Optimization via Mathematical programming
Linear programming (LP) is the best known technique in a family of
optimization tolls called mathematical programming.
It is used extensively in DSS.
Characteristics and Assumptions of LP programming
Linear programming
Every LP problem is composed of the following.
Decision variables Whose values are unknown and are searched for
An objective
function
A linear mathematical function that relates the decision variables
to the goal and measures goal attainment and is to be optimized
Objective function
coefficients
Unit profit or cost coefficients indicating the contribution to the
objective of one nit of a decision variable
Constraints Expressed in the form of linear inequalities or equalities that limit
resources, and/or requirements
These relate the variables through linear relationships
Capacities Which describe the upper and sometimes lower limit on the
constraints & variables
Input-Output
(technology)
coefficients
Which indicate resource utilization for a decision variable
It is easy to interface other optimization software with Excel, database
management system and similar tools.
Heuristic Programming
The determination of optimal solutions to some complex decision
problems could involve a prohibitive amount of time & cost, or may even
be impossible.
The simulation approach may be lengthy, complex, and even inaccurate.
It is sometimes possible to arrive at satisfactory solutions more quickly &
less expensively by sing heuristics.
Heuristics are used primarily for solving ill-structured problems, thy can
also be used to provide satisfactory solutions to certain complex, well
structured problems.
The main difficulty in using heuristics is that they are not as general as
algorithms.
They can normally be used only for the specific situation for which they
were intended.
Another problem with heuristics is that they may obtain a poor solution.
Heuristic programming is the approach of using heuristics to arrive at
feasible and "good enough" solutions to some complex problems; "god
enough" is usually in the range of 90-99.9 % of the objective value of an
optimal solution.
When to use Heuristics, Advantages and limitations of Heuristics
Simulation
To simulate means to assume the appearance of the characteristics of
reality.
DSS deals with semi-structured or unstructured situations. It involves
complex reality, which may not be easily represented by optimization or
other models.
Simulation is one of the most commonly used tolls of DSS.
Major Characteristics
Simulation is a technique for conducting experiments.
Simulation is a descriptive rather than a normative tool.
Once the characteristics value is computed, the best among several
alternatives can be selected.
Simulation is usually called for only when a problem is too complex to be
treated by numerical optimization techniques.
Advantages
Simulation theory is fairly straightforward.
A great amount of time compression can be attained.
Simulation is descriptive rather than normative. This allows the manager
to ask what if questions.
An accurate simulation model requires an intimate knowledge of the
problem.
The simulation model is built for one particular problem and typically will
now solve any other problem. No generalized understanding is required of
the manager; every component in the model corresponds to a part of the
real life model.
Simulation can handle an extremely wide variety of problem types, such
as inventory and staffing, as well as higher managerial level functions
such as long range planning.
Simulation generally allows for inclusion of the real life complexities of
problems, simplifications are not necessary.
It is very easy to obtain a wide variety of performance measures directly
form the simulation.
Simulation is often the only modeling tool for DSS were problem can be
non-structured.
Limitations of Simulations
Linear programming (LP) is the best known technique in a family of
optimization tolls called mathematical programming.
It is used extensively in DSS.
Characteristics and Assumptions of LP programming
Linear programming
Every LP problem is composed of the following.
Decision variables Whose values are unknown and are searched for
An objective
function
A linear mathematical function that relates the decision variables
to the goal and measures goal attainment and is to be optimized
Objective function
coefficients
Unit profit or cost coefficients indicating the contribution to the
objective of one nit of a decision variable
Constraints Expressed in the form of linear inequalities or equalities that limit
resources, and/or requirements
These relate the variables through linear relationships
Capacities Which describe the upper and sometimes lower limit on the
constraints & variables
Input-Output
(technology)
coefficients
Which indicate resource utilization for a decision variable
It is easy to interface other optimization software with Excel, database
management system and similar tools.
Heuristic Programming
The determination of optimal solutions to some complex decision
problems could involve a prohibitive amount of time & cost, or may even
be impossible.
The simulation approach may be lengthy, complex, and even inaccurate.
It is sometimes possible to arrive at satisfactory solutions more quickly &
less expensively by sing heuristics.
Heuristics are used primarily for solving ill-structured problems, thy can
also be used to provide satisfactory solutions to certain complex, well
structured problems.
The main difficulty in using heuristics is that they are not as general as
algorithms.
They can normally be used only for the specific situation for which they
were intended.
Another problem with heuristics is that they may obtain a poor solution.
Heuristic programming is the approach of using heuristics to arrive at
feasible and "good enough" solutions to some complex problems; "god
enough" is usually in the range of 90-99.9 % of the objective value of an
optimal solution.
When to use Heuristics, Advantages and limitations of Heuristics
Simulation
To simulate means to assume the appearance of the characteristics of
reality.
DSS deals with semi-structured or unstructured situations. It involves
complex reality, which may not be easily represented by optimization or
other models.
Simulation is one of the most commonly used tolls of DSS.
Major Characteristics
Simulation is a technique for conducting experiments.
Simulation is a descriptive rather than a normative tool.
Once the characteristics value is computed, the best among several
alternatives can be selected.
Simulation is usually called for only when a problem is too complex to be
treated by numerical optimization techniques.
Advantages
Simulation theory is fairly straightforward.
A great amount of time compression can be attained.
Simulation is descriptive rather than normative. This allows the manager
to ask what if questions.
An accurate simulation model requires an intimate knowledge of the
problem.
The simulation model is built for one particular problem and typically will
now solve any other problem. No generalized understanding is required of
the manager; every component in the model corresponds to a part of the
real life model.
Simulation can handle an extremely wide variety of problem types, such
as inventory and staffing, as well as higher managerial level functions
such as long range planning.
Simulation generally allows for inclusion of the real life complexities of
problems, simplifications are not necessary.
It is very easy to obtain a wide variety of performance measures directly
form the simulation.
Simulation is often the only modeling tool for DSS were problem can be
non-structured.
Limitations of Simulations
No comments:
Post a Comment