Module B

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Module B

• Linear Programming

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What is Linear Programming?

• Mathematical technique
• Not computer programming
• Allocates scarce resources to achieve an
  objective
• Pioneered by George Dantzig in World War II
• Developed workable solution in 1947
• Called Simplex Method

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Definition

• A mathematical technique designed to help
  operations managers plan and make decisions
  necessary to allocate resources.

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Requirements of a Linear Programming Problem

• Must seek to maximize or minimize some quantity
  (the objective function)
• Presence of restrictions or constraints - limits
  ability to achieve objective
• Must be alternative courses of action from which
  to choose
• Objectives and constraints must be expressible as
  linear equations or inequalities

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Shader Electronics Example

• You wish to produce two products (1) Walkman
  AM/FM/Cassette and (2) Watch-TV
• Walkman takes 4 hours of electronic work and 2
  hours assembly
• Watch-TV takes 3 hours electronic work and 1 hour
  assembly
• There are 240 hours of electronic work time and
  100 hours of assembly time available
• Profit on a Walkman is 7 profit on a Watch-TV
  5

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Setting up the problem

• Let
• X1 number of Walkmans
• X2 number of Watch-TVs
• Then
• 4X1 3X2 ? 240 electronics constraint
• 2 X1 1X2 ? 100 assembly constraint
• 7X1 5X2 profit maximize profit

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What is our objective function?

• To maximize profit!
• So we want to maximize profits achieved from our
  2 products with limited resources.
• Maximize 7x1 5x2
• But we have constraints
• 4x1 3x2 ? 240 (Hours of Electronic Time)
• 2x1 1x2 ? 100 (Hours of Assembly Time)