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 / 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 )M
value collection of items subject to limitations on resources consumed Knapsack models are the simplest of all (pure) integer linear programs (ILPs) max. 2 I 1 I 2 I 3 I 4 Value Capacity Each element is either all in or all out of the selection: y j ∆= ˆ 1, if item j selected 0, otherwise Example: Selection of projects subject to limitations ...
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