(weeks, months, years, etc.). Thus, a company might wish to take, over time, a series
of marketing decisions to obtain the highest possible sales. The fundamental principle of this approach is that, independently of previous decisions, it attempts to
determine the optimal decision for the remaining future periods.
The dynamic programming approach subdivides the main problem into a number
of stages or sub-problems). The decision taken at each stage affects not only the next
stage but all other following stages in the model. Although dynamic programming
has been used to solve problems where time plays a significant role, yet time is not
always a relevant variable in all dynamic programming problems.
For example, imagine a company has budgeted capital C to be used on its product
advertisements through different media: television, radio and newspaper. The advertisement can be made several times per week, in each medium, each having its
associated costs and returns. The problem to solve is to determine the number of
advertisements in each medium to obtain the maximum returns, while keeping the
overall cost within the prescribed budget. In this problem, time is not a variable,
though the problem has been distributed into stages and can be solved through by
dynamic programming.
While there are standard ways in formulating problems and solving them
(e.g. linear programming) no such standard approach exists for problems in
dynamic programming. However, it provides a typical “divide and solve” policy: a
large complex example is split into smaller problems, each of which yields solutions
more easily. Nevertheless, some ingenuity might be required before deciding how a
problem can be solved through dynamic programming and how to move towards the
solution. As the data involved gets large, computers may be needed to minimise
processing and calculation time.
13.3.10 Simulation Techniques
Simulation tries to represent real systems or problems through some model or other
device, which will behave in the same manner as the real system under a given set of
conditions.
A model of the system is first developed followed by a set of trial-and-error
experiments to study the temporal behaviour of the system, with quantitative results.
Changes in the real system are replicated in the model, whose reactions are observed
and then transposed to the real system. This allows understanding the behaviour of
the real system under varying circumstances through a wide range of experiments on
the model.
Simulation is widely used because it is a very powerful operations research
method. When decision-making problems are too complex for analytical solutions
and experimenting with the actual system, even if feasible, is too costly and risky,
management may try the simulation approach. Simulation delivers the solution
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13 Modelling in Infrastructure Planning
of marketing decisions to obtain the highest possible sales. The fundamental principle of this approach is that, independently of previous decisions, it attempts to
determine the optimal decision for the remaining future periods.
The dynamic programming approach subdivides the main problem into a number
of stages or sub-problems). The decision taken at each stage affects not only the next
stage but all other following stages in the model. Although dynamic programming
has been used to solve problems where time plays a significant role, yet time is not
always a relevant variable in all dynamic programming problems.
For example, imagine a company has budgeted capital C to be used on its product
advertisements through different media: television, radio and newspaper. The advertisement can be made several times per week, in each medium, each having its
associated costs and returns. The problem to solve is to determine the number of
advertisements in each medium to obtain the maximum returns, while keeping the
overall cost within the prescribed budget. In this problem, time is not a variable,
though the problem has been distributed into stages and can be solved through by
dynamic programming.
While there are standard ways in formulating problems and solving them
(e.g. linear programming) no such standard approach exists for problems in
dynamic programming. However, it provides a typical “divide and solve” policy: a
large complex example is split into smaller problems, each of which yields solutions
more easily. Nevertheless, some ingenuity might be required before deciding how a
problem can be solved through dynamic programming and how to move towards the
solution. As the data involved gets large, computers may be needed to minimise
processing and calculation time.
13.3.10 Simulation Techniques
Simulation tries to represent real systems or problems through some model or other
device, which will behave in the same manner as the real system under a given set of
conditions.
A model of the system is first developed followed by a set of trial-and-error
experiments to study the temporal behaviour of the system, with quantitative results.
Changes in the real system are replicated in the model, whose reactions are observed
and then transposed to the real system. This allows understanding the behaviour of
the real system under varying circumstances through a wide range of experiments on
the model.
Simulation is widely used because it is a very powerful operations research
method. When decision-making problems are too complex for analytical solutions
and experimenting with the actual system, even if feasible, is too costly and risky,
management may try the simulation approach. Simulation delivers the solution
364
13 Modelling in Infrastructure Planning