Chapter 1 – Introduction to Simulation

Computer Simulation and Modeling

Chapter 1 – Introduction to Simulation
Important Questions from Chapter 1 – Introduction to Simulation

1. Name Entities, Attributes, Activities, Events and State variables for the following systems. Small appliance repair shop, Cafeteria, Grocery store, Laundromat, Automobile assembly line, Fast food restaurant, Taxicab company, Hospital emergency room.

2. Explain steps involved in simulation study with diagram.

3. When Simulation is appropriate & when it is not appropriate?

4. Write a GPSS/H program for single server queue simulation.

5. Grocery Store Example: Let the arrival distribution be uniformly distributed between 1 to 10 minutes and service time distribution is as follows: Service time(min) 1 2 3 4 5 6 Probability 0.04 0.20 0.10 0.26 0.35 0.05 Develop the simulation table and analyze the system by simulating arrival and service of 10 customers. Find out Queue statistics. Random digits for interarrival time and service time are follows: Customer 1 2 3 4 5 6 7 8 9 10 R. D. for Interarrival Time -- 853 340 205 99 669 142 301 888 444 R. D. for Service time 71 59 12 88 97 66 81 35 29 91

6. ABLE-BAKER CARHOP PROBLEM: TIME BETWEEN ARRIVAL (MIN) 0 1 2 3 4 PROBABILITY 0.07 0.26 0.31 0.22 0.14        ABLE’S SERVICE TIME 2 3 4 5  PROBABILITY 0.22 0.31 0.32 0.15         BAKER'S SERVICE TIME 3 4 5 6 PROBABILITY 0.34 0.28 0.16 0.22   DEVELOP THE SIMULATION TABLE AND ANALYSE THE SYSTEM BY SIMULATING ARRIVAL & SERVICE OF 10 CUSTOMERS. RANDOM DIGITS FOR INTERARRIVAL & SERVICE TIME ARE AS FOLLOWS:    CUSTOMERS  RANDOM DIGITS FOR INTER ARRIVAL RANDOM DIGITS FOR SERVICE 1     -      15  2     5      28  3     36      62  4     41      35  5     77      7  6     52      57  7     63      82  8     38      92  9     16      19  10     32       43  CALCULATE SERVER UTILIZATION & MAXIMUM QUEUE LENGTH? FIND OUT AVERAGE WAITING TIME, AVERAGE SERVICE TIME, AVERAGE WAITING TIME OF THOSE WHO WAIT, % BUSY TIME OF ABLE & BAKER & AVERAGE TIME CUSTOMERS SPENDS IN SYSTEM?

7. NEWSPAPER SELLER’S PROBLEM: PAPER SELLER BUYS PAPER FOR 3 RS EACH & SELLS THEM IN 5 RS EACH.NEWS PAPER NOT SOLD AT THE END OF DAY SOLD AS SCRAP AS 50 PAISE EACH.NEWSPAPER CAN BE PURCHASE IN BUNDLE OF 10.THERE ARE 3 TYPES OF NEWS DAYS GOOD, FAIR, POOR WITH PROBABILITIES 0.35, 0.45, 0.20 RESPECTIVELY. THE DISTRIBUTION OF PAPER DEMANDED ON EACH OF THIS DAY GIVEN BELOW: DEMAND GOOD FAIR POOR 40 0.03 0.1 0.44 50 0.05 0.18 0.32 60 0.15 0.4 0.14 70 0.2 0.2 0.12 80 0.35 0.08 0.06 90 0.15 0.04 0 100 0.07 0 0 DETERMINE THE OPTIMAL NUMBER OF PAPERS THE NEWSPAPER SELLER SHOULD PURCHASE? SIMULATE DEMANDS FOR 20 DAYS & RECORD PROFITS FROM THE SELL OF EACH DAY? RANDOM DIGITS FOR TYPE OF NEWS DAY RANDOM DIGITS FOR DEMAND   58      93    17      63    21      31    45      19    43      91    36      75    27      84    73      37    86      23    19      2    93      53    45      96    47      33    30      86    12      16    41      7    65      64    57      94    18      55    98       13

8. THERE IS ONLY ONE TELEPHONE IN A PUBLICBOOTH OF THE RAILWAY STATION. THE FOLLOWING TABLES INDICATE THE DISTRIBUTIONOF CALLERS ARRIVAL TIME & DURATION OF CALLS. SIMULATE FOR 20 ARRIVALS OF CURRENT SYSTEM. IT IS PROPOSED TO ADD ANOTHER TELEPHONE TO BOOTH. JUSTIFY PROPOSED BASED ON THE WAITING TIME OF CALLERS. TIME BETWEEN ARRIVAL(MIN) 2 3 4  PROBABILITY  0.2 0.7 0.1         CALL DURATION (MIN) 2 3 4 5 PROBABILITY  0.15 0.6 0.15 0.1

9. Students arrives at the university library counter with interarrival  times distributed as: Inter-arrival time(min) 1 2 3 4 probability 0.1 0.4 0.3 0.2         The Time for transaction at counter is distributed as: Transaction Time(min) 2 3 4 5 probability 0.15 0.50 0.20 0.15 If more than two students are in the queue, an arriving student goes away without joining the queue. Simulate the system & determine the balking rate of the students.

10. Define the terms used in simulation: Event, Event Notice, Event List, Activity, Delay, Clock. What is bootstrapping?

11. Explain the Event Scheduling Algorithm in detail?

12. A small Store has only one check out counter, customers arrives at this counter at random time that are from 1 to 8 minutes apart. Check out that possible value of interarrival time that has some  probability of occurance. Service time vary from 1 to 6 minutes with the following probability .Here a stopping timeof 60 minutes is set. Simulate the system.

13. Dump Truck problem: Six drump trucks are used to haul coal from the entrance of a small mine to rail road. Fig provides a schematic of the dump truck is loaded by one of the two loaders. After a loading the dump truck immediately moves to scale to be weighted as soon as possible. Both loader and scale have a first served waiting line for trucks. Travel time from a loader to the scale is considered negligible. After being weighed, a truck begin a travel time during which time the truck unloads load then afterwords return to the loader queue. The distribution of  loading time,  weighting time and travel time are given together with the random digit. simulate the system.  Distribution of loading Time for Dump Truck : Loading Time(min) 5 10 15 Probability 0.30 0.50 0.20 Distribution of weighting time for Dump truck: Weighting Time (min) 12 16 Probability 0.70 0.30 Distribution of travel for Dump truck: Travel  time(min) 40 60 80 100 probability 0.40 0.30 0.20 0.10

14. Demand for widgets follows the probability distribution shown: Daily Demand 0 1 2 3 4 Probability 0.33  0.25  0.20  0.12  0.10 Stock is examined every 7 days (the plant is in operation every day) and, if the stock level has reached 6 units, or less, an order for 10 widgets is placed. The lead time (days until delivery) is probabilistic and follows the following distribution: Lead Time (Days) 1 2 3 Probability 0.3 0.5 0.2 When the simulation begins, it is the beginning of the week, 12 widgets are on hand, and no orders have been backordered. (Backordering is allowed.) Simulate 1 weeks of operation of this system. Analyze the system.

15. In a drive-in restaurant where carhops take orders and bring food to the car. Cars arrive in the manner shown in Table A. There are two carhops - Able and Baker. The distribution of their service times is shown in Tables B & C. Table A Interarrival Distribution of Cars Time between Arrivals(Minutes) 1 2 3 4 Probability 0.25 0.40 0.20 0.15 Table B Service Distribution of Able Service Time (Minutes) 2 3 4 5 Probability 0.30 0.28 0.25 0.17 Table C Service Distribution of Baker Service Time (Minutes) 3 4 5 6 Probability 0.35 0.25 0.20 0.20 Estimate the system measures of performance for a simulation of 1 hour of operation.

16. The paper seller buys the papers for 33 cents each and sells them for 50 cents each. Newspapers not sold at the end of the day are sold as scrap for 5 cents each. Newspapers can be purchased in bundles of 10. Thus, the paper seller can buy 50, 60, and so on. There are three types of newsdays, good, fair, and poor, with probabilities of 0.35, 0.45, and 0.20, respectively. The distribution of papers demanded on each of these days is given in Table A. The problem is to determine the optimal number of papers the newspaper seller should purchase. Accomplish this by simulating demands for 110 days and record profit from sales each day. Table A Distribution of Newspapers Demanded    Demand Demand Probability Distribution  Good Fair Poor 40 0.03 0.10 0.44 50 0.05 0.18 0.22 60 0.15 0.40 0.16 70 0.20 0.20 0.12 80 0.35 0.08 0.06 90 0.15 0.04 0.00 100 0.07 0.00 0.00 Table B Random-Digit Assignment for Type of Newsday   Type of Newsday Probability Good 0.35 Fair 0.45 Poor 0.20 Simulate the problem setting a policy of buying a 80 papers each day, demands for papers over the 100-day time period to determine the total profit.

17. The maximum inventory level, M, is 11 units and the review period, N, is 5 days. The distribution of the number of units demanded per day is shown in Table A. In this example, lead time is a random variable, as shown in Table B. Assume that orders are placed at the close of business and are received for inventory at the beginning of business as determined by the lead time. Table A Random-Digit Assignments for Daily Demand Daily Demand 0 1 2 3 4 Probability 0.10 0.25 0.35 0.21 0.09 Table B Random-Digit Assignments for Lead Time Lead Time (Days) 1 2 3 Probability 0.6 0.3 0.1 The problem is to estimate, by simulation, the average ending units in inventory and the number of days when a shortage condition occurs.

18. A large milling machine has three different bearings that fail in service. The cumulative distribution function of the life of each bearing is identical, as shown in Table A. When a bearing fails, the mill stops, a repairperson is called, and a new bearing is installed. The delay time of the repairperson's arriving at the milling machine is also a random variable, with the distribution given in Table B. Downtime for the mill is estimated at Rs. 10 per minute. The direct on-site cost of the repairperson is Rs. 15 per hour. It takes 20 minutes to change one bearing, 30 minutes to change two bearings, and 40 minutes to change three bearings. The bearings cost Rs. 40 each. Table 2.22 Bearing-Life Distribution Bearing Life (Hours) 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 Probability 0.10 0.13 0.25 0.13 0.09 0.12 0.02 0.06 0.05 0.05 Table B Delay-Time Distribution Lead Time (Minutes) 5 10 15 Probability 0.6 0.3 0.1 A proposal has been made to replace all three bearings whenever a bearing fails. Management needs an evaluation of this proposal. Represent a simulation of 20,000 hours of operation under the current & proposed method of operation.

19. A firm sells bulk rolls of newsprint. The daily demand is given by the following probability distribution: Daily Demand (Rolls) 3 4 5 6 Probability 0.20 0.35 0.30 0.15 Lead time is a random variable given by the following distribution: Lead Time (Days) 1 2 3 Probability 0.36 0.22 0.42 Develop the distribution of lead-time demand based on 20 cycles of lead time. Prepare a histogram using intervals 0-2, 3-6, 7-10, ………..