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Posted By: b.thirumaya prabhu Member Level: Gold Posted Date: 01 Jun 2008
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2005 Jawaharlal Nehru Technological University Jawaharlal Nehru Technological University B.E Computer Science mathematical modelling and stimulation(MMS) Question paper
Code No: RR410508 Set No. 1
IV B.Tech I Semester Regular Examinations, November 2005
MATHEMATICAL MODELLING & SIMULATION
( Common to Computer Science & Engineering and Electronics &
Computer Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
. . . . .
1. Illustrate graphically the following special cases of L. P. P. [6+5+5=16]
(a) Multiple optimal solutions
(b) Feasible solutions
(c) Unrestricted variable.
2. Solve the following transportation: [16]
1 2 3 4 Supply
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
Requirement 7 5 3 2
3. (a) What are the types of inventory? Why they are maintained? [6]
(b) A particular item has a demand of 9,000 units/year. The cost of one pro-
curement is Rs. 100 and the holding cost per unit is Rs. 2.40 per year. The
replacement is instaneous and no shortages are allowed determine. [10]
i. the economic lot size
ii. the number of orders per year
iii. the time between orders
iv. total cost per year if the cost of one unit is Rs. 1.
4. (a) State various types of items in inventory control techniques. [6]
(b) The following thirty numbers represent the annual value in thousand of ru-
pees of some thirty items of materials selected at random. Carry out an ABC
analysis and list out the values of ‘A’ items only: [10]
1 2 4 9 75 4 25
3 6 13 2 4 12 30
100 2 7 40 15 55 1
11 15 8 19 1 20 1
3 5
5. With respect to queuing theory, explain the following [8+8=16]
1 of 2
Code No: RR410508 Set No. 1
(a) Cost models in queuing theory
(b) Non-poisson queues.
6. A project has the following characteristics [16]
Activity Optimistic time pessimistic time Most likely time
(days) (days) (days)
1-2 1 5 1.5
2-3 1 3 2
2-4 1 5 3
3-5 3 5 4
4-5 2 4 3
4-6 3 7 5
5-7 4 6 5
6-7 6 8 7
7-8 2 6 4
7-9 5 8 6
8-10 1 3 2
9-10 3 7 5
Construct a PERT Network. Find the critical path and variance for each event.
Find the project duration at 95% probability.
7. (a) What is a pseudo-random number generator? How to construct it? [6]
(b) What is an inverse transformation method? Where do you use it? [4]
(c) Give any random number generation algorithm [6]
8. (a) Distinguish model verification and validation [4]
(b) Explain conceptual and operational model-building process. [12]
. . . . .
2 of 2
Code No: RR410508 Set No. 2
IV B.Tech I Semester Regular Examinations, November 2005
MATHEMATICAL MODELLING & SIMULATION
( Common to Computer Science & Engineering and Electronics &
Computer Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
. . . . .
1. (a) Explain briefly the general methods for solving O. R. models. [6]
(b) Ozark Farms uses at least 800 lb of special feed daily. The special feed is a
mixture of corn and soybean meal with the following compositions.
lb per lb of feed stu_
Feed Stu_ Protein Fiber Cost($lb)
Corn 0.09 0.02 0.30
Soybean 0.60 0.06 0.90
The dietary requirements of the special feed stipulate atleast 30% protein and at
most 5% fiber. Ozark Farms wishes to determine the daily minimum - cost feed
-mix. Formulate it as an L. P. model [10]
2. (a) Give an algorithm to solve an “Assignment” problem? [8]
(b) What is an unbalanced assignment problem? Explain it with at least one
example. [8]
3. (a) What are the types of inventory? Why they are maintained? [6]
(b) A particular item has a demand of 9,000 units/year. The cost of one pro-
curement is Rs. 100 and the holding cost per unit is Rs. 2.40 per year. The
replacement is instaneous and no shortages are allowed determine. [10]
i. the economic lot size
ii. the number of orders per year
iii. the time between orders
iv. total cost per year if the cost of one unit is Rs. 1.
4. (a) Explain ABC analysis. [8]
(b) What are its advantages and limitations, if any. [8]
5. In the production shop of a company, the breakdown of the machines is found
to be poisson with an average rate of 3 machines per hour. Breakdown time at
one machine costs Rs.40/- per hour to the company. There are two choices before
the company for hiring the repairmen, one of the repairmen is slow but cheap, the
other fast but expensive. The slow-cheap repairman demands Rs.20/- per hour and
will repair the broken down machines exponentially at the rate of Rs.4/- per hour.
The fast-expensive repairman demands Rs.30/- per hour and will repair machines
exponentially at an average rate of Rs.6/- per hour which repairman should be
hired. [16]
1 of 2
Code No: RR410508 Set No. 2
6. (a) Define the terms: [8]
i. Normal cost
ii. Crash cost
iii. Normal time
iv. Crash time
(b) Define “Critical path”, “Slack time” and “Dummy activity” with reference to
PERT and CPM. How can uncertainty be incorporated in PERT models. [8]
7. Explain the execution of simulation algorithm in [8+8=16]
(a) SIM SCRIPT
(b) GPSS
8. Explain the process of calibration and validation of simulation models. [16]
. . . . .
2 of 2
Code No: RR410508 Set No. 3
IV B.Tech I Semester Regular Examinations, November 2005
MATHEMATICAL MODELLING & SIMULATION
( Common to Computer Science & Engineering and Electronics &
Computer Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
. . . . .
1. (a) What is a model? Discuss various classification schemes of models. [6]
(b) Find all basic solutions for the problem [10]
Max z = x1 + 2x2
such that
x1 + x2 _ 10
2x1 - x2 _ 40
andx1, x2 _ 0.
2. Explain briefly: [5+5+6]
(a) North - West corner rule
(b) Minimum matrix method
(c) Vogels approximation method,
for finding an initial basic feasible solution for a transportation problem.
3. (a) Derive the E. O. Q. formula for the manufacturing model with shortages [6]
(b) A manufacturing firm has to supply 3,000 units annually to a customer who
does not have enough space for storing the material. There is a contract that
if the supplier fails to supply the material, a penalty of Rs. 40 per unit per
month will be levied. The inventory holding cost amounts to Rs. 20 per unit
per month and the setup cost is Rs. 400 per run. Find the expected number
of shortages at the end of each scheduling period. [10]
4. (a) Describe the norms you would use for controlling inventories classified by ABC
analysis. [6]
(b) Classify the following 14 items ABC categories: [10]
1 of 3
Code No: RR410508 Set No. 3
Code
N Monthly Consumption (in Rs.)
O.
D-179-0 451
D-115-0 1.052
D-186-0 205
D-191 893
D-192 843
D-193 727
D-195 412
D-196 214
D-198-0 188
D-199 172
D-200 170
D-204 5,056
D-205 159
D-212 3,424
How the policies with regard to safety stocks order quantity, materials control
and inventory system will be di_erent for the items classified as A, B and C.
5. Consider a self service store with one cashier. Assume poisson arrivals and ex-
ponential service times. Suppose that a customer arrive on the average every 5
minutes and the cashier can serve 10 in 5 minutes. Find [16]
(a) The average number of customers queuing for service
(b) The probability of having more than 10 customers in the system
(c) The probability that a customer has to queue for more than 2 minutes
If the service can be speeded upto 12 in 5 minutes by using a di_erent cash register,
what will be the e_ect on the quantities (a), (b) and (c)
6. (a) Explain PERT and its importance in network analysis. What are the require-
ments for applications of PERT techniques. [10]
(b) List at the di_erences between PERT and CPM [6]
7. (a) Explain the role of state descriptor in discrete system simulation [6]
(b) Define the terms [6]
i. Discrete event
ii. Simulation time
iii. Clock time
(c) Explain the representation of time in discrete system simulation [4]
8. Write a short notes on the following [6+5+5]
(a) Output analysis of a single model
2 of 3
Code No: RR410508 Set No. 3
(b) Chi-square test
(c) Kolmogorov-Smirnov test.
. . . . .
3 of 3
Code No: RR410508 Set No. 4
IV B.Tech I Semester Regular Examinations, November 2005
MATHEMATICAL MODELLING & SIMULATION
( Common to Computer Science & Engineering and Electronics &
Computer Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
. . . . .
1. (a) Explain the concept of degeneracy in simplex method with at least one exam-
ple? [4]
(b) Solve the following L. P. problem using Big M method: [12]
Minimize z =2x1 + 5x2
subject to the constraints:
x1 + x2 = 100
x1 _ 40
x2 _ 30
and x1, x2 _ 0.
2. (a) What is a non - linear programming problem? Give two examples of NLPP
stating clearly why do you so classify them? [10]
(b) Give canonical form of non - linear programming problem. [6]
3. (a) Derive the E. O. Q. formula for the manufacturing model with shortages [6]
(b) A manufacturing firm has to supply 3,000 units annually to a customer who
does not have enough space for storing the material. There is a contract that
if the supplier fails to supply the material, a penalty of Rs. 40 per unit per
month will be levied. The inventory holding cost amounts to Rs. 20 per unit
per month and the setup cost is Rs. 400 per run. Find the expected number
of shortages at the end of each scheduling period. [10]
4. (a) Explain the basis of selective inventory control [6] ?
(b) State the di_erent selection techniques adopted in inventory control system.
Give a brief note on each. [10]
5. At a railway station, only one train is handled at a time. The railway yard is
su_cient only for two trains to wait while others is given signal to leave the station.
Trains arrive at the station at an average rate of 6 per hour and the railway station
can handle them on an average of 12 per hour. Assuming poisson arrivals and
exponential service distribution, find the steady-state probabilities for the various
number of trains in the system. Also find the average waiting time of a new train
coming into the yard. [16]
6. A PERT network has the following activities with their time estimates given below:
[16]
1 of 2
Code No: RR410508 Set No. 4
Activity Optimistic (days) Most likely (days) Pessimistic (days)
0-1 2 3.5 8
0-2 3 3.75 6
0-3 1 2.5 7
1-2 3 7.5 9
1-5 4 5.5 10
2-4 2 5 8
3-4 2 2.75 5
3-5 3 6 9
4-5 2 5 8
(a) Construct a network and find the expected completion time of the project.
(b) Find the probability of completing the project 3 days ahead of the expected
schedule.
7. List and discuss various periods in the history of simulation software [16]
8. Discuss the steps in the development of a useful model of input data with suitable
example. [16]
. . . . .
2 of 2
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