Mixed-Integer Linear Programming - McMaster University

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Mixed-Integer Linear Programming (MILP): ModelFormulationBeno t UniversityDepartment of Chemical EngineeringChE 4G03: Optimization in Chemical EngineeringBeno t Chachuat ( McMaster University )MILP: Model Formulation4G031 / 26Mixed-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 / 26Mixed-Integer Linear ProgrammingClass Exercise:Give more examples ofinteger decisionsin the field ofChemical Engineering:1Fluid flow: 2Heat transfer: 3Mass transfer: 4Reactor design: Beno t Chachuat ( McMaster University )MILP: Model Formulation4G033 / 26Mixed-Integer Linear ProgrammingLinear vs.

Benoˆıt Chachuat (McMaster University) MILP: Model Formulation 4G03 9 / 26 Formulating Models for Semi-Continuous Variables Class Exercise: Consider the following blending problem, where the ingredient x 3 is a semi-continuous variable: min x1,x2,x3 18x 1 +3x 2 +9x 3 s.t. 2x 1 +x 2 +7x 3 ≤150 0 ≤x 1 ≤60 0 ≤x 2 ≤30 x 3 = 0∨10 ≤x ...

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