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Discuss the characteristics of optimisation problems

What is optimisation?

Finds the optimal, or most efficient, way of using limited resources to achieve the objectives of an individual of a business.

What is the application of optimisation?

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General Form of an Optimization Problem

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Explore the use of linear programming (LP) in solving optimisation problems

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  1. Understand the problem.
  1. Define the decision variables.
    1. X_1 =number of Aqua-Spas to produce
      X_2 =number of Hydro-Luxes to produce
  1. Define the objective function
    1. MAX: 350X 1 + 300X 2
  1. Define the constraints
    1. For this step, there are types of constraints in other cases, namely Demand Constraints, Resource Constraints, and Non-negativity conditions (which the next step).
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  1. Identify any upper or lower bounds on the decision variables.
    1. X1 >= 0 && X2 >= 0
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Solving LP problems using graphical approach

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In Summary
In Summary
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Special condition

Case 1: Alternate Optimal Solutions
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Case 2: Redundant Constraint
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Case 3: Unbounded Solution
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Case 4: Infeasibility
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FIT3158 - Lab 9 Case studies on Decision Analysis & Decision Trees – Risk and UncertaintyFIT3158 Note - W1 Introduction to Optimisation and Linear Programming