Integer programming algorithms minimize or maximize a function subject to equality, inequality, and integer constraints. Integer constraints restrict some or all of the variables in the optimization problem to take on only integer values. This enables accurate modeling of problems involving discrete quantities such as shares of a stock or yes-or-no decisions. When there are integer constraints on only some of the variables, the problem is called a mixed-integer program MIP. Example integer programming problems include portfolio optimization in finance, optimal dispatch of generating units unit commitment in energy production, design optimization in engineering, and scheduling and routing in transportation and supply chain applications. This is the most general form of integer programming and is called a mixed-integer nonlinear program MINLP.
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