Problem Solving by using Quantitative Models and Computers

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Problem Solving by using Quantitative Models and
Computers
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? A real-world problem
Select an appropriate model
Understand Problem thoroughly
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Input into computer in a way that computer can
understand
Formulate the problem into the model
Solve
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Sensitivity Analysis
Scrutinize and interpret the computer result
Result
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Understanding Problem

• Step 2, understanding problem thoroughly
• Objective,
• Conditions and restrictions,
• Data needed,
• What the result is like.

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Formulate Problem

• Step 4, Formulate the problem into the selected
  model
• Re-describe the problem in terms of the model
• In LP, objective function and constraints
• In transportation model, sources and destinations.

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Input into Computer

• Step 5, Input the problem into computer in a way
  that computer understands
• Select software package for solving the model (QM
  or Excel, for example)
• Input the data into the proper model following
  the data format.

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Work with Results

• Step 8, Scrutinize and interpret the result from
  computer
• Understand the output of computer.
• Observe the result to see whether it is
  reasonable, whether it makes sense.
• Interpret the result from managerial point of
  view.

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Sensitivity Analysis

• Sensitivity analysis is to see how possible
  changes of parameters in the model would impact
  on the optimal solution.

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Additional Restrictions

• Additional restrictions can be dealt with before
  or after the computer solves the problem.
• Before. Re-formulate the model to incorporate
  the additional restrictions.
• After. Modify the computer result to reflect the
  additional restrictions.

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Manipulations

• The real-world problem usually does not fit a
  model perfectly, where manipulations are needed.
• Manipulation is handling some conditions or
  parameters in indirect but equivalent ways.
• Examples
• Prohibited route in the transportation model
• Solving assignment problem by using
  transportation model