###### tags: `Introduction to Operations Management`
# Productivity
## Introduction
### Productivity as a Major Challenge
:::info
“The conservation of our national resources is only preliminary to the larger question of national efficiency. [quote by a USpresident]”
Who is the president quoted here?
In this module: Subway + Airlines
:::

### Introduction to Productivity
Turns out the person who said this was Theodore Roosevelt. More than a hundred years ago, Frederick Winslow Taylor wrote a wonderful book known as The Principals of Scientific Management. This was the opening line of the book. Productivity was a major theme a hundred years ago, and is still a very current topic today.

### Formal Definitions
:::info
**Basic definition of productivity**
Productivity = Units Output produced / Input used

**Example: Labor productivity**
Labor productivity = 4 units per labor hour (looks a lot like an processing time)

**Multifactor productivity**
Productivity = Output / (Capital$ + Labor$ + Materials$ + Services$ + Energy$)

**Waste and Inefficiencies**
Output: productive time; input: total time
Some measures of productivity have natural limits (e .g . labor time , energy)
What reduces productivity?
:::

As mentioned previously, we can define productivity as the ratio between the units of output produced and the input that is used. For example, we can define labor productivity as 4 units per labor hour.

Units might be insurance claims, it might be vehicles or it might be patients. And so that you can think about the output produced, the vehicles, the insurance claims, or the patients per labor hour as a productivity measure. Notice that those are exactly the processing time that we discussed previously.

The beauty of this example is that the only input is labor time. If you think about affirmative very high level perspective, there are many other input factors including capital, labor, materials, services that the firm uses and energy.

People refer to the multifactor productivity as the output divided by the dollar values of all of these input factors. Now stick with the example for labor productivity a little longer.

What keeps us from having a perfect productivity? Think about the output in the productivity definition as productive time or value add time and the input as the total time.

Productivity is then simply the percentage of labor time that is spent productively.

Now clearly, you cannot have a productivity in this case of higher than 100%. You can never get more than 60 productive minutes out of a worker per hour. Similarly, if you think about the energy efficiency of your house, you might measure the output as the temperature gains that you have in your living room and the input as the amount of oil or gas that you burn in the basement in the heater. Again, you will never generate more heat in the living room than you have consumed in terms of primary energy in the basement.

The interesting question on both of these examples are really what we'd use as the productivity.

This gets us to the idea of waste and inefficiency. Wastes are those things that are driving down productivity and are really at the heart of understanding the productivity in an operation.

### The Efficient Frontier
With the concept of inefficiency in mind, let's revisit the example from the introduction.

This was a group of call centers that we benchmarked along the dimensions of responsiveness and productivity.

For a call center, it is easier to achieve a high productivity. Just staff so that your utilization is really, really high. Now the problem with that of course, is that your responsiveness will be very poor if you have a very high level of utilization. On the other hand, you can increase your responsiveness if you keep your utilization very, very low. Good for your responsiveness, bad however, for your productivity that there exists a tension between those two forces, responsiveness and productivity. Now consider call centers A, B and C. All of these call centers are in a line that we've previously defined as The Efficient Frontier in the industry. This means that there is no player, no company, no call center that dominates competitor A, B or C. When I say dominates, I mean firms that are both faster than we are, and at the same time also cheaper.

Now you notice that competitor D is not on the frontier. For competitor D we have a distance to the frontier, and that is what an inefficiency looks like at this very high level perspective.

### Example: The US Airline Industry
Let's bring the concept of the efficient frontier to life by looking at some data from The US Airline Industry. What I'm showing here is on the X axis, I'm plotting the efficiency of the major U.S. carriers. Here efficiency is measured by how much it costs an airline to produce a certain number of seat miles. On the Y axis I'm showing what the airline is able to command in terms of its prices for these miles.

Observe the Frontier. Observe how these airlines are lining up on a line that looks like this. On the one extreme, you have Hawaiian, which is not able to get high prices, but because of its very focused route structures, able to provide an amazing efficiency. On the other extreme, you have US Airways.

The company is clearly able to command high prices, but has a horrible efficiency. You notice here how Southwest has been able to break that Frontier and shifted upwards to a new level.

Southwest entered this market in many routes by providing its superior operations, allowing it to charge almost the same prices as these legacy carriers, yet operating at an amazing level of productivity.


Now the data that I just showed you was data for the year 1996. Let's take a look what has happened in the airline industry since then. This is updated data from 2011.

We have the same X axis, the Efficiency, and the same Y axis, the Yield. Notice how Southwest, previously a star on the productivity side, is now simply in the middle of the pack. We'll explore the reasons of Southwest's decline in productivity later on in this module. You'll also notice how the legacy carriers, American, United, US Airways, Continental, Delta, have basically suffered an enormous loss in pricing power. They have kept more or less efficiency, but they have dropped down on the revenue side. The new darlings from an operational perspective are companies such as JetBlue and Virgin America. They have redefined the Frontier and the operations of the airline industry.

We define productivity as the ratio between output and input. We will pick up that definition later on in this module when I introduce a concept of productivity ratios, which is a very powerful tool that can help you analyze aggregate firm-level data and compare your productivity with the productivity of peer companies in your industry. We also observe the enemy of productivity, inefficiencies and waste. We defined inefficiencies and waste as the distance between your operational performance and the efficient frontier in an industry.

## The Seven Sources of Waste
The absence of waste makes for high productivity. The last couple of years it has become very fashionable to talk about lean operations. This session today is about lean. It is about waste. And it is about waste reduction which is the process of making an operation lean. Taiichi Ohno, the former chief engineer of Toyota, wrote a wonderful book outlining the principles of the Toyota Production System. Ohno writes, that moving is not necessarily working. This is really deep, let me repeat this. Moving is not necessarily working. And on a session on process analysis, we talked about idle time as a way that workers are unproductive. They're hurting us on labor productivity.

Ono, by outlining these seven sources of waste that we're going to talk about in this session, reminds us that there are other ways you can be unproductive than being idle.

We'll talk about the Toyota production system in great length, later on in this course. A cool byproduct of this is that you're going to have a little bit of Japanese vocabulary to impress your friends and your coworkers. Waste and and this session is about the seven sources of waste.

### Overproduction
So first of the seven sources of waste is overproduction.

At a risk of upsetting my fellow Germans, let me share with you the following example. The average German trashes 81.6 kilograms of food every year. The reason for that? Germans like to buy in large package sizes. This, however, creates a mismatch between supply, what they get into their fridge, and demand, which is what they eat. This is inventory, which we know is bad just from a working capital perspective of the household. But since inventory can also get obsolete, described problem.

### Transportation

Let me illustrate the second source of waste, transportation was another German example. Crabs are fished in the North Sea next to the German and Dutch coastline. They're then shipped 2,500km south to Morocco. Labor is cheap in Morocco and that's where the food is prepared. It is then shipped back to Germany.

This shipment back and forth truly reflects on this idea of moving but not really working. There is no direct value ads by shipping these scrubs up and down through Europe.

Whenever transportation occurs, we see a poor layout of the process. And we are creating lots of extra work that is not necessary at length to the productivity of the operation.

### Rework
The third form of waste is rework. Rework refers to repeating or correcting an operation because of quality problems.

An old Japanese quality saying goes, do it right the first time.

Rework is a pain. Rework consumes capacity and take it away from flow units that could be otherwise served. Rework is, by no means, limited to the world of manufacturing. For example, in healthcare operations, readmission to the ICU is often referred to as a bounce back. Patients get discharged from the ICU but then later on, develop complication in the regular units and bounce back to the ICU. From an operations perspective, this is rework. Re admissions to the hospitals are also a form of rework. Dealing with re admissions has been a major component of the Affordable Care Act, and has become a big thing these days in the healthcare operations community.

### Over-processing
Let me illustrate the first source of waste. Over processing is another healthcare examples.

Oftentimes, you'll notice, when you're in a hospital, it's not entirely clear how long are you going to stay there. The discharge of a patient is crucial for the capacity management of the hospital, but often the hospital lacks clear policies and standards of how long the patient should stay. To the extent that the patient stays longer than needed, the hospital is wasting through over processing. In the day to day life, over processing simply corresponds to stirring a fully mixed cup of coffee. Again, typically the driver behind over processing is that the operator really doesn't know what the exact standard of his work is going to be.

### Motion
Just as transportation was a form of moving, but not working. You often find a similar effect within a work space.

The idea of unnecessary motion, the fifth source of waste, is that you can achieve tremendous productivity improvements by a careful and economic design of the work space. You see this when you look at great athletes. I'm a big cycling fanatic. I often admire the great athletes as they sit on their bike with their upper body not moving at all, all the action being in the legs. They get all the energy, all their capacity is moved towards where it matters, opposed to moving the upper body, which really doesn't help them get forward on the bike.

### Inventory

The sixth source of waste is inventory. Warner viewed this as the biggest waste of all.

His view was product has to flow like water. Wherever there's inventory piling up, we have a mismatch between supply and demand. For physical products, inventory takes the form of raw materials, work in process inventory, or finished products.

This type of inventory is bad because it costs us money. Remember our discussion on the inventory turns. But it is also bad because it requires storage space.

Inventory, as we previously discussed, is by no means limited to the world of manufacturing. Loan applications in a bank might not require a lot of real estate, but certainly an expensive form of inventory because it leads to customer wait time which is a sudden source of waste.

### Waiting
Waiting the seventh and final source of waste is often a direct consequence of inventory.

This is a situation where a flow unit is waiting for a resource. However I noticed that also the opposite can happen. The resource can wait for the flow unit. In this case, waiting takes a form of idle time. Something that we have discussed at great lengths, earlier on in the process analysis module.

### Wasteful vs Lean
The impact of of Arnaut work, and the success of the production system, was long ignored in the western world.

It took until the 1980s and team of researchers of the International Motor Vehicle program around Jim Womack to demonstrate the real power of the Toyota production system. The researchers went out into the world and benchmarked the productivity of automotive plants. In this table here, we see a comparison between a GM plant of the 1980s and a Toyota plant. The table compares a couple of dimensions.

Gross assembly hours per car captures the labor content that we've introduced previously. You'll notice that the Toyota employee take only about half of the time to put a vehicle together. Assembly defects for 100 cars captures how many rework needs there are at the end of the red line. You notice again there are factor of three difference in productivity.

Similar patterns exist for the real estate requirements. And then more significantly in terms of the inventory. Our GM at the time took two weeks of inventory. Toyota employees only required two hours of inventory set at their assembly line.

### Understand Sources of Wasted Capacity

So this was the seven sources of waste. You notice that the first five sources, overproduction, transportation, rework, over processing, and unnecessary motions. In many ways we are resource centric. They look at the worker and ask what did the worker do in the last hour.
Play video starting at :7:43 and follow transcript7:43
Pointing out that not every thing that the worker does is actually valuette.

An experienced management consultant has once told me the following trick. When you go through the process, when you visit a restaurant, a manufacturing plant, just stand still.

Then you turn around for about 360 degrees. And you count the workers that you see as you're doing this. Count those that are directly adding value to the customer. And count those that are idle, or that our engaged and reworked transportation motions or other things that are waste. This gives you very quickly and very casually a sense of how much wastage is in the process. Now, a word of caution. Arguably, this is not how you're going to make yourself popular at work, so don't just stand there turning around and coming up with wise thoughts. But I think you will agree with me that lots of the things that we do at work is not necessarily adding value to the customer. As Ohno reported, moving is not necessarily working. The last two sources of waste, inventory and waiting, are really two sides of the same coin. This is just a reflection of little slow. They look at waste from the customers, from the floor unit's perspective. Pointing out that most of the time, we just sit in the process without getting any value for it. Now, people often refer to an eighth source of waste. This is the waste of intellect. Oftentimes, managers think of their workers as human robots. Just there to execute orders.

Wasting the intellect of workers misses the opportunity of engaging the workers in problem solving and process improvement. This is one of the key ideas behind Kyzan, a piece of Toyota production system that is upon worker involvement.

## Link to Finance
In most organizations I've worked with, I've encountered a large disconnect between the world of operations and the world of finance.
Finance people wear a suit.

They read the Wall Street Journal, and they deal with very big numbers.
Operations people look like me.
They sit with a stopwatch at the bottleneck. Trying to count the seconds that go by.

The disconnect that this creates is very unfortunate, because operations people tend to often be confused chasing so many performance measures. And they forget that your productivity improvements, improvements along other operational performance measures are not the goal in it by themselves. For a for profit organization the goal is to make money, not to increase productivity. On the other hand, the finance folks often struggle with the challenge of how can they go about making their financials more attractive. Even as a CEO you don't show up to the process on Monday morning. Roll up the sleeves and says well today I'm going to improve my margins by 10%. Operational things are the things that are actionable for management.

For this reason I would argue that understanding the operations remains at the heart of business.

### Revisiting the Process Flow Diagram at Subway
Lets go back for our Subway restaurant analysis. We are previously at 95. Station two is the bottom line with the processing time of 47 seconds per customer.

### Subway - Financial Importance of operations
Let's assume that our demand is 100 customers per hour, and that each customer orders six dollars worth of food.

Let's assume further that the purchasing cost of this food is $1.50 and that we have four employees making $15 per hour. Finally, let's assume that we have fixed costs in term of rent, franchise fee, marketing, and overhead of roughly $250 per hour during peak times.

How much profits will we make? Let's start computing the top line. For this, first of all, we need to compute our process capacity.

Since there are 3,600 seconds in the hour, we know that our capacity is driven by the bottleneck and corresponds to 76 sandwiches or customers served.

Next, we know that the flow rate is the minimum between the demand and the capacity.

Not surprisingly, this tells us that we're going to serve 76 customers per hour.

If we multiply this, with the money that we are making per customer, we see that we are having an expected revenue of $459 per hour. Now, the food costs are driving our cogs. And so the food costs are simply our flow rate, multiplied with a $1.50. Our staffing is simply the number of employees times the weight trade.

And fixed cost as simply, the $250. If you combine these numbers, we're going to get our bottom line profit.
Play video starting at :3:30 and follow transcript3:30
In our case here, this is $459 minus the cogs minus the staffing, minus $250, a fixed cost. That gives us $34 for every hour of peak volume.

How do the profit number change as we change some of the operational variables? First consider a change in food cost. Imagine, in the very meaning of the word, that we could slice a salami more thinly. We would get a saving of, say, 10% in our food cost per customers, so instead of $1.50, we would reduce the cost per order to $1.35. We see the profits go up from $34 to $46. An extra $12 or roughly 33% relative to the baseline. Now lets go back to this baseline and evaluate the impact of productivity improvement. In the same way, lets assume where we can cut the processing time at the bottleneck by 10%. This would go down from 47 seconds to 42.3 seconds. The input of profits is amazing. You notice that profits go up from $34 to over $72. This corresponds to well over 100% increase in profit. Just as a result of a 10% productivity improvement. Of course this hinges on the assumption that we have enough demand.

Operations and our demand constraints

are not going to be able to materialize big changes in profits for productivity improvements unless they are able to lay off workers. In contrast if you're constrained by capacity, productivity improvements at the bottleneck make up for real profit improvements.

In this case we see that every second counts. Four seconds at the bottleneck means doubling your profit. Understanding this connection between the operational variables and the financial variables is key.

### Summary
Every second counts. In this session we saw that productivity improvement in an operation can lead to very significant financial rewards. However, not all seconds are created equal. If you are improving the productivity of a non-bottleneck resource, or if you are currently constrained by demand rather than by your capacity, productivity improvements might translate into small labor costs reductions, but they will not have the big rewards that we saw in the Subway case.

Such big rewards tend to happen primarily in organizations that have high fixed costs. High fixed cost operations tend to have lower marginal costs and so every unit of flow. Every extra customer that you serve. Their revenue will go directly into the bottom line. Finding out what areas in an operations will lead you to the biggest financial rewards is a key skill that we will continue to work on in this module.

## KPI trees
Last session we saw how small changes in operational variables can have big financial rewards. One tool that helps us understand that relationship between operational variables and financial variables is the KPI tree, where KPI stands for key performance indicators. KPI trees are powerful ways to visualize. So the relationship between the many operational variables and the financial bottom line. KPI creates also the starting point for sensitivity analysis that would formally let us identify those operational variables that yield the biggest financial improvements. Let's go back to our restaurant example from the last session. And see KPI trees in action.
### Subway – EBIT tree
<img src="https://docs.google.com/drawings/d/e/2PACX-1vTJLgbRMkyiBJzXySemCB5EH_Kt3-uVZF2lipWFtSHjD32KXNbMRDhbaM1620LIuoGbkfzVpwhgveR5/pub?w=948&amp;h=505">

The number that we care about in the restaurant is the daily profit. What drives this profit? Profit is simply revenue minus cost. What drives the revenue here? Revenue is driven by the flow rate, the number of customers that we serve. Times the dollars that we make per customer. In our example there was $6 per customer.

Flow rate, in turn, is defined as a minimum between demand and capacity.

The capacity is driven by the bottleneck because there was a step with the lowest capacity between stations one, two, and three. Now a case. Station two was a bottleneck, and then was in turn driven by the processing time of station two, which consisted of the time of putting the onions on the sandwich, lettuce, tomato, everything else to boxing the napkin. Along with the order.

On the cost side of the business, we have fixed and variable cost.

The variable cost are driven simply by the number of sandwiches that we make times the dollars per sandwich.

Or the dollars per order.

These in turns are driven by the ingredients in the sandwich, including the bread.

The meat, the cheese, the vegetables and again everything all the way up to the napkin.

So we can think of a KPI tree as basically one big mathematical equation that combines the many variables

that showed up in our spreadsheet analysis before the data we need to drive profits. In one visual way.

Evaluating changes in the leaves of the tree and predicting the impact on profits is the idea of sensitivity analysis. For example, we can ask ourselves how much more profits do we make if we can put the onions on the sandwich faster? How much more profits would we make if we would reduce our fixed costs? If we would source our bread any cheaper?

Mathematically, this corresponds to a derivative. We take the partial derivative of profits with respect to an operational variable.

In practice, however, as we saw in the previous session evaluating the impact of change is much easier. It doesn't require any calculus. All we have to do is build an Excel spreadsheet and evaluate the changes.

Why was the impact of a productivity change so big on profit?

Think about our business from a financial perspective. Let's plot revenue and cost as a function of flow rate.

Our revenues are quite simple. They go up at a slope of $6 per every customer that we serve.

Our costs, however, are a little different. Remember that we have to pay $250 in terms of fixed cost, and another $60 of labor. This amount of money we have to spend even if we don't sell any sandwiches.

From then onwards this line slopes up, but now at a much lower slope than the revenue curve. In fact the slope is simply $1.50 per customer capturing our variable cost. You see that here we have a point at which we stop making money. This is typically called the break even point.

In our baseline analysis, in the previous session, we noticed that we were just beyond that break even point. We made a little bit of profit. However, from then onwards having an additional customer through the system, has a very strong marginal effect. Every customer, that we serve, brings us $4.50 that go right into the bottom line.

### Summary
Is the juice worth the squeeze? Changing an operation is hard but there are many operational variables that we could focus on. The KPI tree is a powerful tool that helps us identify those operational variables that we should focus on. The KPI tree is also a powerful visual that helps us understand the casual system that connects all these operational variables with the financial bottom line. So I suggest to you that you always start any operational improvement projects by first mapping out the process, drawing out the process flow diagram. Then you do the process analysis calculating the operational variables that we introduced in the first module. And then you build a KPI tree to help you understand how these operational variables drive financial performance.

## OEE Framework /Quartile Analysis
### Overall Equipment Effectiveness
This is the overall equipment effectiveness. It's a fraction of time that the resource is adding value. This is an important ingredient when you are then predicting the upside of any operational productivity improvements.

Consider a piece of equipment in a production process. Equipment can be expensive, especially in production settings, such as semiconductors, or highly automated assembly. We want to find out how much of the time the equipment is actually used productively.

Say we study the equipment for 100 hours.

The first thing that we observe is that from these 100 hours the machine is not running all the time.

The machine is what we call in downtime. Downtime can be driven by things such as machines break downs, or changeovers. Changeovers we'll discuss in the module on product variety. Those are times when the machine is moved from producing one type of product to another. This, really then, leaves us with fifty-five hours that the machine is running. But even those fifty-five hours are reduced further. Idle time because of line balancing issues, and reduced speed because of poor operator training, drives us down in our example to forty-five hours.

But it gets even worse. From those forty-five hours of net operating time, we're producing defects, and we have to ramp up production, producing scrap, potentially during startup.

In this example here, the total number of losses accumulate to an overall equipment effectiveness of 30%. This is simply driven by the 55% of the time that we have as downtime, 82%, namely, the ratio between forty-five and fifty-five did we lose before because of lower speed, and 67%, thirty relative to forty-five that are driven by quality losses. So we notice that our overall equipment effectiveness is 30%, we get eighteen minutes of value out of each hour of work that we spend at the machine. Often times that you will notice, is that even with an OEE of 30%, the people actually operating the equipment might require that you invest in more equipment. After all, the equipment and the workers around it, seem to be busy most of the time. But, as reported, moving is not working. The OEE helps us to realize that in this case we have almost a 3x in productivity improvement potential without investing anything further in additional equipment.

### OEE of an Aircraft

Let's apply the OEE framework to the case of an aircraft. We can think of the equipment as an aircraft seat. The seat is only adding value if it is in the air and it has a paying customer sitting in it. What percentage of the time do you think a typical airline seat actually adds value?

When I ran the analysis for the big U.S. carriers, I found the following.

On the left here I started with 365 days in the year, and the twenty-four hours that are in a day.

Most of the time is lost because the plane is either at the gate, or it is in maintenance.

This is not too surprising. Most of the effect is driven by the fact that nobody wants to fly from Philadelphia to Chicago at 2:00 in the morning, and it's just not profitable for the airlines to fly at crazy hours. The other chunk here is maintenance that is required for the planes.

This leaves us with an amount of time that is typically referred to as a block time. This is the time that the plane is actually moving.

But moving includes taxi and landing, not, at least from the customer's perspective, necessarily a value add.

After subtracting this as a 10% of the time, typically, that an aircraft is in taxi and landing, we get the time that the seat is in the air.

But not every minute that the seat is in the air is adding value because seats often fly empty. Typical aircraft utilizations are in the low eighty percentages. And so, we have to subtract another ten to 20% to adjust for the fact that we're flying empty seats.

If you combine all of these effects together, and if you compute the AEE OEE of the aircraft seat, you typically get a number that is around 30%. You might think that that number is low, but I can assure you it's dramatically higher than what it was some ten years ago. The OEE framework applies to equipment as well as it does to people. So folks at McKenzie, where I've picked up the OEE framework, in that case it's OPE, the overall people effectiveness.

### Overall People Effectiveness

Let me illustrate this with an example. In a research collaboration that I'm currently conducting with a VA hospital system, I'm trying to measure how doctors are spending their time. I'm trying to determine their OPE. Lets start with the total time that we have the doctor on payroll.

Well, doctors are sometimes on vacation, and sometimes sick themselves, which gives us a total time the doctor is in the practice.

Now, not every minute of the time is booked for appointments. Even though doctors in primary care, in particular, tend to be very busy, they still have some empty appointment slots that leads to idle time for the doctor.

This gets us to the total time that the doctor is booked for appointments. Some of the patients, however, have an appointment and then don't show up. No shows, or cancellations, thus further reduce the OEE of the doctor.

After adjusting for cancellations, we get the total time that the doctor spends with the patient.

This is where things get dicey from a data perspective. Most health systems that I know have relatively little data above what actually happens during the doctor patient encounter.

In the case of the VA system, we used video cameras to document minute by minute what goes on when the doctor speaks to the patient.

It's interesting to see that a good number of the patients that are spending time with the doctor really don't have to be seen by a medical doctor, and could be seen easily by a nurse, or another physician extender. Moreover, if you go minute by minute through the processing time, typically that's a twenty minute encounter, you find that the doctor spends many things doing that are not really requiring the knowledge of a medical doctor.

Rewriting scripts for refills for medications, patient counseling, and social work. This gets you the real true value add time for the doctor.

### Example
Consider the following example. We have a car manufacture that operates a 3D printing lab where computer models of designs are turned into physical models. The lab is open here for twelve hours a day.

Now, you see that, the lab spends a fair bit of time each day on things that are not directly value add. Value add time is the seventy minutes that it takes to crunch out one of these models, and lots of other things are going on. So, take a look for yourself, you might want to pause this video and ask yourselves the following two questions.

How many good models are produced every day, and what is the OEE of this lab?

Now to see this, consider the following calculation. Let's start with the question of how many good models are produced each day. We know that we have 720 minutes available per day. Of that, thrity minutes per day are subtracted because of the startup effect. That leaves us with 690 minutes a day.

If we ask ourself how long it takes to produce one model, we have to go for seventy minutes of production plus thirty minutes of set up. So if you take 690 minutes divided by 100 minutes, nd remember here that you can only start a new job if you are going to finish it during the time, before 6:00 P.M., you see that you're going to get each day, you're going to get six models per day.

Finally, of those six models one-third, i.e., two, one-third need to be scrapped, and thus, it leaves you with four good models per day.

Now you do the calculation backwards. From these four models per day, basically, that warrants 280 minutes of productive times per day.

You multiply this with the six days a week that the lab is opening, because there's one day of maintenance, that gives you a total productive time per week of 1,680 minutes. This is 1,680 minutes per week of value add time.

However, on the other hand, you can clearly simply see that twelve hours a day, sixty minutes an hour, and seven days a week corresponds to 5,040 available minutes per week.

So if you want to draw a little chart here this 5,000 is the available time, and this time is a real value add time. The OEE is simply the ratio of this number to this number, which is 33%.

If you want to be more fancy in the graphics, you can now take out for each of these losses, be it the scrap, the start up effects, the set up times, or the maintenance, you can quantify the magnitude as you go from the left to the right. But as a first start, I would always encourage you to start with the very left, the available time, and at the very right, the value add time.

### Summary

Now let me end the session by reading you another quote from Frederick Taylor.

Employers derive the knowledge of how much a given class of work can be done in a day through either their own experience, which has frequently grown hazy with age, from casual and unsystematic observation of the man, or a test from records.

Having data on what workers actually do during their time is very difficult. Moreover, this is even worse when we're dealing with knowledge workers. If you think about observing doctors, observing insurance agents, or underwriters in a bank, this is really hard and doesn't fit the culture that most organizations have. The OAE framework has been powerful because it lets your document, what you have learned during these observations, and identify the fraction of the work time that was truly value add. The OAE analysis will also tee up the productivity improvement study, where you can ask yourself how much of a profit left as we have seen in our discussion of can I get by reducing these various forms of waste.

## Line balancing/ capacity sizing
One of the most obvious forms of capacity wastage is idle time. Idle time happens for two reasons. First, by definition, every resource that is not the bottleneck would have some excess capacity compared to the bottleneck. This will translate into idle time. Second, if you're currently constrained to a demand, even the bottleneck resource will have some idle time. In this session we will talk about ways of reducing idle time. First, we'll talk about the concept of line balancing.
Line balancing is about sharing the work equally among the resources in the process. We'll then talk about scaling up the process capacity as the amount potentially fluctuates. We can add or subtract workers from the line, adjusting our capacity and saving us from incurring idle time when the demand is low.
### Staffing / Capacity Sizing

### Line Balancing and Staffing to Demand
Let us re-visit the subway example. Early on, we computed that the labor content at the subway line was 120 seconds per customer.

Now we assume that we have 80 customers arrive every hour.

Previously we had determined that the processing times for the three operators were 37 seconds per customer at station one, 46 seconds, and 37 seconds at station two and three respectively. The idea of line balancing is to divide up the work evenly, so we want to take some of the work from worker two and spread it to worker one and three.

A powerful way of doing this is by first reminding ourselves of the flow rate that this process has to operate under. This is the idea of takt time. Takt time determines that we have to produce a unit every 45 seconds to keep up with demand. After all, every hour, 3600 seconds, we have to make 80 units.

So 45 seconds per unit is the takt time.

Tact is a word that comes from the German word Takt which stands for the beat of the music. In the process everyone has to dance to the beat of demand. Every person should serve a customer and move him forward to the next station at a speed of 45 seconds.

Assuming a perfect line balance, the takt time also helps us find how many people we need to staff in the line. 120 seconds of labor content divided by 45 seconds of takt time gives us that we need, round it up, three people to do the work.

Now admittedly, this is an ideal calculation. I cannot have worker 2 put half of a tomato on the sandwich and worker 3 put the other half. The task often cannot be divided as easily as second by second. However I find that starting with such an ideal calculation, that's why it's called the target manpower, is often very eye opening and it reminds you of the true productivity improvement potential that exists in the process. It is then up to you to design the task of the process so that line balancing will become possible.

### What Do You Do When Demand Doubles? Ideal Case Scenario

Now imagine that demand picks up to 160 customers per hour.

The takt time changes. We now have to divide 3,600 seconds in an hour divided by 160 units per hour, equals to a new takt time of 22.5 seconds. So instead of serving a customer every 45 seconds, we're serving a customer every 22 and a half seconds. The takt of the music has picked up. This is also reflected in our target manpower calculation. We're dividing the labor content, which is state unchanged at 120 seconds per unit, by the new takt time, and see that in order to fulfill this increased demand, we have to increase our staffing number from three to six.

### Balancing the Line
:::info
Determine Takt time
Assign tasks to resource so that total processing times < Takt time
Make sure that all tasks are assigned
⇒Minimize the number of people needed (maximize labor utilization)
What happens to labor utilization as demand goes up?
Difference between static and dynamic line balancing
:::

Let's summarize our calculation for line balancing.

Line balancing starts with computing the takt time. It's the demand that drives everything as we're executing the process. Once we have the takt time, we take the various tasks that make up for the flow unit, and we will divide them among the workers so that the total processing time for each worker is less than the takt time.

You continue to do this till all of the tasks are assigned to the workers. As you're doing this you try to keep the number of people at a minimum. This can be written as quite a fancy mathematical problem, but oftentimes, at least for smaller scale problems, it can be just tweaked by trying this out a couple of times.

Now, I want you to think about the following question. What happens to labor utilization as demand goes up?

To see the effect on labor utilization, first ask yourself what happens to takt time as demand goes up. More demands means shorter takt time. This makes balancing the line harder. To see this, think about the opposite effect. Think about the case of balancing a line with just one person. Balancing a one person line is trivial. That person will have little idle time, and we have a very high labor utilization. As you go in the opposite dimension, you add more people to the line and reduce the takt time, line balancing becomes increasingly hard.

Finally, I want to acknowledge that the world is certainly not one big math problem to solve. The same holds for the case of line balancing. Instead of finding some fancy algorithm along the lines that I previously described, in practice line balancing is often done dynamically by walking around and looking where inventory piles up. We can then go and reassign either people or tasks so that the flow goes faster. This typically starts by looking at the bottleneck resource. Keep in mind that any activity that we move away from the bottleneck has a potential to increase capacity. Balancing one bottleneck steps however is often a fruitless task.

### Line Balancing and Staffing to Demand

Once you understand line balancing, you can also start dealing with changing demand. Consider the demand trajectory shown up here.

We will refer to this pattern as seasonal demand.

For now let's just observe that the demand changes predictively over the course of the day. The first thing that you do is you level the demand.

You want to avoid to change your takt time or your staffing level every minute by minute. And so you come up with the level of demand while you hold the demand for an hour as fixed. This is arguably an imperfect approximation, but better and more practical than changing your staffing level every minute.

Once you have a level demand, you translate that into a takt time. Remember, more demand means a shorter takt time. Finally, you take this takt time and you translate this into a manpower calculation. This is done based on the target manpower calculation that we reviewed earlier on. As you see in the example here, in the low period settings I can get away with three workers carrying out the six tasks. Once demand picks up, my takt time gets shorter and I have to bring in extra people.

This helps us to scale up and down the process as demand changes. Capacity tends to be fixed, while demand changes often over time.

This leads to temporary mismatches between supply and demand.

Customers wait or resources are idle. The ability of an operation to adjust its capacity and scale it up and down in response to a varying demand is a form of flexibility. Most operations create their flexibility by using either temporary workers, or by using their workers overtime. In this session we saw how a takt time can be used to drive the demand down into the operation. We saw how we can use takt time to compute the staffing level required to run a process. And we also saw how takt time can be used as a form of line balancing.

## Quartile analysis / Standardization
### Call Center Example
:::info
Two calls to the call center of a big retail bank
Both have the same objective (to make a deposit)
Different operators
Take out a stop watch
Time what is going on in the calls.
:::

>> Hello. You're speaking to David. Can I have your name please?
>> Yes. It's Natalie Walker.
>> Good morning. How can I help you today, Ms. Walker?
>> I'm calling because I'd like to make a payment to my account. Can you do that?
>> No problem. Can you give me the seven digit mortgage account number, starting with BCC?
>> Yes, it is B, C, C, six, five, eight.
>> B, C, C, six, five, eight.
>> Two, three, one, four. >> Two, three, one, four. >> Yes.
>> Thank you, Ms Walker. I just need to ask you some basic security questions.
>> Okay, that's fine.
>> Can you give me the first line of your address and the post code, please?
>> It is 48 Church Road, Bolton, and the post code is BO38FD. >> Thank you. And your date of birth, please?
>> Seventh of March, 1979. >> Thank you. And what amount would you like to pay?
>> 500 pounds, please. >
> Would you like to pay by debit or credit card? >> Credit card.
>> Okay. And is it Amex, Visa, or MasterCard? >> MasterCard.
>> Thank you. Can I take the sixteen digit code on the middle of the card, please?
>> Five, five, nine, o.
>> Five, five, nine, o.
>> Seven, one, four, three.
>> Seven, one, four, three.
>> Eight, nine, seven, three.
>> Eight, nine, seven, three.
>> Six, three, two, two.
>> Six, three, two, two.
>> Correct.
>> Thank you. And the expiry date?
>> O, three, thirteen.
>> Thank you. And the full name on the card, please.
>> Jess Natalie Walker. Thank you. And the three digit code at the back of the card?
>> Four, eight, five.
>> Four, eight, five. Bare with me while the payment goes through. Thank you. Your payment has gone through. >> Thank you.
>> Thank you for calling. Is there anything else I can help you with today?
>> No, I think that was all. I will need to make a change later, but I will do that on a later date. So no, that will be all for now.
>> Okay. Thank you. Good bye.

>> Hello, you're speaking to Anna, can I have your mortgage account number please?
>> Yes, it's B,C, C, seven, five, seven.
>> Yeah.
>> One, nine, five, eight.
>> Thank you. Can you confirm your name, please?
>> Scott Jones.
>> Thank you, Mr. Jones. I just need to ask you some basic security questions.
>> Okay. That's fine.
>> Can you give me the first line of your address and the postcode, please?
>> It's The Boathouse, 58 Green Lane, and the post code is TN73CA.
>> Thank you. And your date of birth, please. >> 27th of September, 1981.
>> Thank you. And how can I help you today?
>> I'm looking to make a payment into my account, please.
>> No problem. What amount would you like to pay?
>> 750 pounds.
>> And would you like to pay by debit or credit card?
>> Credit card, please.
>> And is that Amex, VISA, or MasterCard?
>> VISA.
>> Thank you. Can I take the 16-digit code on the card, please?
>> Two, two, five, six.
>> Yeah.
>> Four, zero, eight, zero.
>> Yeah.
>> One, two, five, three.
>> Yeah.
>> Five, eight, seven, nine.
>> Thank you, and the expiry date.
>> Four, twelve.
>> And the full name on the card, please.
>> Scott Jones.
>> And the three digit code at the back of the card.
>> One, five, three.
>> Thank you. Your payment has just gone through.
>> Thank you.
>> Thank you for calling. Goodbye.

So, what did you notice? Who was faster? Who was the better employee? Which of those two employees do you want to have work for you? If the only enemy that we consider in our study of productivity is idle time, we're missing a big opportunity that resides in the processing times themselves. Referred to the first extra words that the first operator was using as unnecessary motion. Though in our case, this really means unnecessary talking.

### Beyond Labor Utilization: Quartile Analysis

To analyze such variation in processing times across operators, I find it is helpful to just collect a sample of processing times for each operator.
Play video starting at :5:50 and follow transcript5:50
The average processing time of process operators will vary.
Play video starting at :5:54 and follow transcript5:54
Instead of simply comparing the best operator and the worst operator based on the averages, I, in this picture show what's called a Quartile Analysis.
Play video starting at :6:4 and follow transcript6:04
The Quartile Analysis compares the highest quartile performing operator, that means the operator was still 25% other operators that are faster than him or her, with the bottom quarter operator, i.e.the operator who has 75% of the other operators faster, and 25% slower. In this slide, I do this for two tasks that exist in a large bank in the underwriting operation for consumer loans. You see on the right of the slide the closing step for this activity.

For closing there are a couple of rather clergical and manual tasks that need to happen and if you observe, a very, very tiny difference between the top quartile and the bottom quartile performer. On the left, you look at the underwriting function itself. For underwriters, the gap between the top performer and the bottom performer varies dramatically for the selected set of activities shown here. So it is interesting that actually in the more knowledge intense activities the variation in productivity is more dramatic.

### Example: Emergency Department
:::info
Analyzed data for over 100k patients in three hospitals
80 doctors and 109 nurses
Up to 260% difference between the 10th %-tile and the 90th %-tile
=> Dramatic productivity effects
:::
In a recent study of over 100,000 patients that were treated in the emergency room of three hospitals, my colleagues and I wanted to investigate to what extent productivity, in the form of processing times, would differ in healthcare settings.

The 100,000 patients were seen over multiple years by a group of some eighty doctors and over 100 nurses.

The results were very similar to what we just saw in the banking settings. We saw about a 260% difference between the 10th quartile and the 90th percent quartile operators.

Again, we see dramatic productivity effects, not coming from idle time, but by looking at processing time across operators.

### Summary
After 300%, the variation that we saw in today's class between the top performing employees and the low performing employees in the service operations were enormous. Call center, bank, hospital, service employees, manufacturing employees, everyone differs according to their productivity.

Reducing these productivity gaps between the top quarter and the bottom quarter employees provides an enormous financial opportunity. Typically, if we can transfer the best practices from the top performers to the bottom performers, the average productivity is going to be lifted upwards.

This should motivate you to go out to the front line and follow the footsteps of Frederick Winslow Taylor. Go out and measure yourself. Measure these productivity times because, typically, this is not data that most organizations currently have available.

Then, take this data, plot it, compare the top and the bottom quartile and you get a sense of the variation in the process. Again, anything you can do to reduce this variation by moving the bottom quartile up to the median or to the top quartile, will give you an enormous productivity boost.
## Productivity Ratios
At the beginning of this module we define productivity as a ratio between output and input. After having spent the last couple of sessions at the front line, looking at an operation at a very micro level, we are now taking more aggregate level perspective. We will again look at the U.S. airline industry. We define labor productivity as a ratio between revenue and total labor expenses. Beyond just defining the labor productivity and comparing it across airlines, our goal is to really dive into understanding the drivers of productivity.

### Basic definitions of productivity
We define productivity as the ratio between output and input often time however, it is difficult to measure output. So it is common in productivity analysis to use revenue numbers instead. We also often have multiple input factors such as labor, materials, capital, and other things. One way to avoid adjusting for these multiple categories is simply to define one productivity ratio for each category. For example, we can speak about the labor productivity as a ratio between revenue and labor expense.

Let's try this out for the U.S. airline industry. In 1995, U.S. Airways had 6.98 billion dollars of revenue. Their labor cost was $2.87 billion. This gives us a labor productivity of 6.98 divided by 2.87 equals to 2.43. 16 years later, the numbers have changed, revenue had grown to 13.34, with the labor expenses being at 2.41. This has increased the labor productivity thus to 5.53. Notice that labor productivity in those 16 years at U.S. Airways more than doubled. The situation at Southwest looks as follows.

In 1995, their labor productivity was given by 2.87 billion dollars in revenue divided by 0.93 billion dollars for labor expenses, equals to 3.08 as the labor productivity. You see here that this was a significantly higher number than U.S. Airways had at that time. 16 years later, Southwest was able to grow its business to 13.65 billion dollars. However, later expenses also grew significantly and were now 4.81 billion dollars, creating a labor productivity of 3.26. Which is actually slightly lower compared to the current number at U.S. Airways.

But what does the higher labor productivity actually mean? Are the workers working any harder? Have we squeezed out the idle time? Is the process underlying the operation smarter than before? What really account for the difference.

Consider again out definition of labor productivity as a ratio between revenue and labor costs.

Now work with me through the following equation. We can rewrite the revenue to the labor costs as the revenue divided by the revenue passenger miles created by the airline, times the revenue passenger miles, times the available seat miles, times the available seat miles divided by the employees, times the employees divided by the labor cost.

Now you might be scratching your head here a little bit. But at least you will hopefully agree with me that mathematically this equation is true. After all, this term cancels against this term, this term cancels against this term and this term cancels against this term, and we are back to the initial expression.

Now what is the benefit of writing the equation this way? It reminds us that there are multiple things going on, that are all driving the labor cost. The labor productivity. We see here in the first factor the revenue to the number of miles that we sell. This is really driven by the airlines pricing power, for that reason, often times this is what's called the yield. How much can we yield? How much do we get out of the capacity that we have available?

The revenue passenger miles divided by the available seat miles really measures to what extent we are able to fill our aircraft. In many ways this is a form of utilization of capacity.

Now the last two of these ratios here are actually really touching the labor. The first of these ratios is how much capacity can we get out of each employee.

The second one looks at the cost of sourcing these employees which is basically their wages.

Notice that these four different ratios catch a four different things. I cannot go to an employee at U.S. Airways and say, hey, your labor productivity is slow, just because the pricing has been done poorly or the aircraft has been flying half empty.

With this is mind, breaking up the aggregate level of productivity into these smaller drivers is quite revealing because it tells you what really is going on in the operation.

### Labor Productivity Comparison between Southwest and US Airways
[EXCEL](https://drive.google.com/file/d/1NbNStSbDy0atjuLBzpdg0v0080GG1Ooy/view?usp=sharing)
Let's apply our new knowledge by going back to the U.S. Airline industry and compare the labor productivity across the big carrier. We said the rate of labor productivity was driven by the ratio between the revenue and the labor cost. For the case of American Airlines, we're dividing the revenue,

divided by the labor cost, and we can copy this to the cells of the other carriers.

We notice quite some variation with Frontier getting a labor productivity ratio of six, and quite interestingly, Southwest being at the bottom of the pack with a productivity ratio of 3.2. We then look into the drivers of this effect, we compute the yield as a ratio between the total revenue and the number of passenger miles that were actually sold by the airline.

For this again we look at the revenue divided by the revenue passenger miles.

And we roll this out across all the carry outs.

You notice that the companies obtaining the biggest prices in the industry are the legacy carriers such as United or U.S. Airways.

Next we look at RPM to ASM which we said was the ratio between the miles that were sold and the miles that were available. In other word, the aircraft utilization. RPM by ASM turns out to be relatively constant across the carriers, with most carriers booking the airplanes up to about 80% utilization. Now consider the ratio between the ASN, which is really the capacity that has been provided and the number of employees. So ASN divided by employees.

If we compare this across the carriers. We see that the leader in productivity on that side is clearly Virgin America.

Southwest though does relatively well compared to its immediate competitors the Legacy Airlines. As a final ratio, we'll look at the FTEs relative to the labor cost. That measures how many people I can hire for a given amount of money.

Technically this is simply one over the wage rate of the employees.

Well when we divide FTE divided by labor cost, we see surprisingly high differences in salaries across airlines.

For example you notice that Southwest by now pays its employees really, really well. Remember you have to take one over this number to get to the actual wages. This is in sharp contrast to how it was some 15 years ago, where Southwest was paying much lower wages than their competitors.

Most of the legacy carriers had gone through bankruptcy and restructuring and by now are paying employees significantly less.

All these four variables together explain variation and labor productivity. So when we say that one company has a higher labor productivity than the other. We really need to be careful in distinguishing between these four forces.

### Summary
Measuring productivity using accurate level data can be easy, however it also can be misleading. As we saw with the data in the U.S. Airline industry, many variables drive labor productivity. Labor productivity is not just under the control of the labor, but things such as the pricing, the fleet utilization have a direct impact on labor productivity. Productivity ratios allow you to take care of these confounding effects and only measure the value of the productivity that you care about. In general in your work I always encourage you to take two approaches. First, look top down, start from the financial and work yourself down into the operations using tools such as a productivity ratio, compliment this with observational data from the front line. Look at the operational data and aggregate them using the tools such as the KPI tree that we saw in an earlier session in this module to look how they are driving financial performance. This is where you get a balanced view of your productivity in the operation.