1. Session 2a
Decision Models Prof. Juran

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

3. Decision Models -- Prof. Juran
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
Decision Models Prof. Juran

4. Decision Models -- Prof. Juran
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
Decision Models Prof. Juran

5. Decision Models -- Prof. Juran
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
Decision Models Prof. Juran

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

7. Decision Models -- Prof. Juran
Formulation
Decision Models Prof. Juran
Decision Models Prof. Juran

8. Decision Models -- Prof. Juran
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
Decision Models Prof. Juran

9. Decision Models -- Prof. Juran
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
Decision Models Prof. Juran

10. Decision Models -- Prof. Juran
Solution Methodology
Decision Models Prof. Juran
Decision Models Prof. Juran

11. Decision Models -- Prof. Juran
Solution Methodology
Decision Models Prof. Juran
Decision Models Prof. Juran

12. Decision Models -- Prof. Juran
Solution Methodology
Decision Models Prof. Juran
Decision Models Prof. Juran

13. Decision Models -- Prof. Juran
Solution Methodology
Decision Models Prof. Juran
Decision Models Prof. Juran

14. Decision Models -- Prof. Juran
Conclusions
Decision Models Prof. Juran
Decision Models Prof. Juran

15. Decision Models -- Prof. Juran
Conclusions
Decision Models Prof. Juran
Decision Models Prof. Juran

16. Decision Models -- Prof. Juran
Conclusions
Decision Models Prof. Juran
Decision Models Prof. Juran

17. Decision Models -- Prof. Juran
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
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
Decision Models Prof. Juran

19. Decision Models -- Prof. Juran
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
Decision Models Prof. Juran

20. Decision Models -- Prof. Juran
Formulation
Decision Models Prof. Juran
Decision Models Prof. Juran

21. Decision Models -- Prof. Juran
Formulation
Decision Models Prof. Juran
Decision Models Prof. Juran

22. Decision Models -- Prof. Juran
Formulation
Decision Models Prof. Juran
Decision Models Prof. Juran

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

24. Decision Models -- Prof. Juran
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
Decision Models Prof. Juran

25. Decision Models -- Prof. Juran
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
Decision Models Prof. Juran

26. Decision Models -- Prof. Juran
Goal Seek
Decision Models Prof. Juran
Decision Models Prof. Juran

27. Decision Models -- Prof. Juran
Solution Methodology
Decision Models Prof. Juran
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
Decision Models Prof. Juran

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

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

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

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

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

35. Decision Models -- Prof. Juran
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
Decision Models Prof. Juran

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

38. Decision Models -- Prof. Juran
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
Decision Models Prof. Juran

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

40. Decision Models -- Prof. Juran
Solution Methodology
Decision Models Prof. Juran
Decision Models Prof. Juran

41. Decision Models -- Prof. Juran
Solution Methodology
Decision Models Prof. Juran
Decision Models Prof. Juran

42. Decision Models -- Prof. Juran
Solution Methodology
Decision Models Prof. Juran
Decision Models Prof. Juran

43. Decision Models -- Prof. Juran
Solution Methodology
Decision Models Prof. Juran
Decision Models Prof. Juran

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

45. Decision Models -- Prof. Juran
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
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
Decision Models Prof. Juran

47. Decision Models -- Prof. Juran
Solution Methodology
Decision Models Prof. Juran
Decision Models Prof. Juran

48. Decision Models -- Prof. Juran
Solution Methodology
Decision Models Prof. Juran
Decision Models Prof. Juran

49. Decision Models -- Prof. Juran
SolverTable Output
Decision Models Prof. Juran
Decision Models Prof. Juran

50. Decision Models -- Prof. Juran
Conclusions
Decision Models Prof. Juran
Decision Models Prof. Juran

51. Decision Models -- Prof. Juran
Conclusions
If daytime calls are very inexpensive, we can dispense with evening calls altogether. However, we will always have to make at least 400 daytime calls, no matter how expensive they are.
Decision Models Prof. Juran
Decision Models Prof. Juran

52. Decision Models -- Prof. Juran
Conclusions
Decision Models Prof. Juran
Decision Models Prof. Juran

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