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How to pick the optimal batch size?


If the batch size is so small, that the process step with the set-up time (assuming, that there is only one) becomes the bottleneck of the process, the process looses on overall efficiency. Thus, the batch size needs to be chosen in a way that assures, that it will not generate a new bottleneck.

If, however, the batch size is too big, any increase in capacity at the station with the set-up time (assuming, again, that there is only one) is ultimately of no use, because it will only lead to inventory piling up somewhere else in the process – wherever the bottleneck may be.

This goes to show, that the ideal batch size is one, in which the station with the set-up time has a processing time which is just identical to the process bottleneck. Only then will the batch size not lead to the creation of a new bottleneck or additional inventory pile-up. This is calculated as:

capacity determined by the batch size = capacity of the bottleneck

b / (s + b * p) = m / p

with:

b = batch size
s = set-up time
p = processing time
m = number of resources

These lecture notes were taken during 2013 installment of the MOOC “An Introduction to Operations Management” taught by Prof. Dr. Christian Terwiesch of the Wharton Business School of the University of Pennsylvania at Coursera.org.

Re-definition of the batch size in accordance with demand


The batch size was previously defined as the number of flow units that are produced between two set-ups. While this definition is correct, it does not take into account the actual demand for the flow units. If a process is able to produce multiple flow units (e.g. cheeseburgers and veggie sandwiches) with one set-up time in between, a batch in a mixed-model production is re-defined as a number of mixed flow units produced during a certain amount of time (before the used pattern of production is repeated). The additional set-up times for switching between the flow units during the production of the batch have, of course, to be recognized.

This brings us to the following formula:

target flow = batch size / (set-up time + batch size * processing rate)

Here, the target flow is defined as the number of flow units needed per time frame in order to stay on top of the demand (e.g. 100 units per hour). The processing rate is determined by the bottleneck of the process or by the demand while set-up time and batch size have previously been defined.

If the goal is determining the ideal batch size, the formula can be resolved for the batch size. The result has to be set in ratio to the demand for the various flow units within the batch in order to find out, how many flow units of each type are produced within the ideal batch size. Note, that the set-up time needed to start the production pattern at the beginning is part of the overall set-up time and thus needs to be included in the total sum of set-up times needed for this calculation.

Obviously, the batches will become larger and the inventory will become bigger the more set-ups are necessary as long as the overall demand does not change (but is simply spread out over more offered product choices). Variety thus leads to more set-ups and thus to more inventory, which is one of the biggest problems associated with offering more variety.

These lecture notes were taken during 2013 installment of the MOOC “An Introduction to Operations Management” taught by Prof. Dr. Christian Terwiesch of the Wharton Business School of the University of Pennsylvania at Coursera.org.
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