Abcd.docx

[Type the document title] 8) 2006 JULY a) What is random Number? A random number is a number generated using a large set of numbers and a mathematical algorithm which gives equal probability to all numbers occurring in the specified distribution. Random numbers are most commonly produced with the help of a random number generator. Random numbers have important applications, especially in cryptography where they act as ingredients in encryption keys. b)

Define monte carlo simulation. Describe various steps in monte carlo simulation Monte Carlo simulation, or probability simulation, is a technique used to understand the impact of risk and uncertainty in financial, project management, cost, and other forecasting models. Steps in monte carlo simulation Step 1: Create a parametric model, y = f(x1, x2, ..., xq). Step 2: Generate a set of random inputs, xi1, xi2, ..., xiq. Step 3: Evaluate the model and store the results as yi. Step 4: Repeat steps 2 and 3 for i = 1 to n. Step 5: Analyze the results using histograms, summary statistics, confidence intervals,

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c) The Lajwaab Bakery Shop keeps stock of a popular brand of cake. Previous experience indicates the daily demand as given below:

Consider

the

Daily demand

Probability

0

0.01

15

0.15

25

0.20

35

0.50

45

0.12

50

0.02

following

sequence

of

random

numbers:

21, 27, 47, 54, 60, 39, 43, 91, 25, 20 Using this sequence, simulate the demand for the next 10 days. Find out the stock situation, if the owner of the bakery shop decides to make 30 cakes every day. Also estimate the daily average demand for the cakes on the basis of simulated data. Solution. Using the daily demand distribution, we obtain a probability distribution as shown in the following table.

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[Type the document title] Table 1 Daily

Probability

demand

Cumulative

Random

probability

Numbers

0

0.01

0.01

0

15

0.15

0.16

1-15

25

0.20

0.36

16-35

35

0.50

0.86

36-85

45

0.12

0.98

86-97

50

0.02

1.00

98-99

At the start of simulation, the first random number 21 generates a demand of 25 cakes as shown in table 2. The demand is determined from the cumulative probability values in table 1. At the end of first day, the closing quantity is 5 (30-25) cakes. Similarly, we can calculate the next demand for others.

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[Type the document title] Table 2 Demand

Random Numbers

Next demand

Daily production = 30 cakes Left out

Shortage

1

21

25

5

2

27

25

10

3

47

35

5

4

54

35

0

5

60

35

5

6

39

35

10

7

43

35

15

8

91

45

30

9

25

25

25

10

20

25

20

320

10

Total

Total demand = Average demand = Total demand/no. The daily average demand for the cakes = 320/10 = 32 cakes. .

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of

320 days

[Type the document title] 3 JUNE/JULY 2008 7) a) Give a general structure of the queuing system and explain.

(a) Input source: One characteristic of the input source is the size. The size is the total number of units that might require service from time to time. It may be assumed to be finite or infinite. (b) Queue Discipline: A queue is characterized by maximum permissible number of units that it contains. Queues are called finite or infinite, according to whether number is finite or infinite. The service discipline refers to the order in which number of queues are selected for service. (c) Service mechanism: This consists of one or more service facilities each of which contains one or more parallel service channel. If there is more than one service facility, the arrival unit may receive the service from a sequence of service channels.

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[Type the document title] a) 1) FIRST COME- FIRST SERVED First come, first served' is a very very common way of organizing access to a limited resource or service in the real world. It can be explained by saying that whenever the resource is available the person who has been waiting the longest is served, and visualized by thinking of people standing in a single-file line, where the person at the front is always served next and new arrivals join the back of the queue. If you ask someone why this system is the best, they might instinctively say 'It is the most fair'. But can we express what this fairness means in terms of some property, which is maximized for this system and no other? It doesn't mean for instance that people all wait the same time, or even that people who arrive at nearly the same time don't get served a long time apart. 2) LAST COME-FIRST SERVED Motivated by manufacturing and service applications, we consider a single class multiserver queueing system working under the LCFS discipline of service. After entering the queue, a customer will wait a random length of time for service to begin. If service has not begun by this time she will abandon and be lost. For the GI/GI/s+Mqueue, we present some structural results to describe the relation between various performance measures and the scheduling policies. We next consider the LCFS M/M/s+M queue and focus on deriving new results for the virtual waiting time and the sojourn time in the queue (either before service or before abandonment). We provide an exact analysis using Laplace–Stieltjes transforms. We also conduct some numerical analysis to illustrate the impact of customer impatience and the discipline of service on performance.

3) SERVICE SYSTEM

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[Type the document title] The service is provided by a service facility (or facilities). This may be a person (a bank teller, a barber, a machine (elevator, gasoline pump), or a space (airport runway, parking lot, hospital bed), to mention just a few. A service facility may include one person or several people operating as a team. There are two aspects of a service system—(a) the configuration of the service system and (b) the speed of the service.

C) OUT OF SYLLUBUS

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JUNE-JULY 2008 3) A)

1) Prohibited or Restricted problem: A Prohibited problem is the one in which there are one or more restrictions. E. g. says there are 4 contractors – C1, C2, C3 & C4. And there are 4 roads to be repaired – R1, R2, R3 & R4. But contractor C2 cannot or is not allowed to work on R3. This is a prohibited problem Then we assign a very high or infinite value (represented by M) to C2-R3 and proceed with solution. Throughout the solution steps, M does not change. Since M is infinity, no assignment is possible in M. Steps – 1.

Take Dummy (if required) & then convert in Regret matrix (if required)

2.

Do Row minimization and Column minimization.

3.

Cover all Zeroes in the Table with Minimum possible lines. (Start from

maximum zeroes, either row-wise or column-wise). 4.

If optimal, find assignment.

5.

If not optimal, write next table, change values & check again with Minimum

possible lines. 6.

Continue the iterations till optimal solution is reached.

B) OUT OF SYLLUBUS

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C) The critical path in the network diagram has been shown. This has been done by double lines by joining all those events where E-values and L-values are equal. The critical path of the project is : 1 - 2 - 4 - 5 - 7 - 8 - 9 critical activities are B, C, F, H, I, J

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[Type the document title] The total project time is 26

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[Type the document title] NITHIN KUNCHOOR 1BI17MBA33

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