Time Lag Effects - Operations Function

Feedback control in complex systems can bring its own problems, due to time lag between measuring the output deviation and realising the effects of the corrective adjustments. A well-known illustration of this phenomenon was presented by Jay W Forrester in his book, Industrial Dynamics. He had been consulted by a white goods manufacturing concern which had been experiencing wildly fluctuating production levels over a period of years; despite the best efforts of the company's management they had been unable to keep production output in reasonable balance with customer demand. Forrester and his team studied the operations of the company's distribution chain (shown in simplified form in the figure) and formulated a computer simulation model of the factory - warehouse - distributor - retailers.

The figure below (adapted from Forrester, 1965) shows the results obtained when a 10 per cent step-increase in demand at the retail outlets was introduced. This chart is necessarily 'cluttered', to show how the various order, inventory and production levels changed in response to the initial increase in sales.

For our purposes it will be sufficient if you locate the two lines labeled 'Retail sales' and 'Factory production output'. It was found that, because of a series of time-lags in the chain, the feedback signal was greatly amplified by the time it reached the factory, resulting in over-reaction. Note that the production level climbs by 45 per cent, creating an excessive build up of inventories. In response the production level falls to 3 per cent less than the original level, and so on. It takes about 18 months for the fluctuations to be damped out.