Question

A decision maker faced with four decision alternatives and four states of nature develops the following profit payoff table. The decision maker obtains information that enables the following probabilities assessments: P(s1) = 0.5, P(s2) = 0.2,P(s3) = 0.2, and P(s4) = 0.1. (a) Determine the optimal decision using (i) Expected monetary value approach (EMV) (ii) Expected Opportunity loss approach (EOL) (iii) Optimistic (Maximax) approach (iv) Pessimistic (Maxmin) approach (v) Minimax Regret approach

Answer 1

i) $s1\ benefits*0.5+s1\ loss*0.5$

$s2\ benefits*0.2+s2\ loss*0.8$

$s3\ benefits*0.2+s3\ loss*0.8$

$s4\ benefits*0.2+s4\ loss*0.8$

the option with the highest result is the most optimal

ii) $s1\ opportunity\ cost\ of\ realization*0.5+s1\ opportunity\ cost\ of\ non-fulfillment*0.5$

$s2\ opportunity\ cost\ of\ realization*0.2+s2\ opportunity\ cost\ of\ non-fulfillment*0.8$ $s3\ opportunity\ cost\ of\ realization*0.2+s3\ opportunity\ cost\ of\ non-fulfillment*0.8$

$s4\ opportunity\ cost\ of\ realization*0.1+s4\ opportunity\ cost\ of\ non-fulfillment*0.9$

the option with the lowest result is the most optimal

iii) The option that promises the greatest benefit regardless of the risks is the most optimal.

iv) The option promising the least losses regardless of the risks is the most optimal.

v) The variant with the greatest difference between the best and the worst result is the most optimal.