Question

APC industries has been experiencing significant growth and has been having difficulty meeting customer demands recently. They are considering three options to address this issue. They can move to a larger facility, add a second shift or use a subcontractor to assist in production. The annual payoff of each option depends on if the current market continues to expand, hold steady or declines. The expected payoff for each combination is show in the table below

Option Expand Steady Decline

Move to larger facility 250,000 125,000 -90,000

Add a second shift 175,000 80000 -45,000

Subcontract 90,000 15,000 -10,000

a) Which alternative should APC choose under the maximax criterion? (1 mark)

b) Which option should APC choose under the maximin criterion? (1 mark)

c) Which option should APC choose under the LaPlace criterion?

d) Which option should APC choose with the Hurwicz criterion with α = 0.5?

e) Using a minimax regret approach, what alternative should she choose?

f) After reading about economic predictions, APC has assigned the probability that the market will be expand , or be steady or be weak at 20%, 50% and 30 %. Using expected monetary values, what option should be chosen and what is that optimal expected value?

g) What is the most that the APC should be willing to pay for additional information? Use Expected Regret

h) Use the alternative method to verify EVPI (3 marks

Answer 1

Size of First Station	Expand	Steady	Decline	Max Payoff (for maximax)	Min Payoff (for maximin)	Laplace Criterion (for equally likely)	Hurwicz Criterion (0.5)	EMV (0.2-0.5-0.3)
Move to larger facility	250,000	125,000	-90,000	250,000	-90,000	95,000	80,000	85,500
Add a second shift	175,000	80,000	-45,000	175,000	-45,000	70,000	65,000	61,500
Subcontract	90,000	15,000	-10,000	90,000	-10,000	31,667	40,000	22,500

For a),b)c),d),f)

a) Maximax Criterion: (250,000)

i. Find out the maximum payoffs for every decision.

Select the decision which has the maximum of the maximum payoffs

b) Maximin Criterion: (-10,000)

Maximu of the minimum payoffs for every decision.

c) Laplace correction is used for equally likely of all the events: (95,000)

Maximum of  the average pay-off of all decisions for all the events

d) Hurwicz criterion with α= 0.5: (80,000)

Maxmimu of the (Sum of maximum payoff of a decision multiplied with α and minimum payoff of a decision multiplied with (1- α))

e) Minimax Regret Approach: (75,000)

Regret for every decision-event cell by subtracting the cell value from the maximum payoff for an event

Regret Table
Size of First Station	Expand	Steady	Decline	Minimax Regret Decision	Expected Regret (0.2-0.5-0.3)
Move to larger facility	0	0	80,000	80,000	24,000
Add a second shift	75,000	45,000	35,000	75,000	48,000
Subcontract	160,000	110,000	0	160,000	87,000

f) Expected Monetary Value: (85,500)

EMV of a decision is the sum of event-payoff multiplied by the corresponding probability for all the events for that decision

Size of First Station	Expand	Steady	Decline	Max Payoff (for maximax)	Min Payoff (for maximin)	Laplace Criterion (for equally likely)	Hurwicz Criterion (0.5)	EMV (0.2-0.5-0.3)
Move to larger facility	250,000	125,000	-90,000	250,000	-90,000	95,000	80,000	85,500
Add a second shift	175,000	80,000	-45,000	175,000	-45,000	70,000	65,000	61,500
Subcontract	90,000	15,000	-10,000	90,000	-10,000	31,667	40,000	22,500

g) EVPI = Expected Regret: (24,000)

Miniimum of the Expected Regret of a decision which is the sum of regret multiplied by the corresponding probability for all the events for that decision

Regret Table
Size of First Station	Expand	Steady	Decline	Minimax Regret Decision	Expected Regret (0.2-0.5-0.3)
Move to larger facility	0	0	80,000	80,000	24,000
Add a second shift	75,000	45,000	35,000	75,000	48,000
Subcontract	160,000	110,000	0	160,000	87,000

h) EVPI using alternate method = Expected Payoff during Certainty – EMV

Expected Payoff during Certainty = Sum of Maximum Pay-off for an event*Multiplied by Probablity of the event

= 250,000(0.2) + 125,000(0.5) – 10,000(0.3) = 50,000 + 62,500 – 3000 – 85,500

=24,000