Linear Programming

# Linear Programming - OPTIMIZATION LINEAR PROGRAMMING Prof...

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OPTIMIZATION - LINEAR PROGRAMMING Prof. Preetam Basu IIM Calcutta

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Business Optimization In most business situations, managers have to achieve objectives while working within several resource constraints. For example, maximizing sales within an advertising budget, improving production with existing capacity, reducing costs while maintaining service metrics, etc. Mathematical modeling can help in such situations. Linear Programming (LP) is the most important of these techniques. It had its origins during WW2 as a means of improving the effectiveness of men and materiel in the war effort.
LP Model Formulation Decision variables mathematical entities representing levels of activity of an operation Objective function a linear relationship reflecting the objective of an operation Examples: profit maximization, cost minimization Constraint a linear relationship representing a restriction on decision making Steps Involved: Determine the objective of the problem and describe it by a criterion function in terms of the decision variables. Find out the constraints. Do the analysis which should lead to the selection of values for the decision variables that optimize the criterion function while satisfying all the constraints imposed on the problem.

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LP Model Formulation (cont.) Max/min z = c 1 x 1 + c 2 x 2 + ... + c n x n subject to: a 11 x 1 + a 12 x 2 + ... + a 1n x n (≤, =, ≥) b 1 a 21 x 1 + a 22 x 2 + ... + a 2n x n (≤, =, ≥) b 2 : a m1 x1 + a m2 x 2 + ... + a mn x n (≤, =, ≥) b m x j = decision variables b i = constraint levels c j = objective function coefficients a ij = constraint coefficients
LP Model: Example Highlands Craft Stores is a small craft operation that employs local artisans to produce clay bowls and mugs based on designs and colors from the 1700s and 1800s. The two primary resources

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