Page 116 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

(3.1)

where T is the total time to process n batches without overlapping, each batch having m steps of
NO
duration t t , ... , t . For this example, the total time is equal to (8)(3.5 + 0.5 + 3.5 + 2 + 4.0 + 1.0) = (8)
1, 2
m
(14.5) = 116.0 h.

For the process described in Figure 3.1, using the nonoverlapping scheme, the equipment is used
infrequently, and the total processing time is unduly long. However, such a scheme might be employed in
plants that operate only a single shift per day. In such cases, the production of a single batch might be

tailored to fit an 8 or 10 h shift (for this example, the shift would have to be 14.5 h), with the limitation
that only one batch would be produced per day. Although such a scheme does not appear to be very
efficient, it eliminates prolonged storage of intermediate product and certainly makes the scheduling
problem easy.

The total time to process all the batches can be reduced by starting a batch before the preceding batch has
finished. This is equivalent to shifting backward the time blocks representing the steps in the batch
process, as shown in Figure 3.2.

Figure 3.2 Backward Shifting of Batches, Giving Rise to Overlapping Sequencing

This shifting of batches backward in time leads to the concept of overlapping sequencing of batches. The
limit of this shifting or overlapping process occurs when two time blocks in consecutive batches just
touch each other (assuming that cleaning, inspection, and charging times are included). This situation is
shown in Figure 3.3.

Figure 3.3 The Limiting Case for Overlapping Batch Sequencing