Simulation Practice Problems

1. There is only one telephone in a public booth of a metro station. Following table indicates the distribution of arrival time and duration of calls:

Time Between arrivals (minutes) 4 5 6
Probability 0.1 .6 0.3

Call Duration (minutes) 3 4 5 6
Probability 0.14 0.6 0.12 0.14

Simulate for 100/500/1000 times. Conduct 3 such trials. It is proposed to add another telephone to the booth. Justify the proposal based on the waiting time of caller.Generate graphs to support your answer.

2. A baker needs to find out the cookies he need to bake each day. The probability distribution for the cookies customers is as follows:
Number of customers/day 7 9 11 14
Probability 0.35 0.30 0.15 0.20



Cookies sold Rs 8 per dozen. The cost Rs 5.5 per dozen to make. All cookies not sold at the end of
the day are sold at half price to a local grocery store. Simulate for 100/500/1000 times. Conduct 3
such trials to identify how many dozen cookies he should bake each day.

3. There is only one telephone in a public booth of in a market. Following table indicates the distribution of arrival time and duration of calls:

Time Between arrivals (minutes) 6 7 8
Probability 0.1 .6 0.3


Call Duration (minutes) 4 5 6 7
Probability 0.14 0.6 0.12 0.14

Simulate for 100/500/1000 times. Conduct 3 such trials. It is proposed to add another telephone to the booth. Justify the proposal based on the waiting time of caller.Generate graphs to support your answer.


4. Students arrive at the university library counter with inter-arrival times distributed as :

Time between arrivals(Minutes) 5 6 7 8
Probability 0.35 0.30 0.15 0.20

The time for transaction at the counter is distributed as:
Time between arrivals(Minutes) 3 4 5 6
Probability 0.15 0.5 0.20 0.15

In case more then two students are in the queue, an arriving student goes away without joining the queue. Simulate the system and determine balking rate of the students.

5. Consider a milling machine having three different bearings that fail in service. The distribution of life of bearings is identical as follows:

Bearing Life(hours) Prob
1000 0.13
1100 0.23
1200 0.25
1300 0.1
1400 .09
1500 .12
1600 0.02
1700 0.06
1800 0.05
1900 0.05

Whenever bearing fails repair person is called and a new bearing is installed. The delay of repair person random that follows distribution given below:

Delay Time Prob
5 0.6
10 0.3
15 0.1

Downtime for mill Rs 10 per min, direct on site repair cost Rs 30 per hour. It takes 20 mins to change one bearing ,30 to change two and 40 minutes to change three. A proposal is to follow following procedure:

Whenever a bearing fail, two bearings are replaced:
a. One that has failed
b. Another one out of other two remaining bearings with longest operational time.

Simulate and evaluate the proposal. The total cost per 10,000 bearings hours will be used as the measure of performance.

6. Students arrive at the university library counter with inter-arrival times distributed as :

Time between arrivals(Minutes) 5 6 7 8
Probability 0.35 0.30 0.15 0.20

The time for transaction at the counter is distributed as:
Time between arrivals(Minutes) 3 4 5 6
Probability 0.15 0.5 0.20 0.15

In case more then two students are in the queue, an arriving student goes away without joining the queue. Simulate the system and determine balking rate of the students.



7. Consider a situation of a company that sells refrigerators. The system they use to maintain inventory is to review the situation after fixed number of days say N. and make a decision about what is to be done. The policy is to order upto a level (order up to level say M) using following relationship:

Order Quantity =(Order up to level) – Ending Inventory + Shortage Quantity

No. of refrigerators ordered each day is randomly distrubted as follows:
Demand probability
0 0.1
1 0.25
2 0.3
3 0.21
4 0.09

Lead Time (number of days after the order is placed to the supplier before arrival) is distributed as follows:

Lead time (days) probability
1 0.6
2 0.3
3 0.1

Simulate the order up to inventory system for 100,1000 trials. Assume M=11,N=5. Check efficiency of the system.

8 . Estimate by the simulation, the average number of lost sales per week for an inventory system that functions as follows:

a. Whenever inventory level falls to or below 10 units, an order is placed,Only one order
can be outstanding at a time
b. The size of each order is equal to 20-I where I ,inventory level when order is placed.
c. If a demand occurs during a period when inventory level is zero, the sale is lost.
d. Daily demand is distributed as follows:

Demand Probability
0 0.1
1 0.25
2 0.3
3 0.21
4 0.09
e. Lead time distributed normally b/w 0-5 days (integer) only.
f. Simulation starts with 18 units in inventory.
g. Assume that orders are placed at the close of business day and received after the lead time has occurred. Thus, if lead time is one day, the order is available for distribution on the morning of the second day of business following the placement of the order.
h. Let simulation run for 5 weeks.



9. There is only one ATM in market. Following table indicates the distribution of arrival time and duration of calls:

Time Between arrivals (minutes) 4 5 6
Probability 0.1 .6 0.3



Call Duration (minutes) 3 4 5 6
Probability 0.14 0.6 0.12 0.14

Simulate for 100/500/1000 times. Conduct 3 such trials. It is proposed to add another ATM to the market. Justify the proposal based on the waiting time of caller. Generate graphs to support your answer.


10. A shopkeeper needs to find out the breads he need to bread each day. The probability distribution for the cookies customers is as follows:

Number of customers/day 7 9 11 14
Probability 0.35 .30 0.15 0.20

Bread sold Rs 15 per pack. It cost Rs 5.5 per pack. If not sold at the end of the day are sold at half price to a local grocery store. Simulate for 100/500/1000 times. Conduct 3 such trials to identify how many dozen cookies he should bake each day.


11. Consider a milling machine having three different bearings that fail in service. The distribution of life of bearings is identical as follows:

Bearing Life(hours) Prob
1000 0.13
1100 0.23
1200 0.25
1300 0.1
1400 .09
1500 .12
1600 0.02
1700 0.06
1800 0.05
1900 0.05

Whenever bearing fails repair person is called and a new bearing is installed. The delay of repair person random that follows distribution given below:
Delay Time Prob
5 0.6
10 0.3
15 0.1

Downtime for mill Rs 10 per min, direct on site repair cost Rs 30 per hour. It takes 20 mins to change one bearing ,30 to change two and 40 minutes to change three. A proposal is to follow following procedure:

Whenever a bearing fail, all bearings are replaced. Simulate and evaluate the proposal. The total cost per 10,000 bearings hours will be used as the measure of performance.

12. Consider multiple hard disk computer system having 4 disks that fail in service. Disk having bad sectors need to be replaced. The distribution of life of different disks is given below:
Disk Life(years) Prob
10 0.13
11 0.23
12 0.25
13 0.1
14 .09
15 .12
16 0.02
17 0.06
18 0.05
19 0.05

Whenever there is a bad sector in the disk that disk is replaced by the hardware engineer. Hardware engineer need to be called from outside. He may take 1/2/3 days to arrive random that follows distribution given below:
Delay (days) Prob
1 0.6
2 0.3
3 0.1

Downtime for the computer system Rs 100 per min, direct on site cost of replacement by hardware
engineer is Rs 30 per hour. It takes 20 mins to change one disk ,30 to change two, 40 minutes to change three and 60 minutes to change four. A proposal is to follow following procedure:

Whenever a disk has bad sector replace all disks in anticipation. Simulate and evaluate the proposal. The total cost per 10,000 bearings hours will be used as the measure of performance.


13. Consider the simulation of a management game. There are three players A,B,C. Each player has two strategies which they play with equal probabilities. The players select strategies independently. The following table gives the payoff.

Strategies A (payoff) B (Payoff) C (payoff)
A1-B1-C1 10 -5 5
A1-B1-C2 0 8 2
A1-B2-C1 9 3 -2
A1-B2-C2 -4 5 9
A2-B1-C1 6 1 3
A2-B1-C2 0 0 10
A2-B2-C1 6 10 -6
A2-B2-C2 0 4 6

Simulate 100 players and determine payoff.


14. Consider a milling machine having three different bearings that fail in service. The distribution of life of bearings is identical as follows:

Bearing Life(hours) Prob
1000 0.13
1100 0.23
1200 0.25
1300 0.1
1400 .09
1500 .12
1600 0.02
1700 0.06
1800 0.05
1900 0.05

Whenever bearing fails repair person is called and a new bearing is installed. The delay of repair person random that follows distribution given below:
Delay Time Prob
5 0.6
10 0.3
15 0.1
Downtime for mill Rs 10 per min, direct on site repair cost Rs 30 per hour. It takes 20 mins to change one bearing ,30 to change two and 40 minutes to change three. A proposal is to follow following procedure:

Whenever a bearing fail, two bearings are replaced. Simulate and evaluate the proposal. The total cost per 10,000 bearings hours will be used as the measure of performance.


15. A baker needs to find out the packets of bread he need to bake each day. The probability distribution for the cookies customers is as follows:
Number of customers/day 7 9 11 14
Probability 0.35 0.30 0.15 0.20

Cookies sold Rs 8 per dozen. The cost Rs 5.5 per dozen to make. All cookies not sold at the end of the day are sold at half price to a local grocery store. Simulate for 100/500/1000 times. Conduct 3 such trials to identify how many dozen cookies he should bake each day.


16. Students arrive at the university library counter with inter-arrival times distributed as:

Time between arrivals(Minutes) 5 6 7 8
Probability 0.35 0.30 0.15 0.20

The time for transaction at the counter is distributed as:
Time between arrivals(Minutes) 3 4 5 6
Probability 0.15 0.5 0.20 0.15

In case more then two students are in the queue, an arriving student goes away without joining the queue. Simulate the system and determine balking rate of the students.

17. Trucks are used to carry components between two assembly stations A and B. Three types of components (C1,C2,C3) from station A are assembled at station B. The interarrival time of C1,C2,C3 are:

Component Interarrival Time(minutes)
C1 7+/-2
C2 3+/-1
C3 8+/-3

The truck can take only three components at a time. It takes 90 seconds to travel(to and fro) and 30 seconds to unload at station B. The truck waits at station A till it get full load of three components. Simulate the system for 1 hour and determine the average waiting time of three components.

18. There is only one PCO in market. Following table indicates the distribution of arrival time and duration of
service:

Time Between arrivals (minutes) 4 5 6
Probability 0.1 .6 0.3


Call Duration (minutes) 3 4 5 6
Probability 0.14 0.6 0.12 0.14


Simulate for 100/500/1000 times. Conduct 3 such trials. It is proposed to add another PCO booth to the market. Justify the proposal based on the waiting time of caller. Generate graphs to support your answer.