| 초록 |
The scheduling of batch chemical processes has received significant attention from both the academic and industrial communities. Numerous scheduling methodologies have been developed, most of which have focused on the construction of schedules based on time-invariant deterministic data on processing time and other batch characteristics, e.g., yields, parameters for processing time vs. yield curve, etc. When variability in batch data is encountered during execution of a schedule, the information is typically used in a reactive mode to reschedule the plant, to avoid infeasibilities or sub-optimalities in resource allocation induced by the actual batch conditions (Kanakamedala et al., 1994; Bassett et al., 1997). However, these 'reactive scheduling' methodologies seldom seek to model correlation in processing data and use them to anticipate future variations in scheduling parameters in revising the schedule. This is in contrast to control, where stochastic models containing space/time correlation information is used with an optimal estimation technique (e.g., Kalman filtering) for optimal prediction and predictive control. In this study, a new scheduling framework, which we name -"proactive scheduling"- to distinguish it from 'reactive scheduling'-, is developed to handle correlated forms of uncertainty in a dynamic manufacturing environment. Frequently in chemical processes, variations in prior process units propagates to later processing requirements; for example, variability in feed moisture content may affect reaction yields and times at one stage and hence the amount of product to be recovered at a later stage. Since it is possible to observe the process time and yield as well as other relevant measured processing variables at a prior processing stage, this information can be used to update the expected value of the scheduling relevant parameters at a later stage, before the entire schedule is executed. This gives the decision maker extra leverage to change the schedule proactively in anticipation of this pdated value. This correlation information can be represented, in its simplest form, by the covariance of processing conditions or parameters. The main idea of proactive scheduling is then to use observations made at the current time to obtain conditional expectations of future processing parameters. A deterministic scheduling problem is solved repeatedly to revise the schedule as the parameters are continually updated by a Kalman filter based on the information coming from actual execution of the schedule. Historical operation data can be used to estimate the covariance of key parameters. Parameters with a high degree of uncertainty can be updated effectively using this scheme, giving the proactive scheduling a boost in performance over the purely reactive scheduling which would continue to use the average values for parameters. The proactive scheduling approach has been tested on a general multi-purpose batch chemical scheduling problem. |
