Simulation in Operation Research

this ppt is helpful for BBA/B.tech//MBA/M.tech students.
the ppt is on simulation topic...its covers -
Meaning
Advantages & Disadvantages
Uses
Process
Monte Carlo SImulation
Advantages & Disadvantages
Its example

1. SIMULATION OPERATION RESEARCH

2. MEANING re-creation of a real world process in a controlled environment creating laws & models to represent the world running those models to see what happens

3. PROCESS

4. ADVANTAGES & DISADVANTAGES ADVANTAGES DISADVANTAGES flexible expensive used to analyse Require expert knowledge Assist in finding the pros & cons of the real situation complicated Only a method Real situation based on it

5. USES/ APPLICATION Research Risky training Education Manufacturing Services Entertainment Safety engineering Video games Healthcare Technology

6. first used by scientists working on the atom bomb in 1940. used in those situations where we need to make an estimate and uncertain decisions such as weather forecast predictions. a computerized mathematical technique to generate random sample data based on some known distribution for numerical experiments. apply to risk quantitative analysis and decision making problems. used by the professionals of various profiles such as finance, project management, energy, manufacturing, engineering, research & development, insurance, oil & gas, transportation, etc. MONTE CARLO SIMULATION

7. ADVANTAGES & DISADVANTAGES OF MONTE CARLO SIMULATION ADVANTAGES DISADVANTAGES Easy to implement Time consuming Used for numerical experiment Expensive Provide approximate solution Require Expert knowledge

8. Example of Monte Carlo Simulation Dr. Strong is dentist who schedules all her patients for 30 minutes appointments. Some of the patients take more or less than 30 minutes depending on the types of dental work to be done. Summary show the various categories of work with service time. Simulate the dentist’s clinic for four hours and determine the average waiting time for the patient as well as the idleness of the doctor. Assume that all the patients show up at the clinic at exactly their scheduled arrival time starting at 8:00 a.m. Use the following random numbers for handling the above problem – 40, 82, 11, 34, 25, 66, 17, 79 Category of service Service time No. of Patients Filling 45 40 Crown 60 15 Cleaning 15 15 Extraction 45 10 Check-up 15 20

9. SOLUTION

10. Step – I – Establishing Probability distribution First of all we need to make a probability for each category of service For probability, apply following formula – Probability =   Category of service Service time No. of Patients Probability Filling 45 40 40/100 = 0.40 Crown 60 15 15/100 = 0.15 Cleaning 15 15 15/100 = 0.15 Extraction 45 10 10/100 = 0.10 Check-up 15 20 20/100 = 0.20 Total 100

11. Step – II –Cumulative Probability distribution ( Next step is to calculate their cumulative probability) Category of service Service time No. of Patients Probability Cumulative probability Filling 45 40 0.40 0.40 Crown 60 15 0.15 0.40 + 0.15 = 0.55 Cleaning 15 15 0.15 0.55 + 0.15 = 0.70 Extraction 45 10 0.10 0.70 + 0.10 = 0.80 Check-up 15 20 0.20 0.80 + 0.20 = 1.00 Total 100

12. Step – III – Setting random number intervals The Random number intervals corresponds exactly to the probability of outcome. Category of service Probability Cumulative probability Random Number Intervals Filling 0.40 0.40 00 – 39 Crown 0.15 0.55 40 – 54 Cleaning 0.15 0.70 55 – 69 Extraction 0.10 0.80 70 – 79 Check-up 0.20 1.00 80 - 99

13. Step – IV – Generating Random Number Next step is to generate random number But in the question random number are already given Here need to simulate the dentist clinic for 4 hours = 8 patient (30 minutes each)* For select the category of service to each patient check the random number lies in which random number intervals Patient Scheduled arrival Random number Category Service time needed (in min.) 1 8:00 40 Crown 60 2 8:30 82 Check-up 15 3 9:00 11 Filling 45 4 9:30 34 Filling 45 5 10:00 25 Filling 45 6 10:30 66 Cleaning 15 7 11:00 17 Filling 45 8 11:30 79 Extraction 45

14. Step – V – Find out the answer Here we need to find out the average waiting time of patient & idle time of doctor Patient Scheduled arrival Service Start Service duration (in minutes) Service ends Waiting time of patient (in minutes) Idle Time of doctor 1 8:00 8:00 60 9:00 - - 2 8:30 9:00 15 9:15 30 - 3 9:00 9:15 45 10:00 15 - 4 9:30 10:00 45 10:45 30 - 5 10:00 10:45 45 11:30 45 - 6 10:30 11:30 15 11:45 60 - 7 11:00 11:45 45 12:30 45 - 8 11:30 12:30 45 1:15 60 - Total 285 -

15. Continue to V step Average waiting time = = 35.625 minutes Idle time = 0  

16. THANK YOU !!!…