Chap02 - Spreadsheet Modeling Decision Analysis A Practical...

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Spreadsheet Modeling & Decision AnalysisA Practical Introduction to Management Science 6th editionCliff T. Ragsdale
Introduction to Optimization and Linear ProgrammingChapter 2
Introduction§We all face decision about how to use limited resources such as:Oil in the earthLand for dumpsTimeMoneyWorkers
Mathematical Programming...§MP is a field of management science that finds the optimal, or most efficient, way of using limited resources to achieve the objectives of an individual of a business.§a.k.a.Optimization
Applications of Optimization§Determining Product Mix§Manufacturing§Routing and Logistics§Financial Planning
Characteristics of Optimization Problems§Decisions§Constraints§Objectives
General Form of an Optimization ProblemMAX (or MIN): f0(X1, X2, …, Xn)Subject to:f1(X1, X2, …, Xn)<=b1:fk(X1, X2, …, Xn)>=bk:fm(X1, X2, …, Xn)=bmNote: If all the functions in an optimization are linear, the problem is a Linear Programming (LP) problem
Linear Programming (LP) ProblemsMAX (or MIN):c1X1 + c2X2 + … + cnXnSubject to:a11X1 + a12X2 + … + a1nXn<= b1:ak1X1 + ak2X2 + … + aknXn>=bk:am1X1 + am2X2 + … + amnXn= bm
An Example LP ProblemBlue Ridge Hot Tubs produces two types of hot tubs: Aqua-Spas & Hydro-Luxes.

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