer programming application. [6]
b) How goals are set? How priority is set for different goals in Goal programming? Discuss. [5]
c) Discuss Bellman principle of optimality in view to Dynamic programming.
[5]
OR
Q6) a) What is 01 programming? How 0 – 1 IP problems are formulated? State applications. [6]
b) The following table represents arcs and the distances. A person wants to go from city 1 to city 10. The various distances are given in a table. Find the optimal path by Dynamic programming. [10]
Arc 
Distance 
Arc 
Distance 
Arc 
Distance 
Arc 
Distance 
12 
5 
27 
8 
46 
5 
69 
7 
13 
5 
35 
8 
47 
7 
78 
5 
14 
6 
36 
10 
58 
6 
79 
7 
25 
4 
37 
5 
59 
8 
810 
8 
26 
7 
45 
4 
68 
9 
910 
9 
SECTION – II Unit – IV
Q7) a) Electronic equipment contains 500 resisters. When any resister fails it is replaced individually and the cost is Rs. 20 per resister. If all resisters are replaced at the same time the cost is Rs 5 per resister. The % surviving rate S(i) at the end of month ‘i’ is given in the table. [10]
% Survival Rate 

Month (i) 
0 
1 
2 
3 
4 
5 
S(i) 
100 
90 
75 
55 
30 
0 
What is the optimum replacement plan?
b) Discuss dominance rule in Game theory with example.
OR
Q8) a) Discuss net present worth and future worth.
b) Solve the game by graphical method or sub – game method
Strategies 
Player B  
b1 
b2 
b3 

PlayerA 
al 
3 
1  4 
a2 
5 
8  2 
Unit – V 
Q9) a) Arrival rate of the customers at the banking counter follows Poisson distribution with mean 30 per hour. The service rate of the counter also follows Poisson distribution with mean of 60 per hour. Find [10]
i) Probability of having zero customers in the system.
ii) Probability of having 2 customers in the system.
iii) Expected customers in the system
iv) Mean customers in queue.
v) Average waiting time in queue.
b) Derive equation for Economic Production Quantity. State your assumptions. [6]
OR
Q10) a) An automobile factory manufactures a particular type of gear in batches within the factory. The gear is used in the final assembly. The particulars of the gear are :
3 00 00 000 per year 
Demand rate 10 000
Production rate 25 000
Set up cost 180
Carrying cost 2
Annual demand Find :
i) Economic production Quantity.
ii) Time between two setups.
iii) Production period.
units/day
units/day
Rs/setup
Rs per unit per year
iv) Annual holding cost. [2]
v) Annual set up cost and [1]
vi) Annual total cost. [1] b) Discuss minimum cost service rate. [6]
Unit VI
Q11) a) Network is given below with three time estimates.
Act 
12 
13 
14 
25 
26 
36 
47 
57 
67 
a* 
5 
18 
26 
16 
15 
6 
7 
7 
3 
b** 
10 
22 
40 
20 
25 
12 
12 
9 
5 
m*** 
8 
20 
33 
18 
20 
9 
10 
8 
4 
a* – Optimistic time estimate, b** – Pessimistic time estimate,
m*** – most likely time estimate
i) Draw AOA network. [2]
ii) Find expected durations and variances. [2]
iii) Find critical activities and critical path. [4]
iv) How much is expected project duration? [1]
v) Find probability that project takes more than 48 days. [2]
vi) Find probability that project is completed in 45 days. [2]
vii) Find the expected project duration for 95% confidence level? [2]
b) State different types of floats and discuss any one. [3]
OR
Q12) a) Network Immediate Predecessor (IP) table is given below.
Activity 
A 
B 
C 
D 
E 
F 
G 
H 
I 
IP  –  –  – 
A,B 
B 
D 
D,E 
C,F,G 
C,G 
Days 
4 
13 
10 
5 
11 
5 
2 
9 
8 
i) Draw AOA or AON network. [4] 
ii) Find critical activities and critical path. [4]
iii) How long is the project duration? [1]
iv) Tabulate Early Start schedule and Late start schedule times. [3]
v) Tabulate Total floats, Free floats, and Independent floats for any two non – critical activities. [3]
b) Compare CPM and PERT techniques. [3]