Do you know what I find is the biggest pain when you get sick? It's not the pain in your teeth, in your ear, or wherever you have your medical complications. The biggest pain is a pain of waiting. You call the doctor's office, they put you on hold for ten minutes. You want an appointment for this afternoon, you get one for next week. You finally arrive to your appointment, which is at two:00, you sit in the waiting room, and there it is, four:00. Medical care, just like many other services, is all about waiting, waiting, and waiting. But why do customers have to wait? Why can't the care not be instantaneous? In this module, we want to understand the concept of responsiveness. How can we be quick in responding to our customers? Waiting, of course, is just another form of mismatch between supply and demand. When we are waiting, we as patients in the waiting room, are inventory. And it's simply no fun being inventory, when your ear is infected or your teeth hurt. So, understanding the match between supply and demand once again, is going to be a crucial issue of solving this waiting time problem. Now, let's represent a physician office in form of process flow diagram. This is a really simple process flow diagram. We have a waiting room and we have the doc doing the work as the only resource in the system. Let's say, for sake of arguments, that patients arrive at a rate of every five minutes. So, over the course of an hour, we have twelve patients come in per hour. Moreover, let's assume the doctor spends an average ten minutes to serve a patient. That means we have a capacity of six patients per hour. But first, let's ask ourself, what's the implied utilization in the system? Now, remember from our discussion of process analysis, that the implied utilization looks at the ratio between demand and capacity, Which, in this case, is simply twelve divided six equal to 200%.. How long will patients have to wait in this practice? To see how long patients have to wait, let's just do the following thought experiment. Let's just look at the day in the life of the doctor and start early morning, say at eight:00 a.m. when the practice opens. The first patient who comes into the practice, probably, will not have to wait, and gets served immediately. However, as the day unfolds, things get worse. Of course, we have twelve patients per hour come into the practice, and six patients per hour being served. What happens is we have an accumulation of waiting patients. Inventory. How quickly does this accumulation occur? Well, here we have twelve patients come in, We have six patients get served. So, every hour, we're accumulating six patients in the waiting room. For example, at ten:00 a.m., I have twelve patients in the waiting room. At noon, I've been operating for four hours at a capacity short fall of six, and I will have 24 patients in the waiting room. So, the person who comes in here at noon has 24 patients in front of him or her. Every one of them will take ten minutes and so the waiting time will be a total of 240 minutes. Quite a long time, a pretty scary example. Let's look at another example. Here is another doctor's office. Same thing, same process flow diagram, and a patient arriving every five minutes. So, twelve patients arriving per hour. It takes this doctor here, however, only four minutes to serve the patient. So, a capacity is much higher, and the doctor can have a capacity of fifteen patients per hour. We can compute the utilization now as the ratio between the flow rate to capacity and the flow rate, remember, is a minimum of demand and capacity. And so, the flow rate is twelve, the capacity is fifteen, and we have a utilization of 80%.. Surely, in this practice, no patient will ever have to wait or maybe, they have to. Imagine this doctor would be called Dr. Toyota Now, Dr. Toyota runs a very proper practice. His patients arrive exactly every five minutes. So, one at seven:00,00, one at seven:05,05 seven:10, and so on. Moreover, Dr. Toyota knows what he is doing. He has standardized his work to a four-minute processing time. The patient is still half undressed, after four minutes Dr. Toyota says, sorry got to go, business is business. Well, this is arguably a very unrealistic example. I make things realistic in just a moment, but I want you to see a very important point. It is indeed possible to run a business with a utilization of 80%. And have no waiting at all. Look how the patients arrive and when they leave. Four minutes of work, a minute of idle time for Dr. Toyota, four minutes of work, a minute of idle time and none of these patients ever will have to work, wait. Now arguably, my story of Dr. Toyota was very unrealistic. What type of doctor would serve exactly every patient in four minutes? What type of patients would arrive and get sick exactly one patient every five minutes? Now, what do we mean with unrealistic? More realistically, we would say that the arrival times when these patients come to the practice are somewhat random. I will formalize the idea of randomness in just a moment, but consider the example here of twelve patients spread out over 60 minutes in less of an assembly line fashion. Moreover, look at the processing times for these twelve patients, some of them are longer, Others is shorter. This, I think what most of us would mean with a more realistic set of processing times and the arrival times. Now, look what happens in this more realistic setting. Notice, first of all, that our utilization has still remained at 80%. Because after all, the average time between two customers' arrivals is one customer every five minutes, Twelve customers over the hour, and the average processing time has remained at four minutes. Yet, despite its utilization of 80%,, you see that the picture changes dramatically. I noticed that some patients, if you consider the patient number five and six here, these poor folks have to wait three or four times as long as their actual service times. Instead of looking at the patient wait times and service times, I can also look at the inventory. And you see that at certain moments and times, I might have three, if not four, patients in the practice. All of that at the utilization of 80%.. When a doctor has six patients per hour arriving to her waiting room, and the doctor can only see three patients per hour, the times the patients will have to wait get longer and longer. This is clearly a result of insufficient capacity. Whenever you encounter waiting problems, the first thing that you should think about is what can I do to inccrease the capacity of the resource? What we've done in our earlier discussion in the module on productivity analysis, is a really good toolbox to free up some capacity. We also talked about flexibility, and making sure that we have the capacity available at the right time. However, we notice in this session, that oftentimes waiting is not just driven by insufficient capacity, but it's driven by variability. We notice that variability doesn't average itself out. Think about it. Would you jump into the lake, headfirst, if the lake is deep ten feet on average? Averages really only tell half of the story. For this reason, in this module, we'll focus a lot on variability, which is an important way to describe both the demand process and the supply process beyond the simple averages.
