Chapter 1
Stimulation = giving you the ability to try out approaches and test ideas for improvement
Solutions are often obtained using algorithms. Algorithms provide fixed computational rules that are
applied repetitively to the problem, with each repetition (called iteration) moving the solution closer
to the optimum.
Heuristic = solution method that finds good, but in general nog the optimum solution
- Advantage: quick
- Disadvantage: the quality of the solution (relative to the optimum) is unknown
Relaxation = a problem that is easier to solve, obtained by removing one or more constraints (not
necessarily feasible)
Note: If the optimum solution of the relaxation is a feasible solution of the original problem, it is also
the optimum solution of the original problem.
Note: If the optimum solution of the relaxation is an infeasible solution of the original problem, it is a
better solution than the optimum solution of the original problem.
Goal Heuristic Relaxation
Maximization Lower bound Upper bound
Minimization Upper bound Lower bound
Always provides a feasible Solution not necessarily feasible
solution for the original problem
The optimum solution of the relaxation provides information about the quality
of the solution determined by a heuristic
The principle phases for OR include:
1. Definition of the problem – decision alternatives, objective and constraints
2. Construction of the model – algorithms, simplify or use heuristics, use simulation
3. Solution of the model
4. Validation of the model
5. Implementation of the solution
Sensitivity analysis: Obtaining additional information about the behaviour of the optimum solution
when the model undergoes some parameter changes.
o A sensitivity analysis is particularly important when the parameter values cannot be
estimated accurately.
Dimension of the problem = the number of decision variables.
Coefficients: The numbers in front of the variables (objective coefficients and constraint coefficients).
Right-hand sides (RHS): The limits on the resources.
Parameters: The coefficients and the right-hand sides are the parameters of the problem.
There are two types of constraints: functional constraints and non-negativity constraints
Stimulation = giving you the ability to try out approaches and test ideas for improvement
Solutions are often obtained using algorithms. Algorithms provide fixed computational rules that are
applied repetitively to the problem, with each repetition (called iteration) moving the solution closer
to the optimum.
Heuristic = solution method that finds good, but in general nog the optimum solution
- Advantage: quick
- Disadvantage: the quality of the solution (relative to the optimum) is unknown
Relaxation = a problem that is easier to solve, obtained by removing one or more constraints (not
necessarily feasible)
Note: If the optimum solution of the relaxation is a feasible solution of the original problem, it is also
the optimum solution of the original problem.
Note: If the optimum solution of the relaxation is an infeasible solution of the original problem, it is a
better solution than the optimum solution of the original problem.
Goal Heuristic Relaxation
Maximization Lower bound Upper bound
Minimization Upper bound Lower bound
Always provides a feasible Solution not necessarily feasible
solution for the original problem
The optimum solution of the relaxation provides information about the quality
of the solution determined by a heuristic
The principle phases for OR include:
1. Definition of the problem – decision alternatives, objective and constraints
2. Construction of the model – algorithms, simplify or use heuristics, use simulation
3. Solution of the model
4. Validation of the model
5. Implementation of the solution
Sensitivity analysis: Obtaining additional information about the behaviour of the optimum solution
when the model undergoes some parameter changes.
o A sensitivity analysis is particularly important when the parameter values cannot be
estimated accurately.
Dimension of the problem = the number of decision variables.
Coefficients: The numbers in front of the variables (objective coefficients and constraint coefficients).
Right-hand sides (RHS): The limits on the resources.
Parameters: The coefficients and the right-hand sides are the parameters of the problem.
There are two types of constraints: functional constraints and non-negativity constraints
