Jawaharlal Nehru Technological University Hyderabad 2007 B.E Computer Science MATHEMATICAL MODELLING AND SIMULATION - Question Paper

ii. Heuristic method.
(b) calculate 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 select that 1 which maximizes z.
2. (a) Distinguish ranging from transportation model and assignment model. [4]
(b) 4 new machines M1,M2 and M3 and M4are to be installed in a machine
shop. There are 5 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 four six 10 five 6
M2 seven four - five 4
M3 - six nine six 2
M4 nine three seven two 3
obtain the optimal assignment schedule. [12]
3. (a) A news paper boy buys papers for five paise every and sells them for six paise every.
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 every day’s demand is independent of the previous day’s, how many papers
should be order every day?
(b) discuss the subsequent terms in inventory: [6]
i. Lead time
ii. Re-order point
iii. Safety stock

4. (a) discuss ABC analysis. [8]
(b) elaborate its advantages and limitations, if any. [8]
5. discuss different decision models generally used in queuing theory with their
formulations. Also provide suitable examples. [16]
6. A small maintenance project consists of the subsequent 12 jobs with duration in days.
Summarize the CPM computations 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. explain any 4 reasons for solving operations research issues by simulation.
[16]
8. (a) Distinguish model verification and validation [4]
(b) discuss conceptual and operational model-building process. [12]

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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: three hours Max Marks: 80
ans any 5 ques.
All ques. carry equal marks

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1. (a) describe the following: [3]
i. incoming vector
ii. outgoing vector
iii. pivot element.
(b) Solve the subsequent 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. discuss 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 issue.
3. (a) define 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 1 setup is Rs. 400 and the holding
cost / unit/ month is Rs. 0.15. obtain the optimum lot size and the total
cost per year, assuming the cost of one unit as Rs. 4. Also, obtain the maximum
inventory. [12]
4. (a) State different kinds of items in inventory control techniques. [6]
(b) The subsequent thirty numbers represent the annual value in thousand of ru-
pees of a few thirty items of materials opted at random. Carry out an ABC
analysis and list out the values of ‘A’ items only: [10]
1 two four nine 75 four 25
3 six 13 two four 12 30
100 two seven 40 15 55 1
11 15 eight 19 one 20 1
3 5

5. A telephone exchange has 2 long distance operators. The telephone company
obtains that, during the peak load, long distance calls arrive in a poisson fashion at a
an avg. rate of 15 per hour. The length of service on these calls is approximately
exponentially distributed with mean length of five 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 subsequent 12 jobs with duration in days.
Summarize the CPM computations 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. explain any 2 techniques for generating random numbers. [16]
8. List out the commonly used parameter estimators for different probability
distributions. [16]

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Earning:   Approval pending.