1. Module C9 Simulation Concepts

2. NEED FOR SIMULATION Mathematical models we have studied thus far have “closed form” solutions –Obtained from formulas -- forecasting, inventory, queuing –Obtained by algorithms -- linear programming, PERT/CPM However, each of these models had to satisfy a restrictive set of assumptions –Many “real-life” situations do not meet these conditions SIMULATION can be used to get “good” results

3. BACKGROUND Simulation is, in fact, the most used management science technique Simulation is not an optimization procedure like the one used to solve linear programs However, if you are considering one of a set of options, simulation can indicate which of these options appears to be the best in the set.

4. BASIC IDEA Recognize the components of the system under study Develop a random number mapping that will “map” random numbers from a (computer generated) random number table into events

5. PSEUDO RANDOM NUMBERS Random numbers should be uniformly distributed: –each digit in a random number should have a probability of 1/10 of occurring after any other digit –no pattern should exist in the random numbers Random numbers generated by a computer program are done so by an algorithm and the above conditions may be slightly violated The result is that the random numbers are not truly random - they are PSEUDO RANDOM NUMBERS

6. BENEFIT OF USING PSEUDO RANDOM NUMBERS The string of random numbers can be regenerated This allows us to compare policies under exactly the same conditions

7. PROBABILITIES AND RANDOM NUMBERS Typically computer generated random numbers are numbers between 0 and 1 –We can “lop off” the decimal for convenience The probabilities of possible events will be expressed as 1-digit, 2-digit, 3-digit, or …. probabilities -- the random numbers we use/assign should be of the same length

8. RANDOM NUMBER MAPPINGS Suppose that the number of students that miss a MSIS 361B class have been observed to be 0, 1, 2, 3, or 4 with the following probabilities: NUMBER 0 1 2 3 4 PROB..21.35.19.15.10 RN Map 00-20 21-55 56-74 75-89 90-99

9. APPROACH Generate a set of random numbers and map them into events We will choose the first two digits from column 1 of the random number table in the book

10. Simulation of 5 Classes 1 652 2773 3612 4883 5421 ClassRandom # # Absences

11. ANALYSIS BETTER RESULTS We can now analyze “simulated results” –Average # absences = (2+3+2+3+1)/5 = 2.2 For better results we can: –Repeat this 5-class simulation many times –Run the simulation for many more than 5 classes

12. Module C9 Review Simulation can be used to approximate complex systems Use of pseudorandom numbers Random Number Mapping into Events Calculations How to Gain More Confidence