An Introduction to Operations Management

Lecture notes for
An Introduction to Operations Management
(taught by Prof. Christian Terwiesch / University of
Pennsylvania / online course at www.coursera.org)
compiled by Christian Reinboth
Lecture notes – week one
The four levels of performance
A look at various types of business operations – from a sandwich restaurant to a hospital – reveals,
that the typical customer evaluates business processes based on four basic levels of performance.
(1) Cost
How efficiently can the business operation deliver goods and / or services?
(More efficient businesses can offer goods and / or services at lower prices)
(2) Variety
Can the business fulfil the specific wishes of their heterogenous customer base?
(Most customers do not care about variety itself, but want their wishes to be met)
(3) Quality
Performance quality = How good is the product and / or service offered?
Conformance quality = Is the product and / or service as good as advertised?
(4) Time / Responsiveness
How fast can the wishes of the customer be fulfilled?
There are trade-offs between the four dimensions of performance, e.g. the fastest service with the
highest quality can usually not be offered at the lowest price in comparison to competitors. These
trade-offs can be used by businesses to create unique business strategies (e.g. cost leadership) as
well as to distinguish themselves from their competitors.
The tools of Operations Management can be used to help businesses to reach decisions about
such trade-offs and to evaluate measures to overcome inefficiencies. One way to detect such
inefficiencies is to compare your own business with those of your competitors – and especially
those competitors, who are positioned on the efficiency frontier with no other company being
pareto-dominant on a combination of two out of the four dimensions (e.g. no other company
is cheaper and faster or faster and offering more variability).

Flow rate / throughput, 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.
Process flow diagrams
A process flow diagram is a visual representation of the process flow. The simplified diagrams used
in the first week of the course consist of only three basic elements: Rectangles represent tasks and
activities, triangles represent inventory and arrows indicate the (temporal) flow of the process.
Capacity, bottleneck, process capacity and flow rate
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%.
Labor content, cycle time and idle time
Cycle time, labor content and idle time are indicators for assessing the productivity of a process.
Cycle time: The cycle time is defined as the time between the output of two successive flow units
(e.g. the time between two served customers or two treated patients). It is always equivalent to the
time of the longest process step.
Total labor content: The total labor content is defined as the time sum of all process steps. If, for
example, a process consists of two steps each claiming 20 seconds, the total labor content is 40
seconds.
Idle time: The idle time is defined as cycle time minus processing time. The idle time thus tells
us for how long a resource (e.g. a worker) is not able to do anything, because he has to wait for
another resource. If, for example, one worker in a sandwich restaurant prepares sandwiches while
another operates the register, the second worker has to wait for a sandwich to be finished in order
to collect on the customer. If the demand is maxed out, the idle time at the bottleneck is always 0.
Total idle time: The total idle time is the time sum of all idle time within a process.
Average labor utilization and cost of direct labor
Two important performance measures are the average labor utilization and the cost of direct labor.
Average labor utilization: The average labor utilization is defined as the total labor content divided
by the sum of labor content and total idle time. If, for example, the total labor content is 30 minutes
and the total idle time is 10 minutes, the average labor utilization is 30 / 40 = 0,75 = 75%. The
average labor utilization thus tells us the overall performance or productivity of the process.
Cost of direct labor: The cost of direct labor is defined as the total wages per unit of time divided by
the flow rate per unit of time. It tells us, how many Dollars (or Euros) are being spent in order to get
one flow unit through a process (e.g. to treat one patient or to serve one customer).
Looking at the direct labor costs is very important, even though labor costs seem to make up – at
least at first glance – only a tiny part of the overall costs. But since labor costs are hidden in all
supplies and materials a company buys (that is, the labor costs of the suppliers), a company that
might on the sheet be only paying for materials does in fact pay for externalized labor.
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 above.
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.
Inventory turns
One other important indicator for the evaluation of business organisations (not processes) is the
inventory turnover rate (or number of inventory turns). The turnover rate answers the question of
how much time a Dollar (or Euro) bill actually spends inside an organisation with the organisation
being seen as a black box of sorts. A company has a competitive advantage if it can turn its
inventory faster then the competitors can.
inventory turns = cost of goods sold (COGS) / average inventory
The inventory turnover rate is especially important because inventory creates costs. A business has
to invest money in order to produce or buy an item and store it over a period of time, especially if
the item might also loose value over time. The important indicator here are the inventory costs per
unit, which are calculated as average inventory costs over inventory turns per unit time. If, for
example, the annual inventory costs are 30% and there are 6 inventory turns per year, the per
unit inventory costs are at 5%, meaning that for every unit sold the company has to calculate
5% inventory costs sort of as an internal tax rate. Inventory turns are therefore a good
indicator on how productive an organisation uses its capital.
Why do companies hold inventory?
There are five major reasons for holding inventory:
(1) Pipeline inventory
A pipeline inventory is the minimum inventory an organisation needs in order to function. E.g. a
producer of wine that needs to age for two years in order to be sold needs a minimum inventory
of wine for two years in order to exist.
(2) Seasonal inventory
A seasonal inventory is helpful, if an organisation wants to produce at a constant (cost-efficient)
capacity, yet the demand varies with the seasons. E.g. a toy company can cheaply produce at at
steady pace and build up a seasonal inventory for higher sales during the Christmas holidays.
(3) Cycle inventory
A cycle inventory is helpful if keeping an inventory saves costs associated with buying supplies on
time. A private household will, for example, keep a box of water bottles in the cellar for practical
reasons instead of satisfying the demand for water at the store every time it comes up again.
(4) Safety inventory
A safety inventory is a buffer agains high external demand, e.g. a burger chain keeping an inventory
of pre-made burgers so that customers can be satisfied immediately. Safety inventories are closely
associated with the meme “buffer or suffer”, meaning that if a process is not able to buffer for
variabilities (such as an unexpected external demand) it will loose on flow rate.

(5) Decoupling inventory
Whereas the safety inventory can be seen as the buffer against heightened external demand, the
decoupling inventory can be seen as the buffer against heightened internal demand. Such an
inventory decouples supply from demand and supports a higher (and steadier) flow rate.
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
diagram 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
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.
Lecture notes – week two
What is productivity?
A very basic definition of productivity – the average measure for the efficiency of a production
process – would just be the ratio between process output units and process input units. The labor
productivity might, for example, be four output units (such as car or netbook parts) per labor hour.
If one does not focus on a specific form of process input units (such as labor hours), but instead
takes all kinds of input units into account (such as materials, energy, labor etc.), we are talking
about the so-called multifactor productivity. Since both process input units and process output
units are often difficult to measure and compare, fiscal measurements such as revenue and
costs can be used instead. Fiscal measurements are also needed for comparing different
input units (work time, materials) in the already mentioned multifactor scenarios.
These considerations lead to some basic mathematical expressions:
productivity = output / input
labor productivity = output / labor time
transformation efficiency = output / capacity
multifactor productivity = output (in $) / (capital + labor + materials + services + energy) (in $)
The two main drivers that reduce productivity are waste and inefficiencies. Inefficiencies and waste
can be seen as the distance between a company and the efficiency frontier.
Waste, waste reduction and lean operations
During the first week, the concept of idle time was introduced. In general, idle time is the time
during which a resource is not fully used because of low demand or bottleneck restraints, which, in
turn, reduces productivity. Idle time is, however, not the only (and not even the biggest) source of
waste. Taiichi Ohno – the father of the Toyota Production System – once stated that “moving is not
really working”, which basically means that a loss of productivity does not necessarily need to be
connected to idle time. While, for example, the re-configuration of a machine or the movement of
materials is clearly “working time”, those activities are not directly adding value to the process.
The seven main sources of waste are:
(1) Overproduction: Producing sooner or in greater quantities than the customer actually demands.
Overproduction leads to higher storage costs and material losses (e.g. because food products must
be thrown away after a certain shelf time) and reduces the number of inventory turns. The solution
to overproduction is to match supply and demand as closely as possible.
(2) Transportation: Unnecessary movement of people and / or materials between process steps.
Transportation causes costs and production delays and thus often reduces the overall efficiency of a
process (e.g. peeling crabs caught in the North Sea in Africa before shipping them back to Europe).
The best way to reduce transportation waste is to optimize the process layout (“short ways”).
(3) Rework: Correction processes within the main process. Rework is always the result of a failure
to do something right in the first place. Reworking something creates double labor costs while not

actually producing more, thus productivity is reduced. It also requires holding additional resources
just for reworking, so that normal production processes are not disrupted by reworking processes.
The solution lies in – very simply put – making it right the first time as wells as in analysing and
subsequently eliminating sources of failure.
(4) Over-processing: Doing more than the customer requires, e.g. keeping a patient in the hospital
for a longer period of time than medically absolutely necessary. Over-processing is a form of waste
that might have positive reasons such as workers having higher standards than the customers or
employees being overly proud of their work. Still, over-processing adds to waste and thus to the
reduction of productivity. One possible solution to this problem lies in the definition of quality
and process standards, to which all employees then have to adhere.
(5) Motion: Unnecessary movement of people or parts within a process (similar to #2 but on a
smaller scale), e.g. an office worker having to switch rooms every couple of minutes because the
files are stored in different cabinets. One solution to this problem lies in optimizing the layout of
workspaces (ergonomic design) in order to minimize unnecessary motion.
(6) Inventory: Too many flow units in the system. Inventory has already been discussed at length
during the first week. It is by far the biggest source of waste in most companies and costs a lot of
money because inventory requires costly storage space and drives down inventory turns. Possible
solutions include “on time” production schemes and the reduction of so-called “comfort stocks”.
(7) Waiting: Employees or resources just sitting around waiting for something to happen, e.g. for a
meeting to start, a customer to call or a customer waiting to be served. Per definition, waiting is an
unproductive use of time. Waiting waste includes idle time as well as long flow times.
While the first five sources of waste are resource-centred (What did the employee do? Did it add
value to the process?), the last two sources of waste are really an expression of Little's law. Some
scholars point out that waste of intellect (ignoring the ideas of employees for problem solving and
process improvement because of hierarchical concerns) can very well be seen as an additional
eighth source of waste. A production system that tries to reduce all types of waste at once is
commonly called lean production.
Finance and productivity
For a for-profit organisation, the overall target is not and can not be increasing productivity or
optimising processes – it is making money. However, understanding the value-adding operations
has to be a core goal for every business executive. This is especially the case when operations are
constrained by the bottleneck (and not by low demand). In those cases, even minimal operational
improvements at the bottleneck can have a very high impact on the revenue.
KPI tree
A KPI (KPI = Key Performance Indicators) tree is a tool for visualizing the relationship between
operational variables and financial variables. A KPI tree can be the starting point for a sensitivity
analysis, which allows the identification of those variables, that have the most impact on profit.
Overall equipment effectiveness framework
The term overall equipment effectiveness framework (OEEF / OEF framework) refers to a method
for evaluating the productivity of machines and other resources. In a first step, all the time that is
available on a certain resource is added up. During the following step, the waste times (idle time,

time spent on failures, maintenance time etc.) are identified and also added. By subtracting the
wasted time from the total time, one can then calculate the productive time of the resource. The
ratio between productive time and available time is the overall equipment effectiveness of the
resource. The OEF framework was first introduced by the consulting company McKinsey.
When calculating the OEF framework, we can differentiate between three types of waste times:
- Speed losses: idle time, reduced speed
- Downtime losses: breakdowns, changeovers
- Quality losses: defects, restarts, operator faults
Takt time, target manpower and line balancing
The expression of takt time is derived from the German word “Takt” for the pace of a piece of
music. In operations management, the takt time is defined as the maximum time it can take to
produce a unit in order to keep up with demand. If, for example, the demand is at 6 units per
minute, the takt time would be at 10 seconds per unit.
Once the takt time has been determined, the target manpower can be calculated as the ratio of total
labor content (the time sum of all worksteps needed to produce one flow unit) and takt time. The
target manpower is the number of employees (or other resources) needed to operate the process at
takt time if the work could be divided evenly between them Since this is an idealized calculation,
the outcome will most likely not correspond exactly with reality, one reason being that it is not
always possible to evenly split work between employees if different skills are needed. Still,
calculating the target manpower provides a good starting point for line balancing.
Line balancing is the process of dividing an existing workload as evenly as possible between all of
the available resources in order to increase overall productivity. If, for example, one workstation
has a lot of idle time, maybe it can take over some of the workload from the workstation at the
bottleneck. The basic line balancing procedure consists of four steps:
(1) Calculate the takt time
(2) Assign tasks in a way that keeps all processing times below the takt time
(3) Make sure that all tasks are assigned
(4) Minimize the number of workers needed
The general ability of an organisation to adjust its capacity and scale it up and down in order to
adjust to changes in demand (the so-called staffing to demand) is an important form of flexibility,
which can be achieved e.g. with temp workers or overtime work. A special form of line balancing
is the so-called dynamic line balancing, which includes walking around the workstations during
production, looking for pileups and rearranging resources in order to keep up with demand.
Standardization
One common mistake in process optimisation is to just look at average processing times as well
as at idle times. Instead, it is also important to evaluate the time differences between employees in
order to find examples for best practice approaches. Those approaches can then be looked at while
composing standards. The goal here is to figure out how exactly the top-performing employees
achieve their results – and to find a way in which other employees learn something from them.

Lecture notes – week three
Product variety
There are three different basic forms of product variety:
(1) Fit variety: Customers need to be able to buy different versions (sizes, shapes etc.) of a product
if the product is to be of use for them (personal utility maximization). The more the characteristics
of a product move away from the customer specifications, the less use it has for that customer. This
kind of variability is also known as horizontal differentiation. Examples are different sizes of shoes
or t-shirts, different locations of shops or airports and different departure times of trains or planes.
(2) Performance-based variety: Companies might sometimes offer products of more or less
quality (e.g. a “high end” product and a “standard” product), so that customers can buy according
to their quality needs and / or their financial abilities (price discrimination). This kind of variability
is also known as vertical differentiation. Examples are computers with different processor speeds,
mobile phones with different weights and diamond earrings with different diamond sizes.
(3) Taste-based variety: Customers also want products to come in different versions appealing to
their personal taste in colour, design, sapidity etc. This kind of variability is the outcome of rather
“rugged” individualistic utility functions with local optima and no clear common thread.
A company may therefore choose to aim for more variety for one of the following reasons:
• Their heterogeneous customer base does not accept "one size fits all"-products
(taste-based variety)
• They want to make use of price discrimination mechanisms and offer different quality
versions for different income groups (performance-based variety, market segmentation)
• Their customers actively demand more variety (e.g. by wanting to be offered a broad
range of foods in a restaurant as opposed to being offered the same food every day)
• Saturating a niche and thus preventing competitors from being active in that niche
• Avoiding a direct price competition with competitors by product differentiation
Set-up times
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.).
Mixed-model strategies
Since larger batch sizes lead to (the need for) more inventory, the batch size has to be balanced and
chosen with both the positive (greater capacity) and negative (larger inventories) results in mind. A
strategy, in which smaller batch sizes (down to a size of one just flow unit) are chosen, is called a
mixed-model strategy. Since smaller batch sizes have a negative impact on capacity because of the
set-up time, reducing the set-up time is an important enabler for running a mixed-model strategy.
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.

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
How does product variety affect distribution systems?
The more the demand is divided into smaller and smaller segments, the harder it is to predict.
Once there is more product variety, demand is going to become variable as well. Thus, statistical
indicators such as mean and standard deviation are needed to cope with the so-called variability of
demand. If demand streams are combined, the standard deviation of the combined demand goes up
slower than the standard deviation of the previously uncombined demands. Such an aggregation of
demand is called demand pooling and is an important method for reducing statistical uncertainty.
Reductions in uncertainty can also be achieved through variance reduction or stock building.
Shortening set-up times in order to increase flexibility
Every set-up process can be broken up in external and internal activities. External activities can
be completed while the station in need of the set-up is still running. Such activities can be moved
up front, e.g. preparing patients outside of the operating room while another patient is still being
operated on inside. If set-up times can also be improved through other activities (standardisation,
process optimisation etc.), flow unit types can be changed more often and flexibility is increased.
This idea lies at the heart of the mixed-model production, which also profits from configuring a
network of production facilities for pooling in order to be more flexible in catering to demand.
Better process design
Since the design phase of a process largely determines the later production costs, the question of
how to reduce the negative effects of variety on process performance by clever process design is
becoming more and more important.

One successful method of improving process design is the so-called delayed differentiation. This
method allots keeping as many process steps identical as possible for all products before splitting
the production process up. The decision, which variant of a certain product is actually produced is
thus delayed until the very last possible point in the process. This process design is optimal for
products that differ only mildly (e.g. t-shirts of different colour). Delayed differentiation is made
easy, if variable elements of the product can be isolated (the so-called moduled product design).
An interesting example for delayed differentiation is the casing around the (otherwise completely
identical) iPhones. The hype over the iPhone also shows, that even hugely successful products do
not necessarily need to offer a lot of variation. The reason for this is, that customers can also be
overwhelmed by too much choice. To understand this, one has to understand that most customers
only care about the characteristics e.g. of a computer that provide utility for them – not about the
actual technical specifications (e.g. gaming performance compared to the actual graphic card of a
computer). Companies thus might want to think about limiting their product variety in order to not
make customers nervous by offering too much choice and keeping them from purchasing a product.
Lecture notes – week four
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.
Variability in demand
If there is more demand than capacity, the implied utilization rate rises above 100%, which makes
waiting time unavoidable. The more interesting cases are those, in which there is waiting time even
though the implied utilization rate is below 100%. Such waiting time stems from demand variability
generated by the somewhat random nature of most demand processes, e.g. many customers showing
up at once at some point in time and no customers showing up at all at some other point in time.
In order to calculate with demand variability, we need to define arrival time, inter-arrival time and
average inter-arrival time. The self-explanatory arrival time is defined as the time, when customers
arrive at a business. The inter-arrival time is thus defined as the time between subsequent customer
arrivals. If demand is random, both the arrival times and the inter-arrival times will be drawn from
an underlying statistical distribution (often a Poisson distribution). The average inter-arrival time is
usually denoted with a.

Another important parameter is the coefficient of variation of the arrival time, which is calculated as
the standard deviation over the mean and is denoted as Cv_a. The coefficient of variation is a way
to measure the standard deviation against the mean of the distribution. This is useful, because the
standard deviation itself is not really a good measure for variability, since it does not express
whether a 10 minute deviation is a lot or not.
If the inter-arrival times are drawn from an Poisson distribution, the coefficient of variation is
always 1. This knowledge can be used to calculate other parameters considering this formula:
Cv_a = standard deviation (of inter-arrival times) / mean (of inter-arrival times) = 1
Variability in processing
Variability is not limited to the demand process, but also occurs in processing. The calculations are
basically the same, with the average processing time being denoted with p and the coefficient of
variation being denoted with Cv_p. The coefficient of variation can be seen as a measure of the
degree to which a work process has been standardized.
Calculation of the time in the queue / waiting time
The time in the queue is calculated as follows:
time in queue = activity time * (utilization / 1 – utilization) * ((Cv_a^2 + Cv_p^2) / 2)
with:
activity time = service time factor (average processing time p)
(utilization / 1 – utilization) = utilization factor
((Cv_a^2 + Cv_p^2) / 2) = variability factor
Since the utilization factor is calculated as (u / 1-u), this means that as the waiting time gets higher,
the utilization gets closer and closer to 1. The formula for the time in the queue always delivers an
average value. This so-called waiting time formula can only be used if the demand is lower than
the capacity. If the demand is higher than the capacity, the waiting time will ultimately not be
driven by variability, but rather by insufficient capacity.
The total flow time of a flow object can be calculated as:
total flow time = time in the queue + processing time
Calculation of the time in queue with multiple resources
The previous session was based on the idea, that there was only one resource (one machine, one
worker, one physician) doing all the work (m = 1). But what happens if the capacity is determined
by more than one resource? Calculating waiting times with multiple resources involved makes it
possible to derive staffing plans – or to, in other words, answer the highly important question of
how many resources will need to be put to work in order to meet a waiting time requirement.
The time in the queue with multiple resources is calculated as follows:
time in queue (for multiple m)
= (activity time / m) * (utilization ^ (square ((2(m-1))-1) / 1- utilization)) * ((Cv_a^2 + Cv_p^2) / 2)

= p / m * (u ^ (square ((2*(m-1)-1) / 1-u) * ((Cv_a^2 + Cv_p^2) / 2)
If the time in the queue is known, Little's law allows the calculation of the inventory:
inventory in queue = flow rate in queue (= 1 /a) * time in queue
inventory in process = utilization (u) * number of resources (m)
inventory in total = inventory in queue + inventory in process
Seasonal data
In practice, demand sometimes exhibits seasonal ups and downs with spikes in demand at certain
busy hours, days or weeks. It would be misleading to just ignore those spikes and assume that the
demand during the spikes is drawn from the same statistical function as the rest of the demand. In
those cases, the analysed timeframe has to be sliced up into equal time intervals and every interval
has to be taken as the basis for a separate calculation.
Devising a staffing plan
How many employees will it take to keep the average waiting time for a certain service under a
minute? A simple way of answering such a question and coming up with a staffing plan is doing
the calculation of the time in the queue and to then manipulate the number of employees until a
certain average waiting time is met. When seasonal demand (seasonality) is to be observed, the
calculation has to be redone for every time slice of the day, week or month in consideration.
Reducing waiting time by pooling demand
By pooling demand, the inter-arrival times are shortened and thus the specific demand goes up
(which is intuitive, since pooling demand basically means combining different demand streams).
While the utilization rate is not effected by demand pooling, the waiting time is shortened because
some inefficiencies (idle time at station A while station B is overwhelmed) are eradicated. However,
pooling more and more resources together also decreases the overall efficiency once the demand is
met. Therefore, companies need to find a viable balance between efficiency and responsiveness.
What main benefits and costs are connected with pooling in the context of waiting time?
• Pooling assumes total flexibility (Spanish call center agents will not be able to answer to
German customers, even if the call center company decided to pool all calls together).
• Pooling increases the complexity of the workflow, since demands needs to be shifted
between resources who might be locally apart (e.g. two hospitals or two plants).
• Pooling interrupts the continuity of interaction between the flow unit (customer) and the
resource (worker) and can thus hurt the customer experience because customers will not
want to see a different physician or a different financial consultant on every separate visit.
Order of customer service
All previous contemplations were based on the idea that customers would be served in exactly the
order in which they arrived. But is that an optimal procedure? The idea behind sequencing (which is
also called triaging or prioritizing) is to determine, who should be served first, which is not always
the customer who came in first (e.g. emergencies in a hospital). There are four basic models:

(1) First come-first-serve
This quite self-explanatory model (which is also known as FIFO = first in – first out) is easy to
implement, seems fair and has the lowest variance of waiting time.
(2) Sequencing based on customer importance
Examples for this model are the prioritized treatment of emergency cases in hospitals as well as
serving long-time or more profitable customers first.
(3) Shortest processing time rule
This model minimizes the average waiting time by putting the shortest job first and the longest job
last. This does not impact the total working time but ensures, that those customers with the shortest
working times get served more quickly. The problem with this model is, that it gives customers an
incentive to claim false processing times (“I need only five minutes.”) in order to get served fist.
For this reason, this rule is usually only used in manufacturing or in digital processing, where
processing times can be accurately predicted (and no human customers are directly involved).
(4) Appointment rules
Some business are trying to solve the problem of customers not showing up in regular intervals by
forcing them to show up in regular intervals through appointments. However, this model is quite
impractical for many business (think about fast food restaurants or supermarkets) and downright
impossible for others (think about emergency room treatment where individual demand is nearly
impossible to predict).
Calculating the flow time efficiency
Instead of simply trying to optimize processes in order to cut down on waiting time, it is
also important to look at the customer experience as a whole. How does, for example, a patient
experience an appointment at a physician? The customer experience in this specific case does not
start in the waiting room at the clinic, but also includes driving, parking, checking-in, filling out
forms, driving back home etc. We thus have – so far – looked only at a small part of this entire
customer experience. Many activities along this line of activities are not adding any value for the
customer – for example, getting to the doctors office is important, but does not cure any sickness.
The question of exactly how much time spent in a process (from the customer's perspective) adds
any actual value for the customer can be answered by calculating the flow time efficiency:
flow time efficiency = total value add time of a unit / total time a unit is in the process
This analysis is the basic idea behind the so-called value stream mapping. Here, every process is
split-up between onstage actions (which are visible to the customer), backstage actions (which are
invisible to the customer) and customer actions (which are those actions that the customer performs
by himself) as well as additional support processes. Possible ideas for optimising the waiting time
are moving work off stage (e.g. doing a rental car check-in via the internet), reducing customer
actions (e.g. not retake basic medical information at each hospital visit), removing steps that
offer no value (if possible) or avoiding too much fragmentation due to specialization.

Waiting behaviour of customers
The previous models all assumed, that customers would wait as long as it takes in order to get
processed. In more realistic models, customers will leave the process before getting served because
the waiting time gets too long. Some customers will not even enter the system, if the the demand is
visibly too high (long waiting lines). In these cases, the outflow (completed customers) will differ
from the inflow (customer demand). But what fraction of demand will a business be able to serve?
There are four basic models of possible customer behaviour (which can additionally be mixed):
1) All customers wait in line forever
2) Some customers leave the line after a while
3) Some customers do not enter if the line is too long
4) Waiting time is absolutely impossible (inventory = 0)
Once one knows the probability, with which an incoming customer is not served, one can calculate
how much business a company is missing because of waiting times. Instead of working with the
rather complex formula for calculating this probability, the Erlang Loss Table can be used. This
table denotes all probabilities for combinations of m (number of resources) and r (for the ratio
between the processing time p and the arrival time a).
Lecture notes – week five
The two dimensions of quality
There are tow basic dimensions of quality: Performance quality measures to what extent a product
or service meets the expectations of the customer. Conformance quality measures if processes are
carried out the way they were intended to be carried out.
Conformance quality
The root cause for quality problems is process variability. Were it not for process variability, every
run through a process would result in the optimal output or in the very same error, which would
then be easy to detect. However, due to process variability, some runs through a process result in
optimal outcomes while others result in different kinds of errors. With some very basic statistical
probability tools, we can assess the chances of such errors and defects occurring during a process.
To calculate total error probabilities for an assembly line, one has to look at the error rate of each
work step and calculate their yields (the percentage of error-free flow units the work step produces).
The yield of the process is defined as the percentage of error-free parts which are produced by the
process – which of course depends on the yields of the various work steps. The total process yield
is thereby simply the product of the individual yields:
process yield = yield 1 * …. * yield n
It is noteworthy, that even small defect probabilities can accumulate to a significant error rate, if
there are many steps in a process. For example, if a process workflow consists of 10 steps with
every step having a low defect probability of only 1%, the chances of an completely error-free
product leaving this workflow are only 0,99^10 = 89,5%
The Swiss Cheese model explains, why defects or procedural errors sometimes do not get noticed,
even if there are highly efficient quality checks in place: Since every slice of Swiss Cheese has

some holes (defects) in it, there is a small probability that holes will line up in a way that creates a
hole through a staple of cheese slices. This is then akin to multiple quality checks failing during the
production of the same flow unit – though the chances of this happening might be low, it is bound
to happen from time to time. This insight is also the main reason behind redundant checks, which
means checking a quality attribute more than once to etch out all errors that might occur. With
redundancy, a process hat to fail at multiple stations in order for the process yield to be affected.
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.
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.

The Kanban cards concept
A Kanban system is a visual way to implement a pull system. The basis of the system are the so-
called Kanban cards, which basically are work authorization forms. Only if such a Kanban card is
issued (which happens due to demand), work on the next set of units is begun. Since the inventory
kept can never grow bigger than the sum of Kanban cards in circulation, the system allows users to
keep a definitive cap on the inventory. By setting the right number of Kanban cards, one can adjust
the inventory to the needs of the current demand structure. This corresponds with the idea of a pull
system: Rather then having everybody in the process work as hard as possible and pushing the flow
units forward, the demand pulls the flow units through the process via the Kanban cards. Action is
only taken if demand is there, not because there is idle time to spend or flow units are arriving
from some other station in the process. Kanban cards thus support a just-in-time production.
Measuring quality with the capability score
To calculate the capability score (e.g. of a machine used in production or of a supplier), only three
variables are needed: The lower and the upper specification level as well as the standard deviation:
LSL = Lower Specification Level = flow unit needs to have at least XXX (measurable size)
USL = Upper Specification Level = flow unit needs to have no more than XXX (measurable size)
capability score = width of the specification level (USL – LSL) / 6 * standard deviation
Because of the sixfold multiplication of the standard deviation (sigma), this is also known as the six
sigma method. The capability score of a distribution can be translated into the probability of defect
through the normal distribution function of standard spreadsheet software such as Excel.
Statistical process control
There are two types of variation in production and service processes – common cause variation and
assignable cause variation. The common cause variation is the “usual” variation that is caused by
statistical anomalies in the production or service processes. The assignable cause variation is
variation caused by a specific change in the underlying process structure.
There is a simple way to distinguish between common cause variation and assignable cause
variation: Common cause variation falls within the previously mentioned control levels (upper
control limit, lower control limit). Assignable cause variation falls outside those control limits.
The control limits can be set as three standard deviations in each direction from the mean. A
field with a width of six standard deviations will contain 99,7% of all cases. If a sample lies
notably outside of these limits, assignable cause variation is likely to be the reason.
The purpose of so-called statistical process control is to constantly monitor the process output
in order to be alerted to the occurrence of assignable cause variation almost immediately. In the
famous Toyota production system, this is realized through a detect – stop – alert framework which
catches defects quite quickly. This is critical, because defects tend to (a) produce more defects over
time and (b) cause higher monetary losses once the defective flow units get through to the process
bottleneck. Both problems provide huge incentives for figuring out how to detect defects as soon
as possible. Some techniques that can be effectively used here are the drawing of fishbone diagrams
as well as laddering. The idea behind both techniques is to basically ask “why-questions” over and
over again until the actual root caus(es) of defects is (are) identified.

An Introduction to Operations Management

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An Introduction to Operations Management