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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.

Mixed-Integer Linear Programming Linear vs. Nonlinear Integer Programs An IP model is an integer linear program (ILP) if its (single) objective function and all its constraints are linear Otherwise, it is an integer nonlinear program (INLP) Standard Mixed-Integer Linear Programming (MILP) Formulation: min x,y z =∆ cTx +dTy s.t. Ax+Ey ≤ = ≥

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