Chapter 2 - Introduction Chapter 2 We all face decision...

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Introduction to Optimisation and Linear ProgrammingChapter 21Introduction°We all face decision about how to use limited resources such as:– Oil in the earth– Land for dumps– Time– Money– Workers2Mathematical 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.Optimisation3Applications of Optimisation°Determining Product Mix°Manufacturing°Routing and Logistics°Financial Planning4Characteristics of Optimization Problems°Decisions°Constraints°Objectives5General Form of an Optimisation 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 optimisation are linear, the problem is a Linear Programming (LP) problem6
Linear Programming (LP) ProblemsMAX (or MIN):c1X1+ c2X2+ … + cnXSubject to:a11X1+ a12X2+ … + a1nXnb1:ak1X1+ ak2X2+ … + aknXnbk:am1X1+ am2X2+ … + amnXn= bm7An Example LP ProblemBlue Ridge Hot Tubs produces two types of hot tubs: Aqua-Spas & Hydro-Luxes.There are 200 pumps, 1566 hours of labor, and 2880 feet of tubing available.Aqua-SpaHydro-LuxPumps11Labor 9 hours6 hoursTubingn

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