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Session 2a

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Decision Models -- Prof. Juran2 Overview Sensitivity Analysis –Goal Seek and Data Table –Marketing and Finance examples Call Center LP More Sensitivity Analysis –SolverTable

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Decision Models -- Prof. Juran3 Sensitivity Analysis How do key outputs change in response to changes in inputs? Which inputs are the most important? How robust is our decision?

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Decision Models -- Prof. Juran4 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.

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Decision Models -- Prof. Juran5 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

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Decision Models -- Prof. Juran6 Managerial Problem Definition How do the parameters in Black-Scholes affect the option price?

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Decision Models -- Prof. Juran7 Formulation

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Decision Models -- Prof. Juran8 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.

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Decision Models -- Prof. Juran9 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

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Decision Models -- Prof. Juran10 Solution Methodology

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Decision Models -- Prof. Juran11 Solution Methodology

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Decision Models -- Prof. Juran12 Solution Methodology

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Decision Models -- Prof. Juran13 Solution Methodology

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Decision Models -- Prof. Juran14 Conclusions

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Decision Models -- Prof. Juran15 Conclusions

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Decision Models -- Prof. Juran16 Conclusions

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Decision Models -- Prof. Juran17 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%.

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Decision Models -- Prof. Juran18 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?)

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Decision Models -- Prof. Juran19 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).

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Decision Models -- Prof. Juran20 Formulation

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Decision Models -- Prof. Juran21 Formulation

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Decision Models -- Prof. Juran22 Formulation

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Decision Models -- Prof. Juran23 Solution Methodology ABCDEFGH Inputs Current sales40000 Current price$45 Unit variable cost$5 Data on rebates Amount of rebate$10 Pct taking advantage50% Increase in sales30.00% Data on price cut Amount of cut$6 Increase in sales20% 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)

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Decision Models -- Prof. Juran24 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?

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Decision Models -- Prof. Juran25 Goal Seek Similar to Solver, but simpler Specify a Target Cell and a Changing Cell Value must be a number (not a cell reference)

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Decision Models -- Prof. Juran26 Goal Seek

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Decision Models -- Prof. Juran27 Solution Methodology

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Decision Models -- Prof. Juran28 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).

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Decision Models -- Prof. Juran29 What If? Important parameters are not known; they are only estimates. How robust is the rebate strategy?

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Decision Models -- Prof. Juran30 Two-Way Data Table

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Decision Models -- Prof. Juran31 Two-Way Data Table ABCDEFGHIJ InputsBest policyRebate Current sales40000 Current price$45 Unit variable cost$5 Data on rebatesTwo-way data table for best policy Amount of rebate$10Increase from rebate (along side) and from price cut (along top) Pct taking advantage50%Rebate10%15%20%25%30% Increase in sales30%15% 20% Data on price cut25% Amount of cut$630% Increase in sales20%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

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Decision Models -- Prof. Juran32 Two-Way Data Table

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Decision Models -- Prof. Juran33 Two-Way Data Table ABCDEFGHIJ InputsBest policy Rebate Current sales40000 Current price$45 Unit variable cost$5 Data on rebatesTwo-way data table for best policy Amount of rebate$10 Increase from rebate (along side) and from price cut (along top) Pct taking advantage50%Rebate10%15%20%25%30% Increase in sales30%15%Rebate Price cut 20%Rebate Price cut Data on price cut 25%Rebate Price cut Amount of cut$630%Rebate Increase in sales20%35%Rebate 40%Rebate 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 highandthe 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

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Decision Models -- Prof. Juran34 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.

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Decision Models -- Prof. Juran35 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.

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Decision Models -- Prof. Juran36 Call Center Example

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Decision Models -- Prof. Juran37 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.

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Decision Models -- Prof. Juran38 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.

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Decision Models -- Prof. Juran39 Formulation Decision Variables X 1 = Daytime Calls, X 2 = Evening Calls Objective Minimize Z = 2 X X 2 Constraints 0.30 X X X X X X X X X 1 1 X 2 1 X 1, 1 X 2 0

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Decision Models -- Prof. Juran40 Solution Methodology

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Decision Models -- Prof. Juran41 Solution Methodology

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Decision Models -- Prof. Juran42 Solution Methodology

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Decision Models -- Prof. Juran43 Solution Methodology

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Decision Models -- Prof. Juran44 Optimal Solution Make 900 Daytime calls and 100 Evening calls. Total cost = $2,300.

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Decision Models -- Prof. Juran45 SolverTable Similar to Data Table; works with Solver Solves optimization problems repeatedly and automatically One or two inputs can be varied

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Decision Models -- Prof. Juran46 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.

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Decision Models -- Prof. Juran47 Solution Methodology

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Decision Models -- Prof. Juran48 Solution Methodology

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Decision Models -- Prof. Juran49 SolverTable Output

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Decision Models -- Prof. Juran50 Conclusions

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Decision Models -- Prof. Juran51 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.

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Decision Models -- Prof. Juran52 Conclusions

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Decision Models -- Prof. Juran53 Summary Sensitivity Analysis –Goal Seek and Data Table –Marketing and Finance examples Call Center LP More Sensitivity Analysis –SolverTable

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