Linear Programming

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Linear Programming
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Problem Categories LP Methods
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Linear Programming
Aggregate planning Production,
Staffing Distribution Shipping Inventory Stock
control, Supplier selection Location Plants or
warehouses Process management Stock
cutting Scheduling Shifts, Vehicles, Routing
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(No Transcript)
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Basic Concepts

• Objective function
• Decision variables
• Constraints
• Feasible region
• Parameters
• Linearity
• Nonnegativity
• Divisibility

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Graphical Linear Programming

• Define the decision variables
• Define the objective function
• Formulate the constraints
• Plot the constraints
• Identify the feasible solution space
• Plot the objective function (or find the corner
  points)
• Determine the optimum solution using the
  objective function (or corner points)

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Sweet SmellFertilizer Company
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FORMULATIONSweet Smell Company

• LET X1 Pounds Of Compost
• X2 Pounds Of Sewage
• MIN COST .05 X1 .04X2
• SUBJECT TO
• 1X1 1X2 gt 60 (dry weight)
• 1X1 gt 30 (compost minimum)
• 1X2 lt 40 (sewage maximum)

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Linear Programming
X2
80 70 60 50 40 30 20 10 0
1x1 gt 30 (compost)
(0, 60)
1x2 lt 40 (sewage)
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Optimal solution (30,30)
B
1x1 1x2 gt 60 (mix)
(60, 0)
10 20 30 40 50 60 70 80
X1
C
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Corner Point Solution

• MIN COST .05X1 .04X2
• (A) 3.10 .05(30) .04(40)
• (B) 2.70 .05(30) .04(30)
• (C) 3.00 .05(60) .04(0)
• (B) OPTIMAL SOLUTION