1. 1 Lecture 2 Decision Theory Chapter 5S

2. 2  Certainty - Environment in which relevant parameters have known values  Risk - Environment in which certain future events have probabilistic outcomes  Uncertainty - Environment in which it is impossible to assess the likelihood of various future events Decision Environments

3. 3 Maximin - Choose the alternative with the best of the worst possible payoffs Maximax - Choose the alternative with the best possible payoff Minimax Regret - Choose the alternative that has the least of the worst regrets Decision Making under Uncertainty

4. 4 Payoff Table: An Example LowModerateHigh Small facility $10 Medium facility 712 Large facility - 4216 Possible Future Demand Values represent payoffs (profits)

5. 5 Maximax Solution Note: choose the “minimize the payoff” option if the numbers in the previous slide represent costs

6. 6 Maximin Solution

7. 7 Minimax Regret Solution

8. 8 Decision Making Under Risk - Decision Trees State of nature 1 B Payoff 1 State of nature 2 Payoff 2 Payoff 3 2 Choose A’ 1 Choose A’ 2 Payoff 6 State of nature 2 2 Payoff 4 Payoff 5 Choose A’ 3 Choose A’ 4 State of nature 1 Choose A’ Choose A’ 2 1 Decision Point Chance Event

9. 9 Decision Making with Probabilities  Expected Value Approach  Useful if probabilistic information regarding the states of nature is available  Expected return for each decision is calculated by summing the products of the payoff under each state of nature and the probability of the respective state of nature occurring  Decision yielding the best expected return is chosen.

10. 10 Example: Burger Prince  Burger Prince Restaurant is considering opening a new restaurant on Main Street.  It has three different models, each with a different seating capacity.  Burger Prince estimates that the average number of customers per hour will be 80, 100, or 120 with a probability of 0.4, 0.2, and 0.4 respectively  The payoff (profit) table for the three models is as follows. s 1 = 80 s 2 = 100 s 3 = 120 Model A $10,000 $15,000 $14,000 Model B $ 8,000 $18,000 $12,000 Model C $ 6,000 $16,000 $21,000 Choose the alternative that maximizes expected payoff

11. 11 Decision Tree 11.2.4.4.4.2.4.4.2.4 d1d1d1d1 d2d2d2d2 d3d3d3d3 s1s1s1s1 s1s1s1s1 s1s1s1s1 s2s2s2s2 s3s3s3s3 s2s2s2s2 s2s2s2s2 s3s3s3s3 s3s3s3s3 Payoffs 10,000 15,000 14,000 8,000 18,000 12,000 6,000 16,000 21,000 22 33 44

12. 12 Management Scientist Solutions EVPI = Expected payoff under certainty – Expected payoff under risk

13. 13 Lecture 2 Forecasting Chapter 3

14. 14  A statement about the future value of a variable of interest such as demand.  Forecasts affect decisions and activities throughout an organization  Accounting, finance  Human resources  Marketing  Operations  Product / service design Forecast

15. 15 AccountingCost/profit estimates FinanceCash flow and funding Human ResourcesHiring/recruiting/training MarketingPricing, promotion, strategy OperationsSchedules, MRP, workloads Product/service designNew products and services Uses of Forecasts

16. 16 Elements of a Good Forecast Timely Accurate Reliable Meaningful Written Easy to use

17. 17 Steps in the Forecasting Process Step 1 Determine purpose of forecast Step 2 Establish a time horizon Step 3 Select a forecasting technique Step 4 Gather and analyze data Step 5 Prepare the forecast Step 6 Monitor the forecast “The forecast”

18. 18 Types of Forecasts  Judgmental - uses subjective inputs  Time series - uses historical data assuming the future will be like the past  Associative models - uses explanatory variables to predict the future

19. 19 Judgmental Forecasts  Executive opinions  Sales force opinions  Consumer surveys  Outside opinion  Delphi method  Opinions of managers and staff  Achieves a consensus forecast

20. 20 Time Series Forecasts  Trend - long-term movement in data  Seasonality - short-term regular variations in data  Cycle – wavelike variations of more than one year’s duration  Irregular variations - caused by unusual circumstances

21. 21 Forecast Variations Trend Irregular variatio n Seasonal variations 90 89 88 Figure 3.1 Cycles

22. 22 Smoothing/Averaging Methods  Used in cases in which the time series is fairly stable and has no significant trend, seasonal, or cyclical effects  Purpose of averaging - to smooth out the irregular components of the time series.  Four common smoothing/averaging methods are:  Moving averages  Weighted moving averages  Exponential smoothing

23. 23 n Sales of gasoline for the past 12 weeks at your local Chevron (in ‘000 gallons). If the dealer uses a 3- period moving average to forecast sales, what is the forecast for Week 13? Example of Moving Average n Past Sales Week Sales Week Sales Week Sales Week Sales 1 17 7 20 1 17 7 20 2 21 8 18 2 21 8 18 3 19 9 22 3 19 9 22 4 23 10 20 4 23 10 20 5 18 11 15 5 18 11 15 6 16 12 22 6 16 12 22

24. 24 Management Scientist Solutions MA(3) for period 4 = (17+21+19)/3 = 19 Forecast error for period 3 = Actual – Forecast = 23 – 19 = 4

25. 25 MA(5) versus MA(3)

26. 26 Exponential Smoothing Premise - The most recent observations might have the highest predictive value.  Therefore, we should give more weight to the more recent time periods when forecasting.

27. 27 Exponential Smoothing  Weighted averaging method based on previous forecast plus a percentage of the forecast error  A-F is the error term,  is the % feedback F t+1 = F t +  ( A t - F t )

28. 28 Picking a Smoothing Constant .1 .4 Actual

29. 29 Linear Trend Equation  F t = Forecast for period t  t = Specified number of time periods  a = Value of F t at t = 0  b = Slope of the line F t = a + bt 0 1 2 3 4 5 t FtFt a Suitable for time series data that exhibit a long term linear trend

30. 30 Linear Trend Example F11 = 20.4 + 1.1(11) = 32.5 Linear trend equation Sale increases every time period @ 1.1 units

31. 31 Actual vs Forecast Linear Trend Example 0 5 10 15 20 25 30 35 12345678910 Week Actual/Forecasted sales Actual Forecast F(t) = 20.4 + 1.1t

32. 32 Forecasting with Trends and Seasonal Components – An Example  Business at Terry's Tie Shop can be viewed as falling into three distinct seasons: (1) Christmas (November-December); (2) Father's Day (late May - mid-June); and (3) all other times.  Average weekly sales ($) during each of the three seasons during the past four years are known and given below.  Determine a forecast for the average weekly sales in year 5 for each of the three seasons. Year Season 1 2 3 4 1 1856 1995 2241 2280 2 2012 2168 2306 2408 3 985 1072 1105 1120

33. 33 Management Scientist Solutions

34. 34 Interpretation of Seasonal Indices  Seasonal index for season 2 (Father’s Day) = 1.236  Means that the sale value of ties during season 2 is 23.6% higher than the average sale value over the year  Seasonal index for season 3 (all other times) = 0.586  Means that the sale value of ties during season 3 is 41.4% lower than the average sale value over the year

35. 35 Associative Forecasting  Predictor variables - used to predict values of variable interest  Regression - technique for fitting a line to a set of points  Least squares line - minimizes sum of squared deviations around the line

36. 36 Regression Analysis – An Example Home-Size (Square feet)Price 600$72,000 1050$116,300 1800$152,000 922$80,500 1950$141,900 1783$124,000 1008$117,000 1840$165,900 3700$153,500 1092$126,500 1950$122,000 1403$140,000 1680$223,000 1000$99,500 2310$211,900 1300$121,900 1930$169,000 3000$156,000 1362$123,500 1750$136,000 2080$194,900 1344$128,500 2130$302,000 1500$142,000 2400$146,000 2272$180,000 1050$126,500 1610$139,500 Linear model seems reasonable A straight line is fitted to a set of sample points

37. 37 Regression Results  Use MS-Excel macro  Template posted at class website y = 85972.78 + 35.65x Price = 85972.87 + 35.65(Square footage) Forecast price of a 2000 square feet house y = 85972.78 + 35.65(2000) = $157,272.78

38. 38 Forecast Accuracy  Error - difference between actual value and predicted value  Mean Absolute Deviation (MAD)  Average absolute error  Mean Squared Error (MSE)  Average of squared error

39. 39 MAD and MSE MAD = Actualforecast   n MSE = Actualforecast ) 2   n (

40. 40 Measure of Forecast Accuracy  MSE = Mean Squared Error

41. 41 Forecasting Accuracy Estimates Example 10 of textbook

42. 42 Sources of Forecast errors  Model may be inadequate  Irregular variations  Incorrect use of forecasting technique

43. 43 Characteristics of Forecasts  They are usually wrong  A good forecast is more than a single number  Aggregate forecasts are more accurate  The longer the forecast horizon, the less accurate the forecast will be  Forecasts should not be used to the exclusion of known information

44. 44 Choosing a Forecasting Technique  No single technique works in every situation  Two most important factors  Cost  Accuracy  Other factors include the availability of:  Historical data  Computers  Time needed to gather and analyze the data  Forecast horizon