Set-up times often have a significant effect on the performance of a process and can even determine a process bottleneck. The most important definition here is that of the batch: A batch is the number of flow units, which are produced between two set-ups. To calculate the capacity of a process with respect to the batch size, the following formula is needed:

capacity = (batch size) / (set-up time + batch size * time per unit)


Note, that this is the capacity of the process for producing a batch. For example, if the batch size happens to be 10 flow unites per minute, this calculation answers the question of how long it will take to produce one complete batch. This is a deviation from the previous definition of capacity, which did not take the batch size into account and was simply calculated as:

capacity = number of resources / processing time


The capacity can by this basic definition be calculated for every station in a process. It is always m / processing time with m being the number of resources (e.g. workers) being devoted to this process step. If, for example, one worker needs 40 seconds to put together a sandwich, the capacity of this station is 1/40 per second or 1,5 sandwiches per minute. If there are two workers on the same station, the capacity increases to 2/40 per second or 3 sandwiches per minute.

Usually, the larger the batch, the more efficient the production process becomes (economics of scale). Companies with custom-made batches are therefore trying to get their customers to order large batches (sometimes even forcing them). The bigger a batch grows, the more irrelevant the set-up time becomes with the process capacity getting closer and closer to the original definition of m / processing time. This is because the processing time is less and less determined by the set-up time with larger batch sizes. Thus, set-ups reduce capacity – and therefore, companies have an incentive to aim for such large batches. However, large batches also increase inventory – with all of the negative consequences (e.g. storage costs, ageing of shelved products etc.).



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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