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Operations Research Models and Methods
Models Section
Serial Systems

In a serial system, stations are arranged so that the first station receives the raw material for the product. After completing processing at station 1, the partially completed part is passed to station 2, and so on until the finished part leaves at the last station. The three-station example is shown in Fig. 9.

Figure 9. Three station serial system

The important thing to remember about this system is that the output of one station becomes the input to the next. Thus in a system with no losses, the average arrival rate to the first station is must equal the average departure rate from the last station. An Extend model for a three-station system is shown in Fig. 10. The block immediately to the right of the generator block is a Sensor block. It gathers data and computes the difference between the time when a part leaves the system and the time when it enters. This time is the cycle time and it is an important measure of the effectiveness of a manufacturing system.

Figure 10. An Extend model for three serial stations

The theory of queueing networks provides analytical formulas that predict the mean cycle time at each station as a function of the means and standard deviations of the arrival process and service processes. These formulas compute the coefficient of variation at the input to each station. In the model of Figure 10, the coefficient of variation is computed by the block structure above the station. The model is useful for comparing simulation results to the analytical results. .See section 17.4, Non-Poisson Networks, from the text for a discussion.

The CD contains two other models of the three-station system. The Three Station_CV.mox model allows parts to be initially placed at the stations to reduce the effect of the startup transient period. The Three Station_CV Hierarch.mox model uses an hierarchical modeling approach. As illustrated in Figure 11, this model appears simpler because the models of the individual stations are hidden. Double clicking on a hierarchical block reveals the underlying structure.

Figure 11. An Extend model for three serial stations with a hierarchical structure


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Operations Research Models and Methods
by Paul A. Jensen
Copyright 2004 - All rights reserved

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