Question

The table provides the expected profit in thousands of dollars for five marketing strategies and five potential levels of sales:

Level of Sales Strategy ия. 10 L2 20 L3 L5 R0 35 20 25 20 30 M2 M3 20 2525 30 50 생13 10 30 25 15 25 30 20

a) Which Marketing strategy should be selected using the Laplace criterion?

b) Which Marketing strategy should be selected using the maximin rule?

c) Which Marketing strategy should be chosen using the maximax rule?

d) Which Marketing strategy should be selected using the Hurwicz rule with alpha = 0.3?

Please show all calculations.

Answer 1

a)

The Laplace’s insufficient reason criterion postulates that if no information is available about the probabilities of the various outcomes, it is reasonable to assume that they are likely equally. Equal probabilities are assigned to the result of each strategy, from which the highest is chosen.

$E(M1) = \frac{10+20+30+40+50}{5} = 30$

$E(M2) = \frac{20+25+25+30+35}{5} = 27$

$E(M3) = \frac{50+40+5+15+20}{5} = 26$

$E(M4) = \frac{40+35+30+25+25}{5} = 31$

$E(M5) = \frac{10+20+25+30+20}{5} = 21$

Hence M4 would be selected using the Laplace criterion

b)

Wald’s maximin model, also known as pessimist model: select the maximum of the minimum, in other words the lesser of evils.

min (M1) = 10

min (M2) = 20

min (M3) = 5

min (M4) = 25

min (M5) = 10

M4 would be selected by maximin rule.

c)

Optimist model (maximax): select the maximum of the maximum, the best amongst the best.

max (M1) = 50

max (M2) = 35

max (M3) = 50

max (M4) = 40

max (M5) = 30

Both M1 and M4 would be selected by maximax rule.

d)

Hurwicz criterion or optimist-pessimist index: an optimum constant (α) is defined and assigned to the worst result, and another is assigned to the best (1-α). The average weighted value is then calculated and the highest value is chosen.

Given α = 0.3,

For M1: AWV= 0.3*10 + 0.7*50 = 38

For M2: AWV= 0.3*20 + 0.7*35 = 30.5

For M3: AWV= 0.3*5 + 0.7*50 = 36.5

For M4: AWV= 0.3*25 + 0.7*40 = 35.5

For M5: AWV= 0.3*10 + 0.7*25 = 20.5

Hence M1 is choosen.