Читать книгу Control Theory Applications for Dynamic Production Systems - Neil A. Duffie - Страница 32

A production work system such as that illustrated in Figure 2.15 has constant work in progress (WIP) w hours and variable production capacity r(t) hours/day. The lead time l(t) hours then is approximately

Figure 2.15 Production work system with variable capacity.

The relationship between lead time and capacity is nonlinear; however, a linear approximation of this relationship in the vicinity of operating point ro can be obtained using Equations 2.2 and 2.3:

The percent error in lead time calculated using the linear approximation due to deviation of actual capacity r(t) from the chosen capacity operating point ro is shown in Figure 2.16 and calculated using

Figure 2.16 Percent error in lead time due to deviation of actual capacity from capacity operating point chosen for linear approximation.

Clearly, capacity should not deviate significantly from the operating point if this approximation is used in a model. If, for example, lead time is to be regulated by adjusting capacity, capacity might vary significantly from the operating point that was used to design lead-time regulation decision rules. An option⁶ in this case could be to

 calculate the parameters for a linearized model for each of several capacity operating points

 design lead time regulation decision rules for each operating point using the model for that operating point

 switch between decision rules as operating conditions vary.