session 10b

Session 10b

Decision Models -- Prof. Juran

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Overview• Marketing Simulation Models• New Product Development Decision

– Uncertainty about competitor behavior– Uncertainty about customer behavior

• Market Shares– Modeling the dynamics of a 3-supplier

market– Customer loyalty– Benefits of quality improvement

• Pricing Strategy– American Airlines


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Marketing Example: New Product Development

DecisionCavanaugh Pharmaceutical Company (CPC) has enjoyed a monopoly on sales of its popular antibiotic product, Cyclinol, for several years. Unfortunately, the patent on Cyclinol is due to expire. CPC is considering whether to develop a new version of the product in anticipation that one of CPC’s competitors will enter the market with their own offering.

The decision as to whether or not to develop the new antibiotic (tentatively called Minothol) depends on several assumptions about the behavior of customers and potential competitors. CPC would like to make the decision that is expected to maximize its profits over a ten-year period, assuming a 15% cost of capital.


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Costs and Revenues Cyclinol costs $1.00 per dose to manufacture, and sells for $7.50 per dose. The proposed Minothol product would cost $0.90 per dose and sell for $6.00, allowing CPC to protect its market share against lower-priced competition. This would, however, require a one-time investment of $140 million.

Cyclinol Minothol Fixed Cost None $140 million Variable Cost $1.00 $0.90 Selling Price $7.50 $6.00

Competition There is really only one other company with the potential to enter the market, Ahrens MethLabs, Inc. (AMI). Competitive analysis indicates that AMI is 20% likely to introduce a competing product if CPC stays with the higher-priced Cyclinol product, but only 5% likely to enter the market if CPC introduces Minothol.


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Customer DemandAnalysts estimate that the average annual demand over the next ten years will be normally distributed with a mean of 40 million doses and a standard deviation of 10 million doses, as shown below.

This demand is believed to be independent of whether CPC introduces Minothol or whether Cyclinol/Minothol has a competitor.


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CPC’s market share is expected to be 100% of demand, as long as there is no competition from AMI. In the event of competition, CPC will still enjoy a dominant market position because of its superior brand recognition.

However, AMI is likely to price its product lower than CPC’s in an effort to gain market share. CPC’s best analysis indicates that its share of total sales, in the event of competition, will be a function of the price it chooses to charge per dose, as shown below.

The Cyclinol product at $7.50 would only retain a 38.1% market share, whereas the Minothol product at $6.00 would have a 55.0% market share.

Market Share vs. Price

0%

20%

40%

60%

80%

100%

$- $2 $4 $6 $8 $10 $12 $14

Price

Mar

ket S

hare


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QuestionsWhat is the best decision for CPC, in terms of maximizing the expected value of its profits over then next ten years?

What is the least risky decision, using the standard deviation of the ten-year profit as a measure of risk?

What is the probability that introducing Minothol will turn out to be the best decision?


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123456789

10111213141516171819

A B C D E0.70928

No Competition Competition No Competition CompetitionPrice 7.50$ 7.50$ 6.00$ 6.00$

Total Demand 40.2P(Competition) 20% 5%Competition? No NoMarket Share 100.0% 38.1% 100.0% 55.0%Cyclinol Units Sold 40.2 15.3 40.2 22.1Revenue 301.28$ 114.86$ 241.02$ 132.56$ Fixed Cost -$ -$ 140.00$ 140.00$ Variable Cost 1.00$ 1.00$ 0.90$ 0.90$ Annual profit 261.11$ 99.55$ 204.87$ 112.68$ Discount Rate 15%10-year PV $1,310.45 $499.61 $888.20 $425.51

ResultsCyclinol 1,310.45$ Minothol 888.20$ Minothol Better? 0

Cyclinol Minothol

Income statement-like calculations for each of four

scenarios

3 Forecasts:NPV in $millions for each

decisionYes/No New Product Better

U~(0, 1)(whether or not

AMI enters market)

N~(40, 10)(Total market

demand)


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Example: Market SharesSuppose that each week every family in the United States buys a gallon of orange juice from company A, B, or C.

Let PA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define PB and PC similarly for companies B and C.


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If the last gallon of juice purchased by a family is satisfactory, then the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, then the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C.


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Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. Thus, if a customer switches from brand A, there is probability B/(B + C) that he will switch to brand B and probability C/(B + C) that he will switch to brand C. Suppose that 1,000,000 gallons of orange juice are purchased each week.After a year, what will the market share for each firm be? Assume PA = 0.10, PB = 0.15, and Pc = 0.20.


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1 2 3 4 5 6 7 8 9

1 0 1 1 1 2 1 3 1 4 1 5 1 6

A B C D E F G H I J K L M N O P Q R S T U V In p u ts

P ro b a b i li t ie s u n s a t i s f a c to ry E n d in g M a rk e t S h a re s A B C A B C

0 .1 0 0 .1 5 0 .2 0 0 .5 3 0 .3 6 0 .1 1 W e e k A b u y e rs B b u y e r s C b u y e rs # A b a d # B b a d # C b a d B /N o t A # A to B # A to C A /N o t B # B to A # B to C A /N o t C # C to A # C to B

1 2 0 0 2 0 0 2 0 0 2 0 0 2 0 0 2 0 0 1 8 3 3 4 3 1 8 3 3 4 3 0 .5 0 9 9 0 .5 0 1 7 1 6 0 .5 0 2 5 1 8 2 2 2 4 1 9 4 1 8 2 2 2 4 1 9 4 1 8 2 2 5 3 2 3 4 2 5 3 2 3 4 0 .5 2 1 4 1 1 0 .5 5 1 9 1 3 0 .5 4 1 7 1 7 3 2 3 5 1 9 3 1 7 2 2 3 5 1 9 3 1 7 2 2 6 2 4 2 2 2 6 2 4 2 2 0 .5 3 1 2 1 4 0 .5 8 1 6 8 0 .5 5 1 2 1 0 4 2 3 7 1 9 1 1 7 2 2 3 7 1 9 1 1 7 2 2 3 2 4 3 2 2 3 2 4 3 2 0 .5 3 1 4 9 0 .5 8 1 1 1 3 0 .5 5 2 1 1 1 5 2 4 6 1 9 2 1 6 2 2 4 6 1 9 2 1 6 2 2 7 2 7 3 7 2 7 2 7 3 7 0 .5 4 1 6 1 1 0 .6 0 1 5 1 2 0 .5 6 2 3 1 4 6 2 5 7 1 9 5 1 4 8 2 5 7 1 9 5 1 4 8 2 1 4 1 2 6 2 1 4 1 2 6 0 .5 7 8 1 3 0 .6 3 2 7 1 4 0 .5 7 1 6 1 0 7 2 7 9 1 7 2 1 4 9 2 7 9 1 7 2 1 4 9 2 9 1 8 3 1 2 9 1 8 3 1 0 .5 4 1 5 1 4 0 .6 5 1 2 6 0 .6 2 1 9 1 2 8 2 8 1 1 8 1 1 3 8 2 8 1 1 8 1 1 3 8 2 9 1 9 2 9 2 9 1 9 2 9 0 .5 7 1 6 1 3 0 .6 7 1 4 5 0 .6 1 1 6 1 3 9 2 8 2 1 9 1 1 2 7 2 8 2 1 9 1 1 2 7 2 7 2 4 2 8 2 7 2 4 2 8 0 .6 0 2 0 7 0 .6 9 1 9 5 0 .6 0 1 6 1 2

1 0 2 9 0 1 9 9 1 1 1 2 9 0 1 9 9 1 1 1 2 8 3 0 1 9 2 8 3 0 1 9 0 .6 4 1 7 1 1 0 .7 2 2 3 7 0 .5 9 9 1 0

=B7- H 7+ R7+ U 7 = C7- I 7+ V 7+ O 7 =(SU M ($ B$7:$ D$7) ) - (SU M (B8: C8) )

= SU M ( B8: D 8) - SU M ( F8:G8)

= M AX( C8,1) = M AX( D8,1)

= M AX( H8,1) =M AX( I 8,1)

=M AX( J 8,1) = M A X( (F8/ ( F8+ G8) ) ,0.00 00001)

= (H 8-O 8)

=M AX( (E 8/ (E 8+ G8) ) ,0.0000001) =(L8- R8)

= M A X( (E 8/ (E8+ F8) ) ,0 .000 0001 )

=M 8-U 8

= D58/ SU M ($B$58: $D$58)

I n o rd er to k eep th e scale o f th e m od el w i th in th e cap abi l i ties o f C ry stal B al l , w e h av e red u ced th e n u m ber o f u sers to 600.


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1 2 3 4 5 6 7 8 9 10 11

A B C D Inputs

Probabilities unsatisfactory A B C

0.10 0.15 0.20

Week A buyers B buyers C buyers 1 200 200 200 2 224 194 182 3 235 193 172 4 237 191 172 5 246 192 162

=B7-H7+R7+U7 =C7-I7+V7+O7

=(SUM($B$7:$D$7))-(SUM(B8:C8)) B4:D4 contain the probabilities that a given unit of the respective companies’ products will be unsatisfactory. These will be used with Crystal Ball to generate “bad” orange juice using the binomial distribution.


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B7:D7 contain the initial distribution of customers across the three brands. Every week, the number of customers for each brand is calculated using this formula:

number of customers from the previous week - total customers lost + customers gained from one competitor + customers gained from the other competitor = number of customers this week


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For brand A in week 2, this formula is calculated with: B7 - H7

+ R7 + U7 = B8

For brand B in week 2, this formula is calculated with: C7 - I7

+ V7 + O7 = C8

Brand C will have all of the total customers from the previous week minus the Brands A and B current customers, so

=(SUM($B$7:$D$7))-(SUM(B8:C8))


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Now recall that a binomial random variable X is an integer between 0 and n, viewed as the number of “successes” out of n “trials”. The binomial distribution assumes that there is a probability p of a success on any one trial, and that all trials are independent of each other.

In this case, X is the number of gallons that are “bad”, n is the total number of gallons purchased of a particular brand, and p is the probability that any one gallon is “bad”.


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I n t h e fi r s t w e e k , e a c h b r a n d h a s 2 0 0 c u s t o m e r s , s o n w i l l b e 2 0 0 f o r a l l t h r e e b r a n d s , i n t h e s e c o n d w e e k , n i s 2 2 4 f o r B r a n d A , 1 9 4 f o r B r a n d B , a n d 1 8 2 f o r B r a n d C . ( T h e s e w i l l c h a n g e d u r i n g t h e c o u r s e o f t h e s i m u l a t i o n . )

678

B C D E F G H I J K L MA b u y e r s B b u y e r s C b u y e r s # A b a d # B b a d # C b a d

2 0 0 2 0 0 2 0 0 2 0 0 2 0 0 2 0 0 1 8 3 3 4 3 1 8 3 3 4 32 2 4 1 9 4 1 8 2 2 2 4 1 9 4 1 8 2 2 5 3 2 3 4 2 5 3 2 3 4


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678

B C D E F G H I J K L MA b u y e r s B b u y e r s C b u y e r s # A b a d # B b a d # C b a d

2 0 0 2 0 0 2 0 0 2 0 0 2 0 0 2 0 0 1 8 3 3 4 3 1 8 3 3 4 32 2 4 1 9 4 1 8 2 2 2 4 1 9 4 1 8 2 2 5 3 2 3 4 2 5 3 2 3 4

W e h a v e u s e d c o l u m n s E , F , a n d G t o t r u n c a t e t h e s e r a n d o m n v a l u e s s o t h a t t h e y a r e a l w a y s a t l e a s t 1 . T h i s w i l l n o t m a k e a n y d i ff e r e n c e m o s t o f t h e t i m e , b u t o c c a s i o n a l l y o n e b r a n d ’ s c u s t o m e r b a s e w i l l g o t o z e r o i n a l o n g s i m u l a t i o n r u n , c a u s i n g a n e r r o r w i t h C r y s t a l B a l l . ( C r y s t a l B a l l d o e s n ’ t k n o w h o w t o g e n e r a t e a b i n o m i a l v a r i a b l e w h e n n i s z e r o . ) S o w e n e e d t o s e t u p b i n o m i a l r a n d o m v a r i a b l e s , w h e r e t h e n f o r e a c h b r a n d i s g i v e n i n c o l u m n E , F , o r G a n d t h e p i s g i v e n i n B 4 , C 4 , o r D 4 , d e p e n d i n g o n w h i c h b r a n d .


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Note that we have used dollar signs in the cell references, so this can be copied down to the rest of the assumption cells in column H.


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678

E F G H I J K L M# A b a d # B b a d # C b a d

2 0 0 2 0 0 2 0 0 1 8 3 3 4 3 1 8 3 3 4 32 2 4 1 9 4 1 8 2 2 5 3 2 3 4 2 5 3 2 3 4

O u r m o d e l n o w i n c l u d e s r a n d o m n u m b e r s o f “ b a d ” g a l l o n s o f o r a n g e j u i c e f o r e a c h b r a n d e v e r y w e e k . U s i n g t h e s e n u m b e r s o f b a d g a l l o n s , o u r m o d e l i m i t a t e s t h e n u m b e r s o f c u s t o m e r s w h o a b a n d o n e a c h b r a n d e a c h w e e k . N o w w e n e e d t o m o d e l t h e s w i t c h i n g b e h a v i o r o f t h o s e c u s t o m e r s . F o r e x a m p l e , w e h a v e m o d e l e d t h e d e p a r t u r e o f 1 8 c u s t o m e r s f r o m B r a n d A i n t h e fi r s t w e e k , a n d a n o t h e r 2 5 f r o m B r a n d A i n t h e s e c o n d w e e k , b u t w e h a v e n ’ t y e t m o d e l e d w h e r e t h o s e c u s t o m e r s w i l l g o ( B r a n d B o r B r a n d C ) t o g e t t h e i r o r a n g e j u i c e i n t h e f o l l o w i n g w e e k .


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We can use the binomial distribution again here. The number of people who switch from Brand A to Brand B in any given week will be a binomial random variable, with n equal to the total number of people who abandon Brand A in that week, and p equal to the proportion of the non-Brand A market held by Brand B in that week, or B/(B + C).

(Recall that the problem asks us to “Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands.”)


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We’ll set up the ns for these binomial random variables in columns K, L, and M, using MAX functions as before to make sure that they never go below 1.

In column N we calculate the proportion of non-A customers who buy B in the current week, once again using a MAX function to make sure this is never zero.


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The number of A customers who switch from A to Brand C is calculated in column P; it is simply the difference between K7 and O7.

We model the switching behavior of former B customers in columns Q, R, and S, and former C customers in columns T, U, and V.

Finally, the various numbers of switchers are taken into account for the start of the next week in columns B, C, and D.

All of the binomial assumptions (columns H, I, J, O, R, and U) get copied down through row 58, so we can model a 52-week year.


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Suppose a 1% increase in market share is worth $10,000 per week to company A.

Company A believes that for a cost of $1 million per year it can cut the percentage of unsatisfactory juice cartons in half.

Is this worthwhile? (Use the same values of PA, PB, and PC as in part a.)


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There are a number of ways to approach this kind of issue. One elegant way is to run two simulations simultaneously, in which the only difference is (in this case) the different value for PA.

We’ll run the same model as before, but add to it, in parallel, a second model in which PA = 0.05 instead of 0.10.

The old model is in a worksheet called Part (a) and the new model is in a worksheet called Part (b).


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W e ’ l l a d d a n e w f o r e c a s t c e l l i n t h e n e w m o d e l ( c e l l K 4 ) , w h i c h w i l l b e t h e d i ff e r e n c e b e t w e e n t h e t w o e n d i n g m a r k e t s s h a r e s f o r B r a n d A :

1 2 3 4 5

A B C D E F G H I J K I n p u t s

P r o b a b i l i t i e s u n s a t i s f a c t o r y E n d i n g M a r k e t S h a r e s A G a i n A B C A B C

0 . 0 5 0 . 1 5 0 . 2 0 0 . 7 9 0 . 1 8 0 . 0 4 0 . 2 5

= G 4 - ' P a r t ( a ) ' ! G 4

T h e s u m m a r y s t a t i s t i c s f o r t h i s n e w f o r e c a s t c e l l o u g h t t o g i v e u s a g o o d i d e a a s t o h o w B r a n d A ’ s s h a r e w o u l d c h a n g e i f t h e y c o u l d r e d u c e t h e i r p r o b a b i l i t y o f a b a d g a l l o n .


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A 95% confidence interval for the increase in market share is given by:

X ns96.1

1888.0 000,1000301.096.1

000186.0 Or (0.1886, 0.1890)

Let’s take the most pessimistic end of this confidence interval and assume that Brand A will get an 18.56% increase in market share for its $1 million investment. This translates to $188,600 per week, or about $9.8 million per year.


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Summary• Marketing Simulation Models• New Product Development Decision

– Uncertainty about competitor behavior– Uncertainty about customer behavior

• Market Shares– Modeling the dynamics of a 3-supplier

market– Customer loyalty– Benefits of quality improvement

• Pricing Strategy– American Airlines

session 10b

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