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Linear programming

Integer linear programming

Non-linear programming


Linear programming

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Objective function

Reduced costs ...... Required increase in coefficient to make variables positive.

Objective coefficient ranges (Lower limit to Higher limit)

Dual prices .......... Marginal increase of objective value with one unit increase in right hand side constraint

Constraints

Right hand side ranges (Lower limit to Higher limits)

Slacks/surplus........Unused resources

Degeneracy

Applications


Integer programming

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Binary / general integer

Applications

Generator Selection, "0 or production constraint < 0 or max capacity"
A1 < 2100 * A_Start
B1 < 1800 * B_Start
Mailing list purchase, "0 or purchase units < 0 or required purchase"
List1 > 5 * PurcP
List1 <2000 * PurcP
List2 < 5 * PurcP
List2 > 40 * PurcP

Min 20 List1 + 25 List2 + 15 PurcP + 50 PurcP

Mutually exclusive: Project1@+ Project2 < 1

Contingency: Project3 < Project 2

Interactive: Project6 < Project5

Project6 < Project1

Project6 is virtual project, which works as interactive effect

20Project1 + 30 Project2 + 15 Project3 + 10 Project4 + 5Project5 - 2Project6 < 65


Non-linear programming

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Non-linear solution is not necessarily optiomal.


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