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Decision Analysis 1.1 (Costs) - Optimistic, Conservative, Minimax Regret - YouTube
Channel: Joshua Emmanuel
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Welcome!
In this brief video, we will be discussing
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decision making without probabilities where
cost is involved.
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We will cover the Optimistic or Maximax approach,
the Conservative or Maximin approach,
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and also the Minimax Regret approach.
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We will be using this payoff table where Payoffs are costs.
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The approach we will use in this tutorial
is applicable to all cases where smaller payoff
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values are preferred over larger ones.
The objective could be to minimize cost, minimize
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customer waiting time, minimize risk, minimize
distance, and so on.
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The Optimistic or Maximax Approach
Using this approach we choose the alternative
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with the best of the best payoffs. Note that
the payoffs are costs, therefore the smaller
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the better. For d1 , the best payoff is -5
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For d2 , the best is -9
and for d3, the best is -5.
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The overall best is -9.
Therefore the optimistic decision is to choose d2.
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The Conservative or Maximin Approach
Using this approach, we choose the alternative
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that has best of the worst payoffs.
We first choose the worst payoff in each alternative,
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and then choose the best of them.
Since these are costs, for d1, the worst is
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14
for d2 , the worst is 15
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and for d3, the worst is 18.
The best of these worst payoffs is 14
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Therefore the conservative decision is to choose d1.
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The Minimax Regret Approach
Using this approach, we choose the alternative
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with the minimum of all the maximum regrets
across all alternatives.
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Regret is the difference between the best
payoff and the actual payoff received in a
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particular state of nature.
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Therefore for s1 the best payoff is 5 since
we are dealing with costs.
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That is, if you knew s1 was going to occur,
you would have chosen d3.
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So if s1 occurs and you already chose d1,
your regret will be 12 – 5 = 7.
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That is, if you could pay $5 for an item and
you paid $12 instead, your regret will be $7
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Note that if these are profits, we will subtract
all payoffs from the best, which in that case
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would be the largest value. But because they
are costs, we will subtract the smallest from
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other payoffs. Whatever you do, make sure
your regret values are not negative.
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So going back to s1
If instead you chose d2, you’re paying $15
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when you could pay $5 and your regret will
be 15 – 5 which equals 10.
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And if you chose d3, your regret is 5 – 5
which equals 0. That is, there is no regret.
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For s2 your best payoff is -5.
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So if you chose d1, your regret will be -5
minus -5 which equals 0 → no regret.
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Note that the double negative becomes positive.
And you if you chose d2, your regret is 11
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minus -5 which equals 16.
If you chose d3, your regret will be 18 minus
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-5 which equals 23.
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If s3 occurs, the best payoff is -9.
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So if you chose d1, your regret will be 14
minus -9 which gives 23.
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And you if you chose d2, your regret is -9
minus -9 which equals 0.
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If you chose d3, your regret will be -5 minus
-9 which equals 4
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Here is the Regret Table.
Note that after regrets are calculated, the
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approach for determining the best alternative
is exactly the same for profit and cost problems.
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Since the decision is to be made based on
minimax regret, we first determine the maximum
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regret for each alternative, and then choose
the minimum.
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For d1, the maximum regret is 23,
for d2, the maximum is 16,
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for d3, the maximum regret is 23.
The minimum of these maximum regrets is 16.
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Therefore the minimax regret decision is to
choose d2.
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Please leave your comments or questions below.
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Thanks for watching.
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