Читать книгу Control Theory Applications for Dynamic Production Systems - Neil A. Duffie - Страница 25

The decision-making component shown in Figure 2.8 is used to calculate periodic adjustments that increase or decrease the lead time used to plan operations in a production system. Lateness of order completion can negatively affect production operations and customer satisfaction, and it is common practice to increase planned lead times when the trend is to miss deadlines. On the other hand, planned lead times can be decreased when the trend is to complete orders early; this can be a competitive advantage because earlier due dates can be promised when customers are placing or considering placing orders.

Figure 2.8 Discrete-time decision-making component for adjusting planned lead time in a production system as a function of lateness of order completion.

An example of a discrete-time decision rule that could be used periodically to adjust planned lead time is

where lp(kT) days is the planned lead time, ∆lp(kT) days is the change in planned lead time, le(kT) days is a measure of lateness that could be obtained statistically from recent order due date and completion time data, and Kl weeks is a decision-making parameter that needs to be designed to obtain favorable dynamic behavior of the production system into which the decision-making component is incorporated. T weeks is the period between adjustments. This decision rule both increases planned lead time when orders are late and also increases planned lead time when lateness is increasing; the contribution of the latter is governed by the choice of parameter Kl.

The dynamic behavior of the component is illustrated in Figure 2.9b for the case shown in Figure 2.9a where lateness le(kT) increases to 8 days over a period of 6 weeks. The response of change in planned lead time to this increase in lateness is shown in Figure 2.9b for Kl = 2 weeks and Kl = 4 weeks. The period between adjustments is T = 1 week. The response was calculated recursively using the above difference equation in a manner similar to that shown in Program 2.2. As expected, the larger value of Kl results in larger adjustments when lateness is increasing, a stronger response to this trend in lateness.

Figure 2.9 Response of change in planned lead time to lateness in order completion.