Session 2a

1. Session 2a

2. Overview • Sensitivity Analysis • Goal Seek and Data Table • Marketing and Finance examples • Call Center LP • More Sensitivity Analysis • SolverTable Decision Models -- Prof. Juran

3. Sensitivity Analysis • How do key outputs change in response to changes in inputs? • Which inputs are the most important? • How robust is our decision? Decision Models -- Prof. Juran

4. Finance Example • A European call option on a stock earns the owner an amount equal to the price at expiration minus the exercise price, if the price of the stock on which the call is written exceeds the exercise price. Otherwise, the call pays nothing. • A European put option earns the owner an amount equal to the exercise price minus the price at expiration, if the price at expiration is less than the exercise price. Otherwise the put pays nothing. Decision Models -- Prof. Juran

5. Finance Example • The Black-Scholes formula calculates the price of a European options based on the following inputs: • today's stock price • the duration of the option (in years) • the option's exercise price • the risk-free rate of interest (per year) • the annual volatility (standard deviation) in stock price Decision Models -- Prof. Juran

6. Managerial Problem Definition How do the parameters in Black-Scholes affect the option price? Decision Models -- Prof. Juran

7. Formulation Decision Models -- Prof. Juran

8. Solution Methodology Notice the use of “if” statements in cells E10:E11 and B13, so that the same model can be used for both puts and calls. Decision Models -- Prof. Juran

9. Data Table • Similar to copying a formula over many cells, but better for complicated functions (e.g. Black-Scholes) • Specify Row and/or Column Input Cells • Tricky to learn, but worth it Decision Models -- Prof. Juran

10. Solution Methodology Decision Models -- Prof. Juran

11. Solution Methodology Decision Models -- Prof. Juran

12. Solution Methodology Decision Models -- Prof. Juran

13. Solution Methodology Decision Models -- Prof. Juran

14. Conclusions Decision Models -- Prof. Juran

15. Conclusions Decision Models -- Prof. Juran

16. Conclusions Decision Models -- Prof. Juran

17. Marketing Example • Microsoft is trying to determine whether to give a $10 rebate, a $6 price cut, or have no price change on a software product. • Currently 40,000 units of the product are sold each week for $45. • The variable cost of the product is $5. • The most likely case appears to be that a $10 rebate will increase sales 30% and half of all people will claim the rebate. • For the price cut, the most likely case is that sales will increase 20%. Decision Models -- Prof. Juran

18. Managerial Problem Definition Under what circumstances should Microsoft offer the rebate, and under what circumstances should they offer the price cut? (Or should they do neither?) Decision Models -- Prof. Juran

19. Formulation • Decision variables: 3 possible marketing policies. • Objective: Maximize Profit. • Constraints: • Various assumptions have been made (current sales level, current cost structure, consumer behavior in response to marketing policies). Decision Models -- Prof. Juran

20. Formulation Decision Models -- Prof. Juran

21. Formulation Decision Models -- Prof. Juran

22. Formulation Decision Models -- Prof. Juran

23. A B C D E F G H 1 Inputs 2 Current sales 40000 3 Current price $45 4 Unit variable cost $5 5 6 Data on rebates 7 Amount of rebate $10 8 Pct taking advantage 50% 9 Increase in sales 30.00% 10 11 Data on price cut 12 Amount of cut $6 13 Increase in sales 20% 14 15 Profits =B2*(B3-B4) 16 Current $1,600,000 =((B2*(1+B9))*(B3-B4))-((B2*(1+B9)*B8)*B7) 17 With rebate $1,820,000 18 With price cut $1,632,000 =B2*(1+B13)*(B3-B12-B4) 19 20 Solution Methodology Decision Models -- Prof. Juran

24. Under current assumptions, the rebate policy appears to be optimal. • How sensitive is this result to possible errors in our assumptions? • Specifically, how wrong could we be as to the 30% assumption and still be correct in using the rebate? • What is the point of indifference between the rebate and the price cut? Decision Models -- Prof. Juran

25. Goal Seek • Similar to Solver, but simpler • Specify a Target Cell and a Changing Cell • “Value” must be a number (not a cell reference) Decision Models -- Prof. Juran

26. Goal Seek Decision Models -- Prof. Juran

27. Solution Methodology Decision Models -- Prof. Juran

28. Conclusions and Recommendations • Go with the rebate as long as the increase in sales is expected to be at least 16.57%. • Under current assumptions, Microsoft would earn $1,820,000 profit (an improvement of $220,000). Decision Models -- Prof. Juran

29. What If? • Important parameters are not known; they are only estimates. • How robust is the rebate strategy? Decision Models -- Prof. Juran

30. Two-Way Data Table Decision Models -- Prof. Juran

31. A B C D E F G H I J 1 Inputs Best policy Rebate 2 Current sales 40000 =IF(B16=MAX(B16:B18),"Current",IF(B17=MAX(B16:B18),"Rebate","Price cut")) 3 Current price $45 4 Unit variable cost $5 5 6 Data on rebates Two-way data table for best policy 7 Amount of rebate $10 Increase from rebate (along side) and from price cut (along top) 8 Pct taking advantage 50% Rebate 10% 15% 20% 25% 30% 9 Increase in sales 30% 15% 10 20% =E1 11 Data on price cut 25% 12 Amount of cut $6 30% 13 Increase in sales 20% 35% 14 40% 15 Profits 16 Current $1,600,000 17 With rebate $1,820,000 18 With price cut $1,632,000 Two-Way Data Table Decision Models -- Prof. Juran

32. Two-Way Data Table Decision Models -- Prof. Juran

33. A B C D E F G H I J Inputs Best policy 1 Rebate 2 Current sales 40000 3 Current price $45 =IF(B16=MAX(B16:B18),"Current",IF(B17=MAX(B16:B18),"Rebate","Price cut")) 4 Unit variable cost $5 5 Data on rebates Two-way data table for best policy 6 Increase from rebate (along side) and from price cut (along top) 7 Amount of rebate $10 8 Pct taking advantage 50% Rebate 10% 15% 20% 25% 30% 9 Increase in sales 30% 15% Rebate Rebate Price cut Price cut Price cut 10 20% Rebate Rebate Rebate Price cut Price cut =E1 Data on price cut 11 25% Rebate Rebate Rebate Rebate Price cut 12 Amount of cut $6 30% Rebate Rebate Rebate Rebate Rebate 13 Increase in sales 20% 35% Rebate Rebate Rebate Rebate Rebate 14 40% Rebate Rebate Rebate Rebate Rebate Profits 15 Unless Microsoft thinks the sales increase from a price cut 16 Current $1,600,000 will be high and the sales increase from a rebate will be low, 17 With rebate $1,820,000 it looks like the rebate is the way to go. 18 With price cut $1,632,000 Two-Way Data Table Decision Models -- Prof. Juran

34. Conclusions and Recommendations • Unless Microsoft thinks the sales increase from a price cut will be high and the sales increase from a rebate will be low, it looks like the rebate is the way to go. Decision Models -- Prof. Juran

35. Call Center Example • For a telephone survey, a marketing research group needs to contact at least 150 wives, 120 husbands, 100 single adult males, and 110 single adult females. • It costs $2 to make a daytime call and (because of higher labor costs) $5 to make an evening call. • Because of a limited staff, at most half of all phone calls can be evening calls. Decision Models -- Prof. Juran

36. Call Center Example Decision Models -- Prof. Juran

37. Managerial Problem Definition We want to minimize the total cost of completing the survey, subject to the various probabilities of reaching certain types of people at certain times of the day, costs of making calls, and minimum requirements for numbers of calls to certain demographic groups. Decision Models -- Prof. Juran

38. Formulation Decision Variables We need to decide how many evening calls and how many daytime calls to make. Objective Minimize the total cost. Constraints We need to contact 150 wives, 120 husbands, 100 single adult males, and 110 single adult females. At most half of all phone calls can be evening calls. Decision Models -- Prof. Juran

39. Formulation Decision Variables X1 = Daytime Calls, X2 = Evening Calls Objective Minimize Z = 2X1 + 5X2 Constraints 0.30X1 + 0.30X2 ≥ 150 0.10X1 + 0.30X2 ≥ 120 0.10X1 + 0.15X2 ≥ 100 0.10X1 + 0.20X2 ≥ 110 1X1 ≥ 1X2 1X1, 1X2 ≥ 0 Decision Models -- Prof. Juran

40. Solution Methodology Decision Models -- Prof. Juran

41. Solution Methodology Decision Models -- Prof. Juran

42. Solution Methodology Decision Models -- Prof. Juran

43. Solution Methodology Decision Models -- Prof. Juran

44. Optimal Solution Make 900 Daytime calls and 100 Evening calls. Total cost = $2,300. Decision Models -- Prof. Juran

45. SolverTable • Similar to Data Table; works with Solver • Solves optimization problems repeatedly and automatically • One or two inputs can be varied Decision Models -- Prof. Juran

46. Example: Sensitivity to Calling Costs • Starting with the optimal solution to the initial problem, use the SolverTable add-in to investigate changes in the unit cost of either type of call. • Specifically, investigate changes in the cost of a daytime call, with the cost of an evening call fixed, to see when (if ever) only daytime calls or only evening calls will be made. Decision Models -- Prof. Juran

47. Solution Methodology Decision Models -- Prof. Juran

48. Solution Methodology Decision Models -- Prof. Juran

49. SolverTable Output Decision Models -- Prof. Juran

50. Conclusions Decision Models -- Prof. Juran