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Posted Date: 19 Apr 2008 Posted By: acme Member Level: Silver
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2007 Jawaharlal Nehru Technological University B.E Computer Science MATHEMATICAL MODELLING AND SIMULATION Question paper
Code No: RR410508 Set No. 1
IV B.Tech I Semester Regular Examinations, November 2007
MATHEMATICAL MODELLING AND 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) Describe a computational procedure of the simplex method of the solution of
a maximization L. P. problem. [4]
(b) Use duality to solve the following L. P. P: [12]
Maximize z =2x1 + x2
subject to the constraints:
x1 + 2x2 10
x1 + x2 6
x1 - x2 2
x1 - 2x2 1
and x1, x2 0.
2. (a) Distinguish between pure and mixed integer programming problem. [4]
(b) Find the optimal integer solution to the following L.P. P. [12]
Maximize z =x1 + 2x2
subject to the constraints
2x2 7
x1 + x2 7
2x1 11
x1, x2 0 and x1, x2 are integers.
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. Describe various selective inventory management techniques. Explain how these
techniques can be combined to develop broad policy guidelines for selective control.
[16]
5. (a) Define Queue. Explain briefly the main characteristics of queuing system. [8]
(b) What is queuing problem? Explain the transient and steady states of queuing
system. [8]
6. (a) Discuss in brief [8]
i. Dummy activity
ii. Free float
iii. Independent float
iv. Total float
(b) What are the three estimates needed for PERT analysis? How do you use
these estimates to compute the expected activity time and the variance in
activity time? [8]
7. (a) Discuss the uniform random number generator. [8]
(b) Discuss the non-uniform continuous distributed random numbers. [8]
8. Discuss the steps in the development of a useful model of input data with suitable
example. [16]
? ? ? ? ?
Code No: RR410508 Set No. 2
IV B.Tech I Semester Regular Examinations, November 2007
MATHEMATICAL MODEL LING AND 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 stuff
Feed Stuff 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 company manufacturing air - coolers has two plants located at Mumbai and
Kolkata with capacities of 200 Units and 100 units per week respectively. The
company supplies the air coolers to its four show rooms situated at Ranchi, Delhi,
Lucknow and Kanapur which have a maximum demand of 75, 100, 100 and 30 units
respectively. Due to the difference in raw material cost and transportation cost,
the profit per unit in rupees differs which is shown in the table below: [16]
Ranchi Delhi Lucknow Kanpur
Mumbai 90 90 100 100
Kolkata 50 70 130 85
Find the production programme so as to maximize the profit. The company may
have its production capacity at any plant partly unused.
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. What is the ABC analysis? Why it is necessary? What are the basis steps in
implementing it? [16]
5. Patients arrive at a clinic according to a poisson distribution at a rate of 30 pa-
tients per hour. The waiting room does not accommodate more than 14 patients.
Examination time per patient is exponential with mean rate of 20 per hour. [16]
(a) Find the effective arrival rate at the clinic
(b) What is the probability that an arriving patient will not wait?
(c) What is the expected waiting time until a patient is discharged form the clinic?
6. A PERT network has the following activities with their time estimates given below:
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. [16]
7. Explain various steps involved in simulation study. [16]
8. Explain the simulation tools with an emphasis on process orientation and event
orientation by stating some examples for each. [16]
? ? ? ? ?
Code No: RR410508 Set No. 3
IV B.Tech I Semester Regular Examinations, November 2007
MATHEMATICAL MODELLING AND 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) Write a short notes on the following: [6]
i. Analytical method
ii. Heuristic method.
(b) Compute all the basic feasible solutions of the L. P. problem: [10]
Maximize z =2x1 + 3x2 + 4x3 - 7x4
subject to the constraints:
2x1 + 3x2 - x3 + 4x4 = 8
x1 - 2x2 + 6x3 - 7x4 = -3
and choose that one which maximizes z.
2. (a) Distinguish between transportation model and assignment model. [4]
(b) Four new machines M1,M2 and M3 and M4are to be installed in a machine
shop. There are five vacant places A, B, C, D and E available. Because of
limited space, machine M2 cannot be placed at C and M3 cannot be placed at
A. Cij , the assignment cost of machine i to be place j in rupees is shown below:
A B C D E
M1 4 6 10 5 6
M2 7 4 - 5 4
M3 - 6 9 6 2
M4 9 3 7 2 3
Find the optimal assignment schedule. [12]
3. (a) A news paper boy buys papers for 5 paise each and sells them for 6 paise each.
He canot return unsold news papers. Daily demand R for news papers follows
the distribution: [10]
R 10 11 12 13 14 15 16
PR 0.05 0.15 0.40 0.20 0.10 0.05 0.05
If each day’s demand is independent of the previous day’s, how many papers
should be order each day?
(b) Explain the following terms in inventory: [6]
i. Lead time
ii. Re-order point
iii. Safety stock
4. (a) Explain ABC analysis. [8]
(b) What are its advantages and limitations, if any. [8]
5. Explain various decision models generally used in queuing theory with their
formulations. Also give suitable examples. [16]
6. A small maintenance project consists of the following 12 jobs with duration in days.
Summarize the CPM calculations in standard tabular form calculating total, free
and independent floats of the jobs. [16]
Job Duration
1-2 2
3-4 3
5-8 5
7-9 4
2-3 7
3-5 5
6-7 8
8-9 1
2-4 3
4-6 3
6-10 4
9-10 7
7. Discuss any four reasons for solving operations research problems by simulation.
[16]
8. (a) Distinguish model verification and validation [4]
(b) Explain conceptual and operational model-building process. [12]
? ? ? ? ?
Code No: RR410508 Set No. 4
IV B.Tech I Semester Regular Examinations, November 2007
MATHEMATICAL MODELLING AND 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) Define the following: [3]
i. incoming vector
ii. outgoing vector
iii. pivot element.
(b) Solve the following L. P. P. by using simplex method: [13]
Maximize z = 107x1 + x2 + 2x3
subject to the constraints:
14x1 + x2 - 6x3 + 3x4 = 7
16x1 + 1/2x2 - 6x3 5
3x1 - x2 - 3x3 0
and x1, x2, x3 0.
2. Explain briefly: [5+5+6]
(a) North - West corner method.
(b) Minimum matrix method
(c) Vogel?s approximation method,
for finding an initial basic feasible solution for a transportation problem.
3. (a) Describe the basic characteristics of inventory system. [4]
(b) A company has a demand of 12,000 units/year for an item and it can produce
2000 such items per month. The cost of one setup is Rs. 400 and the holding
cost / unit/ month is Rs. 0.15. Find the optimum lot size and the total
cost per year, assuming the cost of 1 unit as Rs. 4. Also, find the maximum
inventory. [12]
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. A telephone exchange has two long distance operators. The telephone company
finds that, during the peak load, long distance calls arrive in a poisson fashion at a
an average rate of 15 per hour. The length of service on these calls is approximately
exponentially distributed with mean length of 5 minutes.
(a) What is the probability that a subscriber will have to wait for his long distance
call during the peak hours of the day.
(b) If the subscriber will wait and serviced in turn, what is the expected waiting
time? Establish the formula used. [16]
6. A small maintenance project consists of the following 12 jobs with duration in days.
Summarize the CPM calculations in standard tabular form calculating total, free
and independent floats of the jobs. [16]
Job Duration
1-2 2
3-4 3
5-8 5
7-9 4
2-3 7
3-5 5
6-7 8
8-9 1
2-4 3
4-6 3
6-10 4
9-10 7
7. Discuss any two techniques for generating random numbers. [16]
8. List out the commonly used parameter estimators for various probability
distributions. [16]
? ? ? ? ?
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