CP-OM-SupC-BB - IDS 302 Supplement C: Linear Programming C....

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C. Probett/Spring 2009 C-1 IDS 302 – Supplement C: Linear Programming
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C. Probett/Spring 2009 C-2 Supplement C Learning Outcomes: L01 Describe the type of problem that would lend itself to solution using linear programming L02 Formulate a linear programming model from a description of a problem L03 Solve linear programming problems using the graphical method L04 Interpret computer solutions of linear programming problems L05 Do sensitivity analysis on the solution of a linear programming problem
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C. Probett/Spring 2009 C-3 Linear Programming Applications There are five common types of decisions in which Linear Programming may play a role: Product mix Blending/Ingredient mix Transportation Production plan Assignment
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C. Probett/Spring 2009 C-4 Real World Success Stories Optimal crew scheduling saves American Airlines $20 million/year Improved shipment routing saves Yellow Freight over $17.3 million/year Optimal traffic control of Hanshin Expressway in Osaka (Japan) saves 17 million driver hours/year Improved production planning as Sadia (Brazil) saves $50 million over three years Production Optimization at Harris Corporation improves on-time deliveries from 75% to 90% Tata Steel (India) optimizes response to power shortage contributing $73 million Gasoline blended at Texaco results in savings of over $30 million/ year
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C. Probett/Spring 2009 C-5 Linear Programming Optimization Models – models that seek to maximize or minimize some objective function while satisfying a set of constraints – an important category of optimization models is linear programming A model represents the essential features of an object, system or problem without unimportant details Mathematical models are cheaper, faster and safer than constructing and manipulating real systems Linear Programming (LP) – A sequence of steps that will lead to an optimal solution to linear-constrained problems, if an optimum exists
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C. Probett/Spring 2009 C-6 Model Components Decision variables : controllable input variable that represents the key decisions a manager must make to achieve an objective Generally use X1, X2, X3, etc. to represent decision variables Objective Function : the evaluation criteria (often maximizing profit or minimizing cost) Objective Function Coefficients - The constant terms in the objective function A Solution - Any particular combination of decision variables Feasible Solutions – solutions that satisfy all constraints Optimal Solution – any feasible solution that optimizes the objective function Constraint : some limitation or requirement that must be satisfied by the solution
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C. Probett/Spring 2009 C-7 Model Components Additional LP requirements: The Objective Function and Constraints must be expressed in linear terms of equations or inequalities Decision variables must be divisible and non-negative Values of parameters are known and constant
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C. Probett/Spring 2009
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This note was uploaded on 10/19/2009 for the course IDS IDS302 taught by Professor Rainer during the Spring '09 term at Institute of Business Administration.

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CP-OM-SupC-BB - IDS 302 Supplement C: Linear Programming C....

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