moduleBa

moduleBa - Operations Operations Management Management...

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B-1 Operations Operations Management Management Linear Programming Linear Programming Module B Module B

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B-2 Outline Outline What is Linear Programming (LP)? Characteristics of LP. Formulating LP Problems. Graphical Solution to an LP Problem. Formulation Examples. Computer Solution. Sensitivity Analysis.
B-3 Mathematical models designed to have optimal (best) solutions. Linear and integer programming. Nonlinear programming. Mathematical model is a set of equations and inequalities that describe a system. E = mc 2 Y = 5.4 + 2.6 X Optimization Models Optimization Models

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B-4 Mathematical technique to solve optimization models with linear objectives and constraints. NOT computer programming! Allocates scarce resources to achieve an objective. Pioneered by George Dantzig in World War II. What is Linear Programming (LP)? What is Linear Programming (LP)?
B-5 Scheduling school buses to minimize total distance traveled. Allocating police patrols to high crime areas to minimize response time. Scheduling tellers at banks to minimize total cost of labor. Examples of Successful LP Examples of Successful LP Applications Applications

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B-6 Examples of Successful LP Examples of Successful LP Applications - continued Applications - continued Blending raw materials in feed mills to maximize profit while producing animal feed. Selecting the product mix in a factory to make best use of available machine- and labor-hours available while maximizing profit. Allocating space for tenants in a shopping mall to maximize revenues to the leasing company.
B-7 Characteristics of an LP Problem Characteristics of an LP Problem 1 Deterministic (no probabilities). 2 Single Objective: maximize or minimize some quantity (the objective function). 3 Continuous decision variables (unknowns to be determined). 4 Constraints limit ability to achieve objective. 5 Objectives and constraints must be expressed as linear equations or inequalities.

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B-8 4x 1 + 6x 2 9 4x 1 x 2 + 6x 2 9 3x - 4y + 5z = 8 3x - 4y 2 + 5z = 8 3x/4y = 8 3x/4y = 8y same as 3x - 32y = 0 4x 1 + 5x 3 = 4x 1 + 5 = 8 Linear Equations and Inequalities Linear Equations and Inequalities 8 3 x
B-9 Formulating LP Problems Formulating LP Problems Word Problem Mathematical Expressions Solution Formulation Computer

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B-10 Formulating LP Problems Formulating LP Problems 1. Define decision variables. 2. Formulate objective. 3. Formulate constraints. 4. Nonnegativity (all variables 0).
B-11 Formulation Example Formulation Example You wish to produce two products: (1) Walkman and (2) Watch-TV. Each Walkman takes 4 hours of electronic work and 2 hours of assembly time. Each Watch-TV takes 3 hours of electronic work and 1 hour of assembly time. There are 225 hours of electronic work time and 100 hours of assembly time available each month. The profit on each Walkman is \$7; the profit on each Watch-TV is \$5.

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moduleBa - Operations Operations Management Management...

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