Question

Build-Rite construction has received favorable publicity from guest appearances on a public TV home improvement program. Public TV programming decisions seem to be unpredictable, so Build –Rite cannot estimate the probability of continued benefits from it relationship with the show. Demand for home improvements next year may be either low or high. But Build-Rite must decide now whether to hire more employees, do nothing, or develop subcontracts with other home improvement contractors. Build-Rite has developed the following payoff table.
Payoffs Demand For Home Improvements
Alternative Low Moderate High
Hire ($250,000) $100,000 $625,000
Subcontract $100,000 $150,000 $415,000
Do nothing $50,000 $80,000 $300,000
Required:
1. What is the decision based on each of the following criteria. Show work in making the decision for each criterion:
a) Maximax
b) Maximin
c) Criterion of realism with coefficient of realism = 0.7
d) Equally likely
e) Minimax regret

Answer 1

Answer:

Answer is given below.

Explanation:

                 demand     Low        Medium         High

Alternative

Hire                            $250000 $100000  $625000

Subcontract              $100000 $150000    $415000

Do nothing                $50000   $80000     $300000

a)Optmistic or Maximax criterion

find the maximum from each course of action and choose

the maximum among maximums

demand         Low         Medium           High         maximum

Alternative

Hire                    $250000 $100000 $625000 $625000

Subcontract          $100000 $150000 $415000 $415000

Do nothing                    $50000 $80000 $300000 $300000

Maximum(maximums) =Max($625000. $415000, $300000)

= $625000

hence, Hire is the decision corresponding to Maximax criterion.

a)Pessimistic or Maximin criterion

find the minimum from each course of action and choose

the maximum among minimums

demand Low Medium High minimum

Alternative

Hire $250000 $100000 $625000 $100000

Subcontract $100000 $150000 $415000 $100000

Do nothing $50000 $80000 $300000 $50000

Maximum(minimum s) Max ($100000.$1 00000.S50000)

= $100000

hence. Hire or subcontract is the decision corresponding to Maximin

Criterion of realism with coefficient of realism,a  0.7

(maximum in (minimum in ‘

findHvalue.  I+(1—a)I I foreach

course of action) i,cousrse of action)

course of action and choose the action which maximises the H value

therefore,

H(Hire)=0.7(625000)+0.3(100000)= $467500

H (Sub contract) 0.7(415000) + 0.3(100000) = $320500

H (Do nothing) = 0.7(300000) + 0.3(50000) «$225000

The course of action with maximum H is Hire

hence, the decision is Hire

d)Equally likely

here we assume that all 3 states of nature e equally likely with  probability (1/3)  we find the expected value for each course of action and choose the

course of action with maximum expected value.

                            1/3                   1/3            1/3

demand             Low              Medium      High

Hire                   $250000 $100000 $625000

Subcontract $100000 $150000 $415000

Do nothing $50000 $80000 $300000

E(Hire) = 1/3 * (250000) + 1/3 *(100000) + 1/3 *(625000)

= $325000

E(Sub contract) =  1/3 *(100000) +  1/3 *(150000)+ 1/3 *(4 15000)

= $22166667

E(Do nothing)=  1/3 * (50000)+ 1/3 * (80000) + 1/3 * (300000)

$143333.333

the course of action with maximum expected value is Hire

hence, the decision is to Hire

e)Minimax regret approach

Here we convert the given matrix into regret matnx by choosing the maximum

pay off from each state of nature and subtracting the maximum from all

elements of that corresponding column.

find the maximum regret for each course of action and choose the minimum

among it.

Regret matrix

demand            Low Medium High maximum

Hire                      0  $50000   0      $50000

Subcontract         $150000 0 $210000 $210000

Do nothing      $200000 $70000 $325000 $325000

the minim among maximum regret values is $50000 and the corresponding

course of action is Hire

Hence, the decision is to Hire.