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Calculating defect costs


When trying to calculate the costs associated with the production of defective parts and / or service results, it is pivotal to determine where in the process the defect has arisen. If an error occurs during the very first process step, little more than simple material costs are lost. If it occurs on the very last process step, we have to forfeit the value of an entire flow unit (including profit). The location of the bottleneck is especially important here. This is because defective flow units that are produced before the bottleneck have to be calculated with input prices while defective flow units that are produced after the bottleneck have to be calculated with the opportunity costs of lost sales. This insight drives the location of testing points in the process, who have to be arranged in a way which maximizes the chances of identifying and catching defective flow units before bigger losses occur.

By implementing a buffer between steps who can produce defective parts, the process flow can be protected against errors. However, producing too much inventory through so-called error buffering might conceal the necessity for improvements of the error rate.

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.

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.

The concept of responsiveness


Responsiveness is the ability of a system or process to complete tasks within a given time frame. E.g. how quick can a business respond to customer demands? If customers are made to wait, they are turned into inventory, potentially resulting in a unpleasant customer experience. Any customer waiting time is also an indicator of a mismatch between supply and demand.

Concepts for solving waiting time problems can include increasing the capacity of the resource at the bottleneck as well as increasing process flexibility in order to ensure, that capacity is available at the right time. It has, however, to be kept in mind that waiting times are most often not driven by either the capacity or the flexibility of a process but rather by variability. Variability in the process flow (e.g. customers arriving at random) can lead to unwanted waiting times even when the implied utilization is clearly below 100%. If analysis builds solely on averages and fails to consider process variability, it can thus be wrongfully concluded that there is no waiting time, when, in fact, there is.

To solve this problem, new analysis methods are needed when dealing with process variability. It is noteworthy, that those methods are only requisite when a process has more capacity than demand – if demand exceeds capacity, it can be safely concluded that there will be waiting time even without looking at the process variability.

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.

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.

Finding the bottleneck in processes with attrition loss


A process with multiple steps might have an attrition loss (of flow units) on every step. Take, for example, a process in which 300 people apply for a job opening and go through a four-step process:

Step A: 300 people apply per mail
Step B: Out of those, 100 people are invited (100/300)
Step C: Out of those, 20 people can make an internship (20/100)
Step D: One of the people doing the internship is hired (1/20)

Unlike the previously analysed processes, not every flow unit makes it to the end of the process (in the example, actually just one flow unit comes through). In this case, it would be misleading to just look at the overall capacity of each resource involved to determine the bottleneck. Instead, the following three steps need to be taken:

Step 1: Determine the capacity of each resource in the process (m / activity time or units per hour)
Step 2: Calculate the service demand for each of these resources considering the drop-out of units
Step 3: Divide the total workload by the available time to calculate the implied utilization

The bottleneck is the resource with the highest implied utilization, which does – again – not need to be the resource with the lowest capacity.

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.

Finding the bottleneck in processes with multiple flow units


Since many flow units (e.g. customers in a shop, patients in a hospital) do not at all need the very same treatment or service, business processes have to serve different needs. Processing times thus might be quite different for each flow unit as well, even the path of flow units through the process might differ. For such processes with so-called multiple flow units, we need new tools to figure out which process step can bee seen as the bottleneck.

Finding the bottleneck in a multiple flow unit scenario takes four easy steps:

Step 1: Determine the capacity of each resource in the process (m / activity time or units per hour)
Step 2: Calculate the service demand for each of these resources considering multiple flow units
Step 3: Add multiple unit demand for every resource to calculate total demand for the resource
Step 4: Divide the total demand by the capacity of the resource to calculate the implied utilization

The highest implied utilization indicates the bottleneck process step. To differentiate between the implied utilization and the “regular” utilization, its best to keep this important difference in mind:

utilization = flow rate / capacity (always between 0% and 100%)
implied utilization = demand / capacity (can very well exceed 100%)

The same calculation can also be done by looking at the required work time:

Step 1: Determine the work time capacity of each resource (e.g. 2 workers x 60 min = 120 min)
Step 2: Calculate the demand for work time at each resource considering multiple flow units
Step 3: Add multiple unit demand for every resource to calculate total demand for the resource
Step 4: Divide the total workload by the available time to calculate the implied utilization

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.
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