Step 1: Formulate the Problem Decision Variables

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Presentation transcript:

Step 1: Formulate the Problem Decision Variables Objective Function (O. F.) Constraints (S. T.) Sign Constraints (URS) Step 2: Create the Standard Form of LP Constraints = (+ s , - e , + a ) Variables >= 0 IE 416, Chap 4:1, June 1999

RMC Inc. Problem, Summary Mixture in Product Raw Material Available Fuel Solvent Material 1 20 tons 2/5 1/2 Material 2 5 tons - 1/5 Material 3 21 tons 3/5 3/10 Profit $/ton 40 30 Source: An Introduction to Management Science By: Anderson, Sweeney, Williams IE 416, Chap 4, May 99

RMC Inc. Problem, Formulation X1 = number of tons of fuel, positive X2 = number of tons of solvent, positive O.F. S.T. Material 1 Material 2 Material 3 IE 416, Chap 4, May 99

RMC Inc. Problem, Standard LP Form IE 416, Chap 4, May 99

Excess and Artificial Variables

Added Simplex Method Practical Variable Application Application Slack Equality of equation s > 0 resource not used BV for initial s = 0 binding constraint simplex tableau Excess Equality of equation e > 0 extra resource required e = 0 binding constraint Artificial Added to > and = No meaning equations desire a = 0 BV for initial a > 0 no solution IE 416, Chap 4:1, Jan 99