Page 418 - PM Integrated Workbook 2018-19

Chapter 15

Example 6

Following up from the pay-off table example, Geoffrey’s Ramsbottom’s table
looks as follows:

Daily supply
40 50 60 70
Probability
salads salads salads salads
40 salads 0.10 $80 $0 $(80) $(160)
Daily
demand 50 salads 0.20 $80 $100 $20 $(60)
60 salads 0.40 $80 $100 $120 $40

70 salads 0.30 $80 $100 $120 $140

How many salads should we supply, using the minimax regret rule?

If the minimax regret rule is applied to decide how many salads should be
made each day, we need to calculate the 'regrets'. This means we need to find
the biggest pay-off for each demand row, then subtract all other numbers in
this row from the largest number.

For example, if the demand is 40 salads, we will make a maximum profit of
$80 if they all sell. If we had decided to supply 50 salads, we would achieve a
nil profit. The difference, or 'regret' between that nil profit and the maximum of
$80 achievable for that row is $80. Regrets can be tabulated as follows:

Daily supply
40 50 60 70
salads salads salads salads
40 salads $80 $0 $(80) $(160)

Daily 50 salads $80 $100 $20 $(60)
demand 60 salads $80 $100 $120 $40

70 salads $80 $100 $120 $140

Maximum
regret $60 $80 $160 $240

A manager employing the minimax regret criterion would want to minimise that
maximum regret, and therefore supply 40 salads only.

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