MCom I Semester Statistical Analysis Simulation Study Material Notes ( part 3 )
Table of Contents
MCom I Semester Statistical Analysis Simulation Study Material Notes ( part 3 ) : Simulations Worksheet Determination of random Numbers Interval Simulation Worksheet Examinations Questions Long Answer Questions Short Answer Questions Objective Questions :
MCom I Business Environment Regulation Foreign Investment Study Material Notes
Advanced Numerical Illustration Related to Simulation
Illustration 15.
A company uses a high-grade raw material. The consumption pattern is probabilistic as given below and it takes two months to replenish stocks :
Consumption per month tonnes): 1 2 3 4
Probability : 0.15 0.30 0.45 0.10
The cost of placing an order is Rs. 1,000 and the cost of carrying stocks is Rs. 50 per month per tonne. The average carrying costs are calculated on the stocks held at the end of each month.
The company has two options for the purchase of raw materials as under:
Option I : Order for 5 tonnes when the closing inventory of the month plus order outstanding is less than 5 tonnes.
Option II : Order for 8 tonnes when the closing inventory of the month plus order outstanding is less than 8 tonnes.
The magazine sells for Rs. 30 per copy and costs Rs. 20 per copy from the publishers. There is a sale or return agreement whereby the publishers will take back unsold copies at cost price less a Rs. 4 per copy handling charge.
The demand pattern of a typical shop has been recorded and is shown in the table. At present, a typical shop orders 400 copies of the magazine a week.
There has been a suggestion that an insight may be gained into the situation if the magazine’s demand pattern is simulated. As a consequence, a random number table has been consulted, 20 number extract from which is shown below:
00 27 74 69 32 17 98 57 71 51
03 96 15 13 56 15 8 3 62 32 17
(1) Allocate random numbers to the demand pattern for a typical shop.
(ii) Using a tabular format, to simulate 20 week operations for a typical shop, ordering 400 copies per week, showing weekly profit or loss, returns and lost sales.
Use random number 00 for week 1, 27 for week 2, and so on.
(iii) Interpret the results of your simulation. Solution.
For determining the demand, first consult the random numbers given in the question. For first week, random number is 00. Random number 00 is falling against demand 0 < 100. The demand is thus 50 copies (ie., 0 + 1/2 x 100). As the typical shop order is 400 copies, 350 copies (i.e., 400-50) are returned. In second week random number is 27 which is falling between random numbers 19-32. The corresponding demand against this random number is 200 < 300, i.e., 250 copies. Thus. 150 copies are returned. In third week, random number is 74 which is falling between random numbers 70-78. The corresponding demand against this random number is 500 < 600, i.e., 550 copies. But the typical shop order is 400 copies only and therefore 150 copies will be refused which is to be treated as lost sales. The procedure may be continued for other intervals. Now,
Profit per item sold = Rs. 30 – Rs. 20 = Rs. 10
Loss per item if not sold = Rs. 4.
would, at the same time, increase profit due to the shops being better able to satisfy demand. The optimum order level could be found by running the simulation several times with different order quantities.
Illustration 18.
XYZ Travel Agency deals with numerous personal callers each day and prides itself on its level of service. The time to deal with each caller depends on the client’s requirements which range from, say, a request for a brochure to booking a round-the-world cruise. If clients have to wait more than 10 minutes for attention it is AB’s policy for the manager to see them personally and to give them Rs. 5 holiday voucher.
Observations have shown that the time taken to deal with clients and their arrival patterns follow distributions below:
Time to deal Minutes : 2 4 6 10 14 20 30
with clients Probability: 0.05 0.10 0.15 0.30 0.25 0.10 0.05
Time between Minutes : 1 8 15 25 arrivals
Probability: 0.2 0.4 0.3 0.1
(i) Describe how you would simulate the operation of the travel agency based on the use of random number tables :
(ii) Simulate the arrival and serving of 12 clients and show the number of customers who receive a voucher (use line 1 of the Random Numbers below to derive the arrival pattern and Line 2 for the serving times) :
Random Numbers
Line 1 : 03 47 43 73 86 36 96 47 36 61 46 98
Line 2 : 63 71 6233 26 16 80 45 60 11 14 10
(iii) Calculate the weekly cost of vouchers, assuming the proportion receiving vouchers derived from
(ii) applies throughout a week of 50 opening hours. Solution.
(i) The problem is analysed to determine the objective (establishing voucher cost) and uncontrolled variables (arrival time and service time) and the simulation logic. Random numbers are then assigned to represent the probability distribution given and then a random number table is used to select according to the probability, the value of servicing time and the time between arrivals. The working sheet would then be used (sce (ii)] to long arrival time and serving time (both randomly selected) and to show waiting time for individual clients.
Determination of Random Number Interval Time to
EXAMINATION QUESTIONS
Long Answer Theoretical Questions
1 What do you understand by “Simulation technique ? Discuss its utility.
2. Explain ‘Pseudo-Random Numbers’ in detail.
3. Define ‘Simulation Technique’ and explain clearly its important elements.
4. What is simulation technique ? What are its advantages and limitations ?
5. Simulation is an especially valuable tool in a situation where the mathematics needed to describe a system realistically is too complex to yield analytical solutions.’ Elucidate.
6. Write any four reasons for solving O.R. problems by simulation.
7. What is Monte Carlo Simulation ? Why is it called so ?
8. What is meant by Monte Carlo method of simulation ? Discuss its uses. Explain the steps involved in Monte Carlo simulation.
9. What are simulation models? Give the classification of simulation models on the basis of nature of environment’ and ‘behavior during period of time’ and explain the various types giving examples.
10. What is the rationale of the simulation technique? Write, giving suitable examples, main reasons for the increasing use of simulation technique.
11. When it becomes difficult to use an optimization technique for solving a problem one has to resort to simulation technique.” Discuss.
12. Clearly describe in detail the procedure of simulation, explaining its various steps.
13. What are Random Numbers? Discuss methods of generation of random numbers.
14. Explain clearly ‘Pseudo-Random Number’s and discuss in detail their basic characteristics.
15. What is simulation? Discuss the important applications of simulation techniques in various fields of business management.
Short Answer Theoretical Questions
1 What is simulation ?
2. Define ‘Simulation Technique’.
3. What are simulation models ?
4. What is the rationale of the simulation technique ?
5. Explain the important elements of the ‘Simulation Technique’.
6. Discuss the advantages of the ‘Simulation Technique’.
7. What is Monte Carlo Simulation ?
8. What are Random Numbers ?
9. Explain ‘Pseudo-Random Numbers’.
10. Discuss the important applications of simulation techniques in various fields of business management.
11. Give the classification of simulation models on the basis of ‘nature of environment’.
12. Give the classification of simulation models on the basis of ‘behavior during the period of time’.
13. Write any four reasons for solving O.R. problems by simulation.
14. Write a short note on the ‘Hertz Model’.
15. Write a short note on Analogue Simulation’.
Objective Questions Write whether the following statements are ‘True’ or ‘False :
1 Simulation is a quantitative technique of decision-making under the condition of certainty. (False)
2. Simulation is an important tool of Operation Research. (True) technique.
3. Probability distribution and Random numbers are used under Simulation (True)
4. Simulation technique was firstly used in the decade of nineteen sixties.
5. “Simulation technique was firstly used by Professor Bayes and Professor John (False) Von Neumann.
6. “Simulation technique was firstly used to determine the complex behavior (True) of Newtron in nuclear-shielding problem.
7. Simulation is sometimes described as a last-resort technique since it is generally then employed when mathematical, analytical and iterative methods (True) are failure.
8. All parameters and functional relations are certainly and clearly defined under (True) deterministic models.
9. At least one parameter or decision-variable or functional relation will be (True) random variable under probabilistic model.
10. One drawback to the use of simulation is that simulation technique does not provide optimal solution. (True)
Fill in the blanks in the following:
1 Simulation is sometimes described as a ……… resort technique.
2. Simulation is an important tool of
3. Simulation is a quantitative technique of decision-making under the condition of ……….
4. ……… distribution and …….. numbers are used under simulation technique.
5. ‘Simulation technique was firstly used in the decade of ………
Ans. (1) Last, (2) Operations Research, (3) Uncertainty. (4) Probability, Random, (5) the Nineteen Sixties
Choose the correct alternative in the following:
1 Which science is related to ‘Simulation’ as an important tool ?
(a) Physics
(b) Chemistry
(C) OR (V)
(d) None of these
2. In which out of the following, simulation was firstly used in :
(a) 1860
(b) 1960
(c) the decade of nineteen sixties (V)
(d) the decade of nineteen seventies
(c) None of these
3. In which condition of the following, simulation is a quantitative technique of decision-making :
(a) under the condition of certainty
(b) under the condition of uncertainty (V)
(c) under the condition of risk
(d) none of these
4. Who out of the following firstly used the ‘Simulation:
(a) Professor Karl Pearson
(b) Professor Yule
(c) Prof. John Von Neumann and Prof. Stanislaw Ulam (1)
(d) None of these
Simulation Study Material Notes
