1. Chapter 13 Supplement Simulation

2. A tool used to imitate real phenomenon using a set of mathematical formulas Provides management with an experimental laboratory to test various models or options (what-ifs) Advanced simulations are completed with a computer (i.e., weather condition simulation)

3. Simulation Applications ApplicationSimulation Objective Staffing bank tellersConsider the waiting time of customers when determining the number of tellers to schedule Emergency ambulance locationAnalyze the response time implications of location options Order processingAnalyze order processing procedures to support just-in-time shipments Aircraft maintenanceDetermine the impact on downtime of preventive maintenance schedules Scheduling of police patrolsInvestigate the impact of targeting crime areas on crime prevention

4. Monte Carlo Simulation Used to predict a discrete number such as customers arriving per hour or expected revenues After determining the probability of particular events occurring, this simulation technique utilizes random numbers to obtain observations It is simulation because it models what is likely to occur in the “real life” situation

5. Example A textbook publishing company is considering the release of three books next year. Because of a cash flow problem, the company is interested in predicting the expected revenue and its range from sales of these books.

6. Expected Sales in Year 1 BookExpected Number of Books to be Sold Selling Price (per book) A200$25 B1,000$10 C3,000$5 Net Sales 200 x $25 = $5,000 $10,000 $15,000 $30,000

7. Probability of Deviations from Expected Sales Deviation (% of Sales)Net Effect of DeviationProbability of Occurrence 80%$30,000 x.80 = $24,000 0.1 90%$27,0000.1 100%$30,0000.4 110%$30,000 x 1.10= $33,000 0.2 120%$36,0000.1

8. Random Number Assignment Table Deviation (%)ProbabilityCumulative Probability Random Number Assignment 800.1 0.0 ≤ RN < 0.1 900.20.30.1 ≤ RN < 0.3 1000.40.70.3 ≤ RN < 0.7 1100.20.90.7 ≤ RN < 0.9 1200.11.00.9 ≤ RN < 1.0

9. Generate Random Numbers 0.06785 0.81075 0.98544 0.31479 0.12484 0.23882 0.23897 0.40374 0.73622 0.36952 0.1451 0.12719 0.99407 0.32694 0.4278 0.00633 0.3849 0.22363 0.54105

10. Running Realizations (random scenario 1) Random NumberCorresponding Deviation in Sales Book (Expected Revenue) Predicted Revenue 0.0678580% of predicted sales A ($5,000) $5,000 x.80 = $4,000 0.81075110%B ($10,000) $11,000 0.98544120%C ($15,000) $18,000 Total = $33,000

11. Running Realizations (random scenario 2) Random NumberCorresponding Deviation in Sales Book (Expected Revenue) Predicted Revenue 0.31479100% of predicted sales A ($5,000) $5,000 x 1.0 = $5,000 0.1248490%B ($10,000) $9,000 0.2388290%C ($15,000) $13,500 Total = $27,500

12. Results of 10 Realizations RealizationExpected Sales Revenue 1$33,000 227,500 331,000 427,500 531,000 627,500 730,000 829,000 932,000 1032,500 Total$301,000 Range of sales revenue is $27,500 to $33,000 with an average of $30,100