ECON 3300 LEC

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ECON 3300 LEC 4

• 09/12/06

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Sensitivity Analysis

• LP model snapshot of a real situation in which
  model parameters assume static values.
• Study of effect of changes in model parameters is
  important Sensitivity analysis
• Changes in objective function coefficients
• Changes in right hand side of the constraints

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Sensitivity Analysis

• Consider General objective function
• max or min zc1x1c2x2
• -Changes in c change in slope of z
• -Changes in slope change in optimum solution
  (different corner point)
• Range of variation for both c1 and c2 Current
  optimum unchanged

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Sensitivity Analysis

• Sensitivity Analysis Determining range of
  optimality for the ratio c2/c1 or c1/c2.
• Consider Reddy Mikks Model optimum at C.
• Lets change objective function to zc1x1c2x2
• Solution at C optimal as long as slope of z
  lies between the slopes of the two intersecting
  lines at C.
• 6x14x224
• x12x26

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Sensitivity Analysis

• Algebraic Representation

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Sensitivity Analysis

• If z c1x1c2x2 coincide with x12x26
  alternative optimal anywhere on line segment CD
• Similarly it holds true for 6x14x224

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Sensitivity Analysis

• Optimal Range Determination
• One of the coefficients holds constant. For
  example if c24 then optimal range for c1

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Sensitivity Analysis
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Sensitivity Analysis Unit worth of Resource

• Sensitivity of the optimum solution to changes in
  availability of resource
• Unit worth of Resource Measure that quantifies
  the rate of change in optimum value in the
  objective function as a result of changes in
  availability of resource

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Sensitivity Analysis Unit worth of Resource

• Reddy Mikks Problem
• Lets consider constraint for Raw material M1
• Current optimum at intersection of lines
  associated with M1 and M2 raw materials
• Change in availability of M1 optimum point C
  slides along DG
• Change in M1 outside the range of DG point C
  infeasible

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Sensitivity Analysis Unit worth of Resource

• D(2,2) and G(6,0) delineate feasibility range
  for M1
• M1 at D 6x14x2624220 tons
• M1 at G 664036 tons
• M1 at C 24 tons (current optimum)
• Range of feasibility 20ltM1lt36
• Let M124D1

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Sensitivity Analysis Unit worth of Resource

• Therefore
• 20lt24D1lt36
• -4ltD1lt12
• where
• D1 Raw material change allowable above or
• below the current level of 24 tons
• As M1 changes between 20 and 36 value of z
  changes at a constant rate because DG is a linear
  segment.

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Sensitivity Analysis Unit worth of Resource

• Let y1 worth per unit of raw material M1

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Sensitivity Analysis Unit worth of Resource

• Raw material M2
• Range of feasibility is delineated by endpoints B
  (4,0) and H(8/3,2)
• H is defined as the intersection of lines ED and
  BC
• M2 at B x12x24204 tons
• M2 at H 8/32220/3 tons
• Range of feasibility 4ltM2lt20/3

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Sensitivity Analysis Unit worth of Resource