# Optimization

May 19th, 2015
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• Math Optimization is an abstraction of the problem of selecting the best choice from available alternatives The typical form of an optimization formulation is minimize subject to

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Optimization1. Introduction to OptimizationOptimization Math Optimization is an abstraction of the problem ofselecting the best choice from available alternativesThe typical form of an optimization formulation isminimizesubject tof0(x1,x2,,xn)fi(x1,x2,,xn) bi,i = 1, , n,(1)where, x = (x1,x2,,xn) are the decision variables,f0(x) is the objective function,fi(x) bi are the constraints, andfi(x) are constraint functions.1/7/2014ESI 5408 Applied Optimization, Spring 20142Optimization Different classes of optimization problems are characterized by specific forms of the objective and constraint functions If f0, f1,, fn are linear functions in x, i.e.,fi(ax+by) = afi(x) + bfi(y), for all x, y in Rn, & a,b in Rthen (1) is a Linear Program Otherwise, it is a Nonlinear Program The task in any Math Program is to find the optimal value of decision variables (x)1/7/2014ESI 5408 Applied Optimization, Spring 20143Where is Optimization Used? Several domains utilize optimization models and algorithms for determining the best alternative, such as Airlines: crew scheduling, flight planning, pricing and revenue management, Healthcare: radiation therapy, surgical scheduling, patient scheduling, bed utilization, staff planning, Manufacturing: scheduling, production planning, inventory management, Supply Chain Management: supply chain design, facility location, routing, Analyt

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