1. Chapter 14 Simulation

2. What Is Simulation? Simulation is to mimic a process by using computers.

3. Simulation and Decision Making Simulation helps pre-view a complicated business process to identify possible problems; It allows to try different decision alternatives, and select the best alternative as the decision.

4. Simulation and Uncertainty Simulation is particularly useful when there exist uncertainties (demand, processing time, for example) in a process with many correlated factors.

5. Probable Events and Random Numbers Probable events: – Tossing a coin, it may land on Head (0.5) or Tail (0.5). – Daily demand of an item can be 4 units (0.3), 5 units (0.45), or 6 units (0.25). Computers can randomly generate a number between 0 and 1. Monte Carlo Technique is using random numbers to do simulations.

6. Monte Carlo Process The Monte Carlo process is an approach of simulating a physical process with randomly generated numbers. The key idea: Probability of a possible actual outcome = Probability of the corresponding possible outcome in the simulation with random numbers

7. How “Monte Carlo” Works Step 1. Put all possible outcomes and their probabilities in a table; Step 2. Calculate cumulative probabilities; Step 3. Use the cumulative probabilities as the cutting points of random number ranges.

8. Simulate Tossing Coins So, we can simulate the result of tossing a coin by generating a random number T so that if T is between 0 and 0.5, then the result is “Head”; if T is between 0.5 and 1, then the result is “Tail”. Possible Outcome Probability Cumulative Probability Head0.5 Tail0.51.0

9. Simulate Tossing a Dice So, (0 to 0.1667) for “landing with 1”; (0.1667 to 0.333) for “landing with 2”; … (0.8333 to 1) for “landing with 6”. Possible outcomeProbability Cumulative Probability 11/61/6 = 0.1667 21/62/6 = 0.3333 31/63/6 = 0.5 41/64/6 = 0.6667 51/65/6 = 0.8333 61/66/6 = 1.0

10. Simulate Daily Demands Daily Demand ProbabilityCumulative Probability Random Number Range 40 units0.2 50 units0.5 60 units0.3

11. =RAND() =RAND() is an Excel function generating a random number between 0 and 1.

12. =IF() Syntax of =IF() function in Excel: =IF(C,a,b) It means: If condition C is true then the function value is a, otherwise the value is b. e.g. For tossing coins: =IF(C4>0.5, ”Head”, ”Tail”) =IF() function can be nested, e.g. =IF(B5<0.2, 40, IF(B5<0.7,50, 60))

13. =VLOOKUP() If we use =IF() function to represent six possible outcomes in tossing a dice case, then we have to have get =IF() function nested for five times, which is too awkward. =VLOOKUP() facilitates our work in that case. Syntax of =VLOOKUP(): =VLOOKUP(value to lookup, range table,2)

14. Range Table for =VLOOKUP() 1 st column contains separating points of ranges – Start from the smallest allowable number of the ranges – In ascending order 2 nd column lists values of =VLOOKUP corresponding to the ranges.

15. =VLOOKUP() for Tossing Dices (1) Set up the table of ranges. – Cumulative probabilities are in the 1 st column, starting from 0 – Possible outcomes are in the 2 nd column.

16. =VLOOKUP() for Tossing Dices (2) Generate the simulation table: – In F5: =RAND() – In G5: =VLOOKUP(F5, $B$6:$C$12, 2) – Copy E5, F5, and G5 down to other rows.

17. Simulate Demands (1) Possible daily demands (from past data): DemandProbability 80.01 90.06 100.11 110.34 120.31 130.10 140.05 150.02

18. Simulate Demands (2) Calculate Cumulative Probabilities: DemandProbabilityCumulative Probability 80.01 90.060.07 100.110.18 110.340.52 120.310.83 130.100.93 140.050.98 150.021.00

19. Simulate Demands (3) Generate Vlookup range table in Excel

20. Simulate Demands (4) Generate Simulations in Excel – In B4: =RAND() – In C4: =VLOOKUP(B4,$E$4:$F$12,2) – Copy A4, B4, C4 down to other rows

21. Tips of using Excel Use cell addresses, relative or absolute, rather than the values in the cells; Use Copy / Paste functions as far as possible; Use multiple columns to decompose complicated formulas; Put the parameters to be changed on the top of the spreadsheet; Put the summary results on top.

22. Simulation for Decision Making A simulation is actually a description of day-by-day or week-by-week business operations. For a decision alternative, the simulation shows its effects on business quality or/and profit. After trying alternatives, the manager can pick one that would be best for business.

23. How Many Cases to Stock? (1) Product BC-6 costs $56.95/case from the supplier, and is sold at the price of $91.80/case. For the cases unsold at the end of a week, the store will sell them to a convenient store at price of $12.50/case. Shortage penalty cost is about $4 per case short. Possible demands of a week and their probabilities are as follows from the past records: Manager Wendy is considering how many cases of product BC-6 to stock at beginning of each week. Weekly demand of BC-6Probability 11 cases0.45 12 cases0.35 13 cases0.2

25. How Simulation Helps Decide How Many Cases to Stock (3) The worksheet each time simulates 52 weeks of business operations. Given the number of cases to order (green cell), Excel gives the operation results of 52 weeks (yellow cells). Decision maker may change the green cell, observe the outcome of 52 weeks in yellow cells, and choose the best order quantity.

26. Inventory Simulation (1) An inventory simulation simulates day-by-day transactions occurred on inventory, such as daily demand of inventoried item, number of units in stock, placing an order, length of lead time, and costs involved. An inventory simulation helps determine when to place an order to the supplier and how many units in an order.

28. How Simulation Helps Make Inventory Decision (3) For each “re-order point” and “order quantity” tried, the simulation shows the total inventory cost (including holding cost, ordering cost, and lost sales cost) of a year. A good re-order point (showing when to place an order) and a good order quantity (showing many units in an order) can thus be selected from many alternatives.

29. Other Examples of Business Simulations with Excel Minutes-by-minutes waiting lines; Gambling game; Production in a workshop; Transactions in a bank; Truck transportation; Department store operations to see the requirements of resources.