# OPSY5315_ModB-Intro.pptx - Introduction to Optimization and...

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Introduction to Optimization and Linear ProgrammingWilliam P. Nanry, Ph.D.Research and Analytics Consultant with DellAdjunct Professor, TAMUCC
Dell - Internal Use - Confidential2IntroductionHow can we best use limited resources?Oil in the earthLand for dumps and hazardous wasteTime for all the activities we must do during the dayWorkPTErrands…MoneyWorkers
Dell - Internal Use - Confidential3Mathematical Programming...Field of Management Science that finds the …Optimal (most efficient) use of limited resources to achieve objectivesa.k.a.Optimization
Dell - Internal Use - Confidential4ApplicationsDetermining Product MixManufacturingRouting and LogisticsFinancial PlanningAirlinesCrew SchedulingAirline RoutingCost of a ticketHow many passengers to overbook?
Dell - Internal Use - Confidential5CharacteristicsDecisions – X1, X2, … , XnObjectiveConstraintslimited resourcesregulationslimited space (haul capacity)
Dell - Internal Use - Confidential6LP Model Formulation Steps :1. Understand the problem2.Identify the decision variables3.State objective function as linear combination of decision variables4. State constraints as linear combinations of decision variables5. Identify upper &/or lower bounds on decision variables
Dell - Internal Use - Confidential7General Form of Mathematical ProgramThe goal of optimization is to find the values of the decision variables that maximize (or minimize) the objective function without violating any of the constraints.mnmknknnbXXXfbXXXfbXXXfXXXf,...,,:,...,,:,...,,:Subject to,...,,Max :Objective21211211210
Dell - Internal Use - Confidential8General Form of Linear ProgramNote: If all the functions in an optimization are linear, the problem is a Linear Programming (LP) problem.mnmnmmknknkknnnnbXaXaXabXaXaXabXaXaXaXcXcXc...:...:...:Subject to...minMax :Objective22112211112121112211
Dell - Internal Use - Confidential9There are 200 pumps, 1566 hours of labor, and 2880 feet of tubing available.An Example LP ProblemBlue Ridge Hot TubsHot Tub Model Aqua-Spa Hydro-LuxPumps 11Labor 9 hours6 hoursTubing 12 feet16 feetUnit Profit \$350\$300
Dell - Internal Use - Confidential10There are 200 pumps, 1566 hours of labor, and 2880 feet of tubing available.