It is well known, that the life cycle of a product can be calculated quite good with a sigmoid curve. Such a curve describes the growth of a population, like bacteria for instance, over time and has a S-shape.
A simple sigmoid curve is the logistic curve, which is symmetric ( point-symmetry ); that means, that the beginning of the growth and the end of it, show the same, but opposite changes in time.
This is seldom the case in real world problems and therefore more general sigmoid curves like the Gomperz function should be used, to model the growth in production of a product for instance, for which the available resources are limited.
Assuming, that the total production can be sold, one can forecast the life cycle of the product.
But in general there are several competing products available and one must develop a more sophisticated mathematical model, to forecast the life-cycle of each product.
With a set of mathematical equations, such more general situation can also be modeled.
Most important for each decision maker is the understanding, that the production output will never only grow, but will reach a constant level and thereafter decrease. Linear forecasting, based on past data often forecasts completely wrong results for the future.
For the mathematical background look at wikipedia:
http://en.wikipedia.org/wiki/Gompertz_curve
A simple sigmoid curve is the logistic curve, which is symmetric ( point-symmetry ); that means, that the beginning of the growth and the end of it, show the same, but opposite changes in time.
This is seldom the case in real world problems and therefore more general sigmoid curves like the Gomperz function should be used, to model the growth in production of a product for instance, for which the available resources are limited.
Assuming, that the total production can be sold, one can forecast the life cycle of the product.
But in general there are several competing products available and one must develop a more sophisticated mathematical model, to forecast the life-cycle of each product.
With a set of mathematical equations, such more general situation can also be modeled.
Most important for each decision maker is the understanding, that the production output will never only grow, but will reach a constant level and thereafter decrease. Linear forecasting, based on past data often forecasts completely wrong results for the future.
For the mathematical background look at wikipedia:
http://en.wikipedia.org/wiki/Gompertz_curve
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