of 8 1. ElCo specializes in manufacturing electronic components. The consultant

Question

of 8 1. ElCo specializes in manufacturing electronic components. The consultant to ElCo has developed the following table concerning a proposed facility. The probabilities for the market levels have been determined to be 30% for strong market, 50% for fair market, and 20% for poor market. Profit (S) Strong Market Fair Market Poor Market Large facility 550 110 -310 130 Medium facility .100 Small facility 100 -30 No facility a) Which facility should be selected based on the optimistic criterion? b) Which facility should be selected based on the pessimistic criterion? c) Which facility should be selected based on the minimax regret criterion? d) Which facility should be selected based on EMV method?? e) What is the expected value of perfect information (EVP) in this situation? f) How much is a perfect forecast of the demand worth? g) Which facility should be selected by using Min EOL method?

Explanation / Answer

This is a Decision Theory example. There are 4 actions out of which one has to be taken as a decision:

1st Action: Create a Large Facility for Manufaturing

2nd Action: Create a Medium Facility for Manufaturing

3rd Action: Create a Small Facility for Manufaturing

4th Action: Create No Facility for Manufaturing

On the above 4 actions, manufacturer has the control. But, on the below given 4 states of nature, he does not have any control

1st state of nature: Strong Market with probability of happening as 30%

2nd state of nature:Fair Market with probability of happening as 50%

3rd state of nature:Poor Market with probability of happening as 20%

Now, one has to pick one of the 4 actions based on the strategy mentioned in (a) - (d)

Note: I will answer only first 4 parts (a) to (d) as per Chegg Policy.

(a) Optimistic Criterion:

For this, one has to have optimism of best payoff from entire situation. Then,

first we look at first action i.e. creating Large Facility. Now,

the best payoff from this action is: maximum values in the row for Large Facility

= max(550, 110, -310) = 50

Similarly, for Medium facility creation, best payoff = max(300,130,-100) = 300

Similarly, for Small facility creation, best payoff = max(200,100,-30) = 200

Similarly, for No facility creation, best payoff = max(0,0,0) = 0

Here, now, we take the Facility with largest payoff among these 4 values , which is facility with payoff

= max(550,300,200,0) = 550

This happens for Large Facility. Hence, this is the answer for (a).

(b) Pessimistic Criterion:

Here we go the opposite of Optimistic way.

So, minimum possible payoff for Large Facility = minimum of row values for Large Facility

= min(550,110,-310) = -310

and minimum possible payoff for Medium Facility = min(300,130,-100) = -100

and minimum possible payoff for Small Facility = min(200,100,-30) = -30

and minimum possible payoff for No Facility = min(0,0,0) = 0

Now, max of above 4 values = max(-310,-100,-30,0) = 0

So, answer to (b) is No Facility to be created.

(c) For minimax regret criterion, first we create a new opportunistic loss (regret) table as below:

Each element in the opportunistic loss table is found taking each state of nature, one at a time, and subtracting each payoff from the largest payoff for that state of nature.

which comes as:

The above table gives the largest possible loss.

For minimax regret criterion , we first find the largest loss on creation of each facility and then minimize the loss i.e. take the smallest of these.

Now, here largest loss table would be:

Now, smallest loss here is: min(310,250,350,550) = 250 which is for Medum Facility

(d) Under EMV Method, we need to find Expected Monetary Value for each Facility.

Now, EMV for Large Facility

= Profit in Strong Market * Probability of Market being Strong

+ Profit in Fair Market * Probability of Market being Fair

+ Profit in Poor Market * Probability of Market being Poor

= 550*30% + 110*50% + (-310)*20%

= 158

Similarly, EVM for Medium Facility

= 300*30% + 130*50% + (-100)*20%

= 135

and EVM for Small Facility

= 200*30% + 100*50% + (-30)*20%

= 104

and EVM for No Facility

= 0*30% + 0*50% + 0*20%

= 0

Now, max(158,135,104,0) = 158, which is for Large Facility

Hence, answer here is Large Facility.

Opportunity Loss(Regret Table) Strong Market Fair Market No Market Large Facility max(550,300,200,0) - 550 max(110,130,100,0) - 110 max(-310,-10,100,0) - (-310) Medium Facility max(550,300,200,0) - 300 max(110,130,100,0) - 130 max(-310,-10,100,0) -(-100) Small Facility max(550,300,200,0) - 200 max(110,130,100,0) - 100 max(-310,-10,100,0) -(-30) No Facility max(550,300,200,0) - 0 max(110,130,100,0) - 0 max(-310,-10,100,0) -0

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