PSCM_ Data Analytics

Transcription

1 PSCM_ Data Analytics Excel Functions and Simulation Sang Jo Kim July 4, 2015 * Reference - Business Analytics: Methods, Models, and Decisions (1 st edition, James R. Evans, Pearson)

2 Contents Excel PivotTable and PivotChart Excel vlookup() Monte Carlo Simulation

3 Excel Menu: Insert - Tables - PivotTable Then, follow wizard steps. PivotTables allow: Exploring Data Using PivotTables Quick creation of cross tabulations Numerous custom-made summary tables and charts

4 * PivotTable and vlookup.xlsx - The data table must have column titles. 3-4

5 Exploring Data Using PivotTables PivotTable Field List Select the fields for: Report Filter Column Labels Row Labels Σ Values Or, before choosing PivotTable, you can select a cell in the data and let Excel prepare a default PivotTable.

6 First Mission using PivotTable

7 2 nd Mission using PivotTable 3 rd Mission using PivotTable 7

8 PivotChart Click the PivotTable you created Choose Option PivotChart from the menu Book DVD East North South West 8

9 vlookup() Database Search (range_lookup = FALSE) VLOOKUP(lookup_value,table_array,col_index_num,range_lookup) lookup_value: The value you want to lookup table_array: The range of cells that VLOOKUP will search for the Lookup_value and the return value. The first column in the cell range must contain the Lookup_value. col_index_num: The column number (starting with 1 for the left-most column of table_array) that contains the return value. range_lookup (optional) FALSE: searches for the exact value in the first column. TRUE: assumes the first column in the table is sorted either numerically or alphabetically, and will then search for the closest value. This is the default method if you don't specify one. 9

10 vlookup() Database Search (range_lookup = TRUE) * Returns the closest number smaller than the value * The first column should be sorted! 10

11 Monte Carlo Simulation Simulation and Risk Analysis Spreadsheet Models with Random Variables Monte Carlo Simulation Using Risk Solver Newsvendor Model

12 Monte Carlo Simulation Origin The modern version of the Monte Carlo method was invented in the late 1940s by Stanislaw Ulam, while he was working on nuclear weapons projects at the Los Alamos National Laboratory. It was named by Nicholas Metropolis, after the Monte Carlo Casino (in Monaco), where Ulam's uncle often gambled. Immediately after Ulam's breakthrough, John von Neumann understood its importance and programmed the ENIAC computer to carry out Monte Carlo calculations. Typical procedure Define a domain of possible inputs. Generate inputs randomly from a probability distribution over the domain. Perform a deterministic computation on the inputs. Aggregate the results. * Source: Wikipedia

13 Spreadsheet Models with Random Variables * Monte Carlo Simulation.xlsx Outsourcing Decision Model Base model: What if the Production volume (Demand) = 1,500?

14 Spreadsheet Models with Random Variables * Monte Carlo Simulation.xlsx Outsourcing Decision Model Suppose production volume is uncertain ~ N(1000,100 2 ) Replace cell B12 (Prod. volume) with =ROUND(NORM.INV(RAND(),1000,100),0) * Press F9 to recalculate =ROUND(NORM.INV(RAND(),1000,100,true),0)

15 Spreadsheet Models with Random Variables Outsourcing Decision Model: Simulation solely using standard Excel functions * Limitation: How many trials would be sufficient? Law of Large Numbers!

16 Law of Large Numbers The Law: The average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed. (ex) Die casting SJ: Bets on {1,2} SP: Bets on {3,4,5,6} Who will win from a die casting? (ex) Newsvendor problem We are maximizing the expected profit The expected profit for a given ordering quantity can be closely achieved only after a Large Number of trials!

17 Monte Carlo Simulation Using Risk Solver Steps for Simulating with the Risk Solver Platform 1. Develop a spreadsheet model. (Deterministic) 2. Determine probability distributions for uncertain input variables. 3. Identify output variables you want to predict. 4. Choose the number of trials and replications. 5. Run the simulation. 6. Interpret the results.

18 Monte Carlo Simulation Using Risk Solver Using Risk Solver Platform Probability Distribution Functions For the Outsourcing Decision Model, assume that two inputs are uncertain demand and unit cost. Demand (production volume) is normally distributed with a mean of 1000 and standard deviation of 100 units. Unit cost has a triangular distribution with a minimum of $160, most likely value of $175, and a maximum of $200.

19 Monte Carlo Simulation Using Risk Solver Using Risk Solver Platform Probability Distribution Functions X X =PsiTriangular(160,175, 200) =PsiNormal(1000,100,PsiTruncate(0, 1E+30))

20 Monte Carlo Simulation Using Risk Solver Using the Distributions Button in Risk Solver Platform Select cell B12. Risk Solver Distributions Common Normal Mean=1000 Stdev=100 Select cell B10 and enter unit cost distribution.

21 Monte Carlo Simulation Using Risk Solver Using the Distributions Button in Risk Solver Platform Normal Distribution dialog for Demand in cell B12 X 0 Truncated Normal Distribution

22 Monte Carlo Simulation Using Risk Solver Using the Distributions Button in Risk Solver Platform Triangular Distribution dialog for Unit Cost in cell B10.

23 Monte Carlo Simulation Using Risk Solver Defining Uncertain Cells in Risk Solver Define worksheet cells for the output variables you want to predict using the Results button in the Simulation Model group. Risk Solver calls these uncertain cells. Uncertain cells must be numeric. The values of these cells will be computed using the randomly generated input values. There will be one value of each uncertain cell generated on each trial of the simulation.

24 Monte Carlo Simulation Using Risk Solver Using the Results Button in Risk Solver Platform Select cell B19. Risk Solver Results Output In Cell Risk Solver then modifies cell B19 (you can do this manually as well). xx =B16-B17+PsiOutput()

25 Monte Carlo Simulation Using Risk Solver Running a Simulation Options, All Options Simulation Tab Trials per Simulation Use at least 5000 trials. Simulations to Run Use more than 1 run if you want to examine variation between runs. Simulation Random Seed Choose a nonzero number if you want to reproduce the exact same results. Sampling Method Use Monte Carlo for more randomized sampling.

26 Monte Carlo Simulation Using Risk Solver Run and View Simulation Results in Risk Solver Choose Simulate, Run Once Frequency tab displays a histogram and summary statistics for the output variable. Chart Statistics support risk analysis via changes to upper/lower cutoffs. Click the down arrow next to Statistics to change the results displayed. Double click on any uncertain output cell to view its results.

27 Monte Carlo Simulation Using Risk Solver Analyzing Simulation Results for the Outsourcing Decision Model

28 Monte Carlo Simulation Using Risk Solver Analyzing Simulation Results for the Outsourcing Decision Model

29 Newsvendor Model A small candy store sells Valentine s Day gift boxes that cost $12 and sell for $18. In the past, at least 40 boxes have sold by Valentine s Day but the actual amount is unknown. After the holiday, boxes are discounted 50%. Determine net profit on the gift boxes. C = 12, R = 18, S = 9 Net profit = R(min{Q,D}) + S(max{0,Q D}) CQ =18(min{Q,D}) + 9(max{0,Q D}) 12Q

30 Newsvendor Model * Monte Carlo Simulation - Newsvendor.xlsx Suppose the store owner kept records for the past 20 years on number of boxes sold. Historical data on boxes sold Original Newsvendor Model

31 Newsvendor Model

32 Newsvendor Model Simulating the Newsvendor Model Using Resampling Generate candy sales by resampling from the 20 historical values. Set demand in B11 as a random variable. Distributions Distribution Wizard Set profit in B17 as the uncertain output.

33 Newsvendor Model Simulating the Newsvendor Model Using Resampling

34 Newsvendor Model Using a Fitted Distribution for Monte Carlo Simulation Generate candy sales by fitting a probability distribution to the 20 historical sales values.

35 Optimization Using Simulation Use the function structure: Concavity or convexity, etc. Systematically choose the decision variable values and observe the objective function values Choose the decision variable values closer to the optimal zone you guess

36 Questions & Discussions? Copyright Malaysia Institute for Supply Chain Innovation 36