Ikea Benchmarking

Linear Programming
      Model Formulation Graphical Solution Method Linear Programming Model Simplex method Solution Solving Linear Programming Problems with Excel Dr A Lung  Student exercises
Kingston University London
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Linear Programming (LP)
• A model consisting of linear relationships representing a firm’s objective and resource constraints • LP is a mathematical modeling technique used to determine a level of operational activity in order to achieve an objective, subject to restrictions called constraints • Pioneered by George Dantzig in WWII, including Simplex Method

Learning objectives:  Identify Objective function and Constraints  Identify Feasible region  Apply Corner-point solution  Describe how to formulate linear models  Use Graphical method of LP
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Types of LP

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Types of LP (cont.)

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Types of LP (cont.)

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LP Model Formulation
 Decision variables
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mathematical symbols representing levels of activity of an operation a linear relationship reflecting the objective of an operation most frequent objective of business firms is to maximize profit most frequent objective of individual operational units (such as a production or packaging department) is to minimize cost a linear relationship representing a restriction on decision making, e.g. an operator can work on m/c A or B, but what ever the mix he/she can only work 8 hours a day
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 Objective function
  

 Constraint
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LP Model Formulation (cont.)
Max/min
subject to: a11x1 + a12x2 + ... + a1nxn (≤, =, ≥) b1 a21x1 + a22x2 + ... + a2nxn (≤, =, ≥) b2 : am1x1 + am2x2 + ... + amnxn (≤, =, ≥) bm xj = decision variables bi = constraint levels cj = objective function coefficients aij = constraint coefficients

z = c1x1 + c2x2 + ... + cnxn

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LP Model: Example
RESOURCE REQUIREMENTS PRODUCT Bowl Mug Labor (hr/unit) 1 2 Clay (lb/unit) 4 3 Revenue ($/unit) 40 50

There are 40 hours of labor and 120 pounds of clay available each day