Operation Research
5th Semester (Mechanical)
Assignment : 6
Unit: 6
Uka Tarsadia University, Bardoli
1. Bharat Transport Company is considering discontinuing its leasing of 12 pickups and delivery
trucks. If it does this, it will have to buy 12 trucks right away and then buy replacement
trucks in the future one by one, as the old ones wear out. The question that the Bharat
Transport Companys manager wants to answer is how many truck will they have to buy
during the next five years (including the initial 12 trucks) in order to keep 12 trucks in all the
operation.
2. Shreeji Hydaulics Ltd. is manufacturing of hydraulic press at Rajkot. They want to sell their
press all over the india. As they come to know from the market survey West Bengal, Punjab
and Maharastra has the potential to buy the hydraulic prss. They have 10 sles representative
working in these three states. The profitability of each representative in three states is given
in table. What will be the optimum allocation if the number of representatives available is
only eight?
Number of
Representative
Profitability in different states
West Bengal
Punjab
Maharashtra
20
31
35
27
40
43
35
45
49
43
51
55
50
60
65
53
67
70
59
75
77
65
81
85
70
88
90
75
95
95
10
75
100
90
3. Batliboi Ltd., manufacturing five different machineries. They have to supply the machineries to the
customer by cargo. There are five items of different weights per unit and values per unit are given in
table. The maximum cargo load is restricted to 19. How many machines should be loaded to maximize the
value?
Machinery
Weight/ Unit
Value/Unit
Lathe Machine
C. G. Patel Institute of Technology, Bardoli
Maliba Campus
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Operation Research
5th Semester (Mechanical)
Assignment : 6
Unit: 6
Uka Tarsadia University, Bardoli
Milling Machine
Radial Drilling
Shaper Machine
11
Planner Machine
13
Define the following terminology:
Stage
Immediate return
Dynamic recursive relation
State Variable
Optimal return
Decision Variable
State transportation function.
4. Distinguish between solution derived from simulation models and solutions derived from
analytical models?
5. What is Monte Carlo simulation? Describe the idea of experimentation (Random sampling) in
simulation.
6. Draw a flow chart to describe the simulation of a simple system.
7. List the advantages, applications, limitations and methodology of simulation.
8. What is dynamic programming? Write step by step procedure to solve a general problem by
dynamic programming approach.
9. Explain Bellmans principle of optimality.
10. What is dynamic recursive relation? Describe the general process of backward recursion
11. Using random numbers to simulate a sample, find the probability that a packet of 6 products does
not contain any defective product, when the production line produces 10 percent defective
products. Compare tour answer with the expected probability.
12. A hardware shop keeps stock of a popular brand of bearing. Previous experience shows the daily
demand for the item with associated probabilities, as given below:
Daily
0
10
20
30
40
50
demand
Probability
0.01
0.20
0.15
0.50
0.12
0.02
Use the following sequence of random numbers to simulate the demand for next 10 days.
Random Numbers: 25,39,65,76,12,05,73,89,19,49
Also estimate the daily average demand for the bearings on the basis of simulated data.
13. A company manufactures 200 motor cycles per day. Depending upon the availability of raw
materials and other conditions, the daily production has been varying from 196 motorcycles to
204 motorcycles, whose probability distribution is given as below:
Production / Day
Probability
196
0.05
197
0.09
198
0.12
C. G. Patel Institute of Technology, Bardoli
Maliba Campus
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Operation Research
5th Semester (Mechanical)
Assignment : 6
Unit: 6
Uka Tarsadia University, Bardoli
199
200
201
202
203
0.14
0.20
0.15
0.11
0.08
204
0.06
The motorcycles are transported in a specially designed three storeyed lorry that can accommodate
only
200
motorcycles.
Using
the
following
random
numbers:
82,89,78,24,52,53,61,18,45,04,23,50,77,27,54,10. Simulate the process to find out.
(a) The average number of motorcycles waiting in the factory.
(b) The average number of empty spcaces on the lorry?
14 .A book binder has one printing press, one binding machine and manuscripts of 7 different books.
Below:
Book
1
2
3
4
5
6
7
Printing
Time(Hours
20
90
80
20
120
15
65
)
Binding
25
60
75
30
90
35
50
time (hours)
Decide the optimum sequence of processing of books in order to minimize the total time required to bring
out all the books.
15. Solve the following Linear Programming (L.P.) problem using Dynamic Programing (D.P.) technique.
Maximize
5 x+ 9 y
subject to
x +3 y 3,
5 x+3 y 27both x y are 0,
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Maliba Campus
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