Читать книгу Control Theory Applications for Dynamic Production Systems - Neil A. Duffie - Страница 28

In the example illustrated in Figure 2.12, Company A obtains unfinished orders from a supplier, distant Company B, and then performs the work required to finish them. Both companies are assumed to process orders at the same rate as they are received. Unfinished orders are shipped from Company B to Company A, and the time between an order leaving Company B and arriving at Company A is a constant D days. Companies A and B have lead times LA and LB days, respectively, which is the time between when the company receives an order and when the company has completed processing the order; lead times are assumed to be constant and can be modeled as delays.

Figure 2.12 Lead time and transportation delays in a two-company production system.

If the order input rate to Company B is demand ri(t) orders/day and the order input rate to Company A is rA(t) orders/day, the order output rates from Companies B and A, rB(t) and ro(t), respectively, are

Shipping is described by

Combining the delays, the relationship between demand and the completed order output rate of Company A is