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Scrapping or reworking?


Should a damaged unit be dropped from the process or should it be reworked? In order to answer that question it has to be noted, that reworking defects can turn a process step into a bottleneck, which has not been the bottleneck before. Reworking defects (and thus, defects themselves) can have a significant impact on the process flow and on the location of the bottleneck. The bottleneck can therefore not longer be determined by just looking at the capacity of the process steps. Instead, one has to take into account the capacity changes in relation to the scrap and reworking rates.

To figure out where the new bottleneck is, we have to assume that the process as a whole will be executed in a way in which the demand is met, so that there is a match between the process output and the demand at the end of the process. The process therefore needs to start with more flow units then actually needed, so that enough flow units will be left over to satisfy demand. By working the process diagram backwards and determining the new demand for each process step, we can then discover where the new bottleneck will be located.

Instead of completely scrapping a flow unit, flow units can also be reworked, meaning that they can be re-introduced to the process and given a work-over to get rid of defects. This must also be taken into account when trying to figure out whether the location of the bottleneck changes, because some of the process steps will now have to process the same flow unit twice in rework, which will have an impact on their implied utilization. The location of the bottleneck can be determined by finding the process step with the highest implied utilization.

If the demand is unknown, the bottleneck can be located through four simple steps:

(1) Assume that the flow rate is an unknown demand D (e.g. 100 flow units).
(2) Figure out the demand D_x for each process step if D is to be reached.
(3) Divide D_x by the capacity of the process step to get the implied utilization.
(4) Identify the process step with the highest implied utilization. This step is the bottleneck.

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.

Little’s law


Little’s law was named after the American professor John Little (1950s). It defines the relationship between the inventory, the flow rate and the flow time, who have all been already defined previously.

inventory = number of flow units in the process
flow rate = rate at which flow units are being processed
flow time = time a single flow unit spends in the process

Little’s law: inventory (I) = flow Rate (R) * flow Time (T)

Little’s law is important, because it can help us calculate one of the three variables. Once two of the variables are known, the third one is set by the law. This also means that, form the standpoint of an executive, two variables can be picked by management while the third one then falls into place.

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.

Capacity, bottleneck, process capacity, flow rate and utilization


In order to perform the following calculations, processing time has to be defined as the time that is spent on a certain task (e.g. one station in a sandwich restaurant). We will also need the previously introduced definitions of flow rate and flow time.

Capacity: The capacity can be calculated for every station in a business process. It is always m / processing time with m being the number of resources (e.g. workers) being devoted to the station. 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.

Bottleneck: The bottleneck is defined as the process step (station) in the flow diagram with the lowest capacity (the “weakest link”). Although the bottleneck is often the process step with the longest processing time, it is important to always look at the capacities for making a judgement.

Process capacity: The process capacity is always equivalent to the capacity of the bottleneck. It is useful, to calculate a comprehensible number, such as customers per hour or parts per day (instead of a hard to comprehend number such as 1/40 customer per second or 1/345 part per second).

Flow rate: Even though the flow rate was previously defined, the definition needs to be augmented as the flow rate being the minimum of demand and process capacity. While the flow rate logically can never be higher than the capacity of the bottleneck, it can very well be lower, if the demand is insufficient.

Utilization: The utilization tells us, how well a resource is being used. It is calculated as flow rate divided by capacity (e.g. 1/40 / 1/25). The utilization always lies between 0% and 100%.

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.

Flow rate / throughput, flow unit, inventory and flow time


The three most important performance measures of a business process are flow rate / throughput, inventory and flow time. In the following definitions, the term “flow unit” will be used a lot. A flow unit is the basic unit of analysis in any given scenario (customer, sandwich, phone call etc.).

Flow rate / throughput: The number of flow units (e.g. customers, money, produced goods/services) going through the business process per unit time, e.g served customers per hour or produced parts per minute. The flow rate usually is an average rate.

Flow time: The amount of time a flow unit spends in a business process from beginning to end, also known as the total processing time. If there is more than one path through the process, the flow time is equivalent to the length of the longest path.

Inventory: The number of flow units that are currently handled by a business process, e.g. the number of customers in a store, the number of enrolled students in an university etc. pp.

It should be kept in mind that the definition of inventory in Operations Management is different from the definition used in accounting. While the number of bottles on stock qualifies as inventory in both Operations Management and accounting, the number of patients waiting at a dentists office would not be seen as inventory in accounting – but is, in fact, inventory in Operations Management.

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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