Question

A machine shop owner is attempting to decide whether to purchase a new drill press, a lathe, or a grinder. The profit from each purchase will be determined by whether the company succeeds in getting a government military full contract, partial contract or no contract. The profit from each purchase associated with each contract outcome is shown in the following payoff table:

Purchase         Full Contract      Partial Contract     No Contract

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Drill press        $26,000    $34,000              $10,000

Lathe                 34,000                   24,000                18,000

Grinder               54,000                   22,000                20,000

(a) What is the best decision using the maximax criterion? What is the payoff for it?

(b) What is the best decision using the maximin criterion? What is the payoff for it?

(c) Determine the average payoff value for each decision. What is the best decision using the equal likelihood criterion? What is the average payoff for it?

(d) Determine the regret table for this problem. What is the best decision using the minimax regret criterion? What is the regret for it?

(e) What is the best decision using the Hurwicz’s criterion if α = 0.8? What is the payoff for it?

Answer 1

a)

Maximax	States of Nature
Size of First Station	Full Contract	Partial Contract	No Contract	Maximum
Drill Press	26000	34000	10000	34000
Lathe	34000	24000	18000	34000
Grinder	54000	22000	20000	54000
Appropriate Decision will be Grinder
Payoff = 54000

b)

Maximin	States of Nature
Size of First Station	Full Contract	Partial Contract	No Contract	Minimum
Drill Press	26000	34000	10000	10000
Lathe	34000	24000	18000	18000
Grinder	54000	22000	20000	20000
Appropriate Decision will be Grinder
Payoff = 20000

c)

Equal Likely Hood	States of Nature
Size of First Station	Full Contract	Partial Contract	No Contract	Equla Likelyhood
Drill Press	26000	34000	10000	23333
Lathe	34000	24000	18000	25333
Grinder	54000	22000	20000	32000
Equal Likely Hood	1/3	1/3	1/3
Appropriate Decision will be Grinder
Payoff = 32000

d)

Minimax Regret	States of Nature
Size of First Station	Full Contract	Partial Contract	No Contract
Drill Press	26000	34000	10000
Lathe	34000	24000	18000
Grinder	54000	22000	20000
Regret Table	States of Nature
Size of First Station	Full Contract	Partial Contract	No Contract	Maximum
Drill Press	28000	0	10000	28000
Lathe	20000	10000	2000	20000
Grinder	0	12000	0	12000
Appropriate Decision will be Grinder
Regret = 12000

e)

Hurwicz	States of Nature
Size of First Station	Full Contract	Partial Contract	No Contract	H
Drill Press	26000	34000	10000	29200
Lathe	34000	24000	18000	30800
Grinder	54000	22000	20000	47200
Appropriate Decision will be Grinder
Payoff = 47200