Question

A company financing itself or merging with an engineering firm
profit of the R&D department in the next 10 years
predicted their values ​​as follows:
   Very successful   Succesful   Unsuccessful
Develop it yourself   250   150   -100
Unıte 350   100   -100

The subjective (subjective) possibilities for the success of R&D are 0.4, 0.4, 0.2, respectively.
It has been identified.
a) Which decision should be taken according to the expected value criterion?
b) Which decisions according to Maksimaks, maksimin, Laplace, Hurwicz (α = 0.50) decision criteria
should be taken?

Answer 1

a).

Expected value is calculated as weighted average with given probabilities.

Expected value of "Develop it yourself"= (0.4*250)+(0.4*150)+(0.2*-100)= 100+60-20= 140

Expected value of "Unite"= (0.4*350)+(0.4*100)+(0.2*-100)

= 140+40-20= 160

So, According to expected value criterion, "Unite" decision should be taken.

b).

Maksimaxs:

This is an optimist model, where best of the best is chosen.

As, 350>250, Unite should be chosen.

Maksimin:

This is an pessimist model, where best of the worst is chosen.

As worst is same in both scenarios which is -100, this model is impartial to both.

Laplace:

Laplace models atribute equal probabilities and then takes the decision based on highest expected value.

For "Develop it yourself", we get= (1/3)*250+(1/3)*150+(1/3)*-100= 100

For "Unite", we get= (1/3)*350+(1/3)*100+(1/3)*-100= 116.66

So, "Unite" should be chosen.

Hurwicz:

For Hurwicz, alpha is assigned to best result, (1-alpha) is assigned to worst result. Then weighted average is taken and decision is taken on best value.

For "Develop it yourself", we get (0.5)*250+(1-0.5)*-100

= 75

For "Unite", we get (0.5*350)+(1-0.5)*-100= 125

So, Unite should be chosen.