Linear Program

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Linear Program
MAX CBXB CNBXNB s.t. BXB
ANBXNB b XB ,
XNB 0
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Important LP Equations
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Important LP Derivatives
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Duality
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Duality
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Unbounded Solution
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Infeasible Solution
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Multiple Optima
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Degeneracy
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Complementary Slackness

• derived from duality

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Reduced Cost

• Negative derivative of objective function with
  respect to a variable
• At optimality
• Zero for all basic variables
• Non-negative for all non-basic variables (max)
• Non-positive for all non-basic variables (max)

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Multi-input, Multi-output
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Mixing / Blending
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Spatial Equilibrium (GAMS Ex.)
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Sequencing
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Sequencing
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Storage
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Lexicographic preferences
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Weighted Preferences
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Well behaved, Separable Function
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Well behaved, Separable Function
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Well behaved, Separable Function
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Disequilibrium Known Life
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Disequilibrium Unknown Life
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Equilibrium - Unknown Life
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Fixed Costs
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Fixed Capacity
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Minimum Habitat Size
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Minimum Habitat Size
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Warehouse
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Mutual exclusive products
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Either-Or-Active constraints
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Distinct Variable Values
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Badly behaved non-linear functions
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Badly behaved non-linear functions
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Non-linear Programming

• Specification often straightforward
• Solving more difficult
• scaling (manual vs. computer)
• lower bounds to avoid division by zero and other
  illegal operations
• local versus global extremes