A machine shop owner is attempting to decide whether to purchase a new drill pre
ID: 3841139 • Letter: A
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
__________________________________________________
Drill press $60,000 $40,000 $16,000
Lathe 40,000 30,000 24,000
Grinder 32,000 28,000 26,000
**Please do not use computer software, Please write out everything**
(c) What is the best decision using the minimax regret criterion? What is the regret for it?
(d) What is the best decision using the Hurwicz’s criterion if = 0.6? What is the payoff for it?
Explanation / Answer
(c) The best decision using the minimax regret criterion:
Purchase
Full Contract
Partial Contract
No Contract
Drill press
$60,000
$40,000
$16,000
Lathe
$40,000
$30,000
$24,000
Grinder
$32,000
$28,000
$26,000
The minimization of regret is highest for one decision has been made instead of another. In a situation that a decision has been made that causes the expected payoff of an event to be less than expected, this criterion encourages the avoidance of regret. It also called opportunity loss.
The minimax regret strategy minimises the maximum regret and it is useful for a risk-neutral decision maker. 'Regret' in this context is defined as the opportunity loss through the company succeeds in getting a government military full contract, partial contract or no contract.
We need to find the biggest pay-off for each profit row then subtract all other numbers in this row from the largest number.
Purchase
Full Contract
Partial Contract
No Contract
Maximum Regret
Drill press
$0
$0
$10,000
$10,000
Lathe
$20,000
$10,000
$2,000
$20,000
Grinder
$28,000
$12,000
$0
$28,000
Maximum regret select the maximum from the table and the regret is the minimum of the maximum table.
The best decision using the minimax regret criterion is the drill press and the regret is $10,000.
(d) The best decision using the Hurwicz’s criterion if = 0.6
The Hurwicz-criterion represents a compromise between the optimistic and the pessimistic approach to decision making under uncertainty. The measure of optimism and pessimism is expressed by an optimism - pessimism index, <0, 1>. The more this index is near to 1, the more the decision maker is optimist. By means of the index , a weighted average of the best payoff (its weight = ) and the worst payoff (its weight = 1-) is computed for each alternative and the alternative with the largest weighted average should be chosen (see formula for Hurwicz criterion).
If =1, the above rule is the maximax criterion, whereas if =0, it is the maximin rule.
If we choose = 0.6 at determining the best size of the order in table, the weighted average (WA) of the largest and the smallest profit for each size of the order has the following values.
H (Ai ) = (row maximum) + ( 1 - ) (row minimum) - for positive-flow payoffs (profits, revenues)
H (Ai ) = (row minimum) + ( 1 - ) (row maximum) - for negative-flow payoffs (costs, losses)
Purchase
Full Contract
Partial Contract
No Contract
Weighted Average
Drill press
$60,000
$40,000
$16,000
$42,400
Lathe
$40,000
$30,000
$24,000
$33,600
Grinder
$32,000
$28,000
$26,000
$29,600
Hurwicz decision rule is followed:
1. Select a coefficient of optimism value .
2. For every action alternative compute its Hurwicz weighted average H.
3. Choose the action alternative with the best H as the chosen decision ("Best" means Max {H} for positive-flow payoffs, and Min {H} for negative-flow payoffs).
Hence the best decision using the Hurwicz’s criterion drill press and the regret is $42,400.
Purchase
Full Contract
Partial Contract
No Contract
Drill press
$60,000
$40,000
$16,000
Lathe
$40,000
$30,000
$24,000
Grinder
$32,000
$28,000
$26,000
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