Decision Theory

An operations manager's staff has compiled the information below for four manufacturing alternatives $($A$,$ B$,$ C$,$ and D$)$ that vary by production technology and the capacity of the machinery. All choices enable the same level of total production and have the same lifetime. The four states of nature represent four levels of consumer acceptance of the firm's products. Values in the table are the net present value of future profits in millions of dollars.

States of Nature

$1$

$2$

$3$

$4$

Alternative A

$50$

$55$

$60$

$70$

Alternative B

$30$

$50$

$80$

$130$

Alternative C

$70$

$80$

$70$

$65$

Alternative D

$100$

$10$

$150$

$220$

$($a$)$ Assuming a maximax strategy, which alternative would be chosen?

$($b$)$ If maximin were used, which would be chosen?

$($c$)$ If the states of nature were equally likely, which alternative should be chosen?

$($d$)$ Expected value indicates that there is a $0\mathrm{.}1$ probability of acceptance level $1,0\mathrm{.}2$ chance of acceptance

level $2,0\mathrm{.}4$ chance of acceptance level $3,$ and $0\mathrm{.}3$ chance of acceptance level $4.$

$($e$)$ Using minimax regret, which alternative should be chosen?