Chapter 1 Formulations BW 1 q Integer Programming
Chapter 1. Formulations (BW) 1
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Applications q Numerous applications Ø Transportation (train scheduling) Ø Airline crew scheduling, plane scheduling Ø Production planning, distribution, SCM, logistics Ø Energy, Eletricity generation planning Ø Telecommunicaton network design, operation Ø Buses for the handicapped Ø Ground holding of aircraft Ø Cutting problems Ø …. Ø Too many to list. q Provides very strong modeling capabilities (much better than LP alone), but usually difficult to solve (The solution set is not convex) Paradigm change: linear nonlinear convex non-convex q Recent advances in theory and software makes IP a practical option. Integer Programming 2013 4
1. 1 Modeling Techniques q Integer Programming 2013 5
Binary choice q Integer Programming 2013 6
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Forcing constraints q Integer Programming 2013 10
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Relation between variables q Integer Programming 2013 12
Disjunctive constraints q Integer Programming 2013 13
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Restricted range of values q Integer Programming 2013 18
Arbitrary piecewise linear cost functions q Piecewise linear, not necessarily convex, cost function (separable piecewise linear convex cost function can be modeled as LP (min problem, but non-convex (or non-concave) function cannot be modeled as LP) Integer Programming 2013 19
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q Alternative formulation Integer Programming 2013 21
Set covering, set packing, set partitioning q Integer Programming 2013 22
Sequencing problem with setup times q Integer Programming 2013 23
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Uncapacitated lot sizing (ULS) (NW) q Integer Programming 2013 26
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