2011年ACCA考试《F5业绩管理》讲义（31）
3 Shadow prices and slack 3.1 IntroductionSlackwｗw.ExamＷ.CoM
§ Slack is the amount by which a resource is under-utilised. It will occur when the optimum point does not fall on the given resource line.
§ Slack is important because unused resources can be put to another use, e.g. hired out to another manufacturer.
Illustration 6 – Slack
In the Hebrus example the optimum point Q lies on both the cutting and assembly time lines; therefore both resources are fully utilised. (These are referred to as the ‘critical constraints’ in this example.)
This can be checked from the constraint inequalities.
The optimal solution was x = 4, y=4
Cutting time:
Available = 36, utilised = 6x + 3y = (6 × 4) + (3 × 4) = 36
Assembly time:
Available = 48, utilised = 4x + 8y = (4 × 4) + (8 × 4) = 48
Hence all available time in both departments is utilised.
If, however, the optimum had been at P (x = 0, y = 6) then, because P does not lie on the cutting time line, there would be slack cutting time.
Cutting time utilised = (6 × 0) + (3 ×6) = 18.
Slack = 36 – 18 = 18 hours.
Shadow (or dual) prices
§ The shadow price of a resource is an increase in value (usually extra contribution ) which would be created by having available one additional unit of a limiting resource at its original cost.
§ It therefore represents the maximum premium that the firm should be willing to pay for one extra unit of each constraint. This aspect is discussed in more detail below.
§ Non-critical constraints will have zero shadow prices as slack exists already.
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