Transcription of Mixed-Integer Linear Programming - McMaster University
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Mixed-Integer Linear Programming - McMaster University
Mixed-Integer Linear Programming (MILP): ModelFormulationBeno t UniversityDepartment of Chemical EngineeringChE 4G03: Optimization in Chemical EngineeringBeno t Chachuat ( McMaster University )MILP: model Formulation4G031 / 26 Mixed-Integer Linear ProgrammingInteger Programs (IP)An optimization model is anInteger Programifany ofits decisionvariables is discreteIfallvariables are discrete, the model is apure integer programOtherwise, the model is amixed-integer programInteger variables appear inmanyproblems:Trays in a distillation columnNumber of employees (1000 s)Number of parallel chemical reactorsWhether or not to operate boiler#2on MondayScheduling people and equipment totasks over timeCan be solved continuous, thenrounded to nearest integerNot appropriate to solve con-tinuous and round afterBeno t Chachuat ( McMaster University )MILP: model Formulation4G032 / 26 Mixed-Integer Linear ProgrammingClass Exercise:Give more examples ofinteger decisionsin the field ofChemical Engineering:1 Fluid flow: 2 Heat transfer: 3 Mass transfer: 4 Reactor design: Beno t Chachuat ( McMaster University )MILP: model Formulation4G033 / 26 Mixed-Integer Linear ProgrammingLinear vs.
Benoˆıt Chachuat (McMaster University) MILP: Model Formulation 4G03 14 / 26 Assignment Models (cont’d) Generalized assignment constraints encompass cases where allocation of i to j requires fixed space s i,j within j capacity b j: Linear assignment models minimize/maximize a linear objective function of the form: X i∈I X j∈J c i,jy i,j ...
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