Do you know what I find is the biggest pain when you get sick. It's not the pain in your teeth and your ear or wherever you have your medical complications. The biggest pain is the 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 o'clock. You sit in the waiting room until it is four o'clock. 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 be instantaneous? In this module we want to understand the concept of responsiveness. How can we be quick and responding to our customers? Waiting of course is just another form of a mismatch between supply and demand. When we are waiting we as patients in the waiting room are inventory. It's simply no fun being inventory when your ear is infected or your teeth hurt. Understanding the match between supply and demand, once again, is going to be a crucial issue of solving this waiting time problem. Let's represent the physician's office in the form of a process flow diagram. This is a really simple process for a diagram. We have a waiting room, and we have the doc doing the work. It's the only resource in the system. Now say for the sake of argument, that patients arrive at the rate of every five minutes. So over the course of an hour, we have 12 patients come in per hour. Moreover, let's assume the doctor spends on average ten minutes to serve a patient. That means we have a capacity of six patients per hour. Now 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 12 divided by six equals 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 a day in the life of the doctor and start early morning, say at 8:00 AM when the practice opens. The first patient who comes into the practice probably will not have to wait. He'll get served immediately. However, as the day unfolds, things get worse. Because we have 12 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, we have 12 patients come in. We have six patients get served. So every hour we are accumulating six patients in the waiting room. For example at 10:00 A.M. I have 12 patients in the waiting room. At noon I've been operating for four hours at the capacity showed full 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 10 minutes, and so the waiting time will be a total of 240 minutes, quite long time, but pretty scary example. Let's look at another example. Here's another doctor's office. Same thing, same process flow diagram, and a patient arriving every five minutes. So 12 patients arriving per hour. It takes this doctor here however only four minutes to treat the patient so our capacity's much higher and the doctor can have a capacity of 15 patients per hour. We can compute the utilization now as the ratio between the flow rate to capacity. And the flow rate remember is the minimum of demand and capacity. So if the flow rate is 12, the capacity is 15. 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 7:00, 7:05, 7:10, and so on. Moreover, Dr. Toyota knows what he's 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 gotta go, business is business. Well, this is arguably a very unrealistic example. I'll 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 Doctor Toyota. Four minutes of work. A minute of idle time. And none of these patients ever will have to wait. Now, arguably, my story of Doctor 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. Now we'll formalize the idea of randomness in just a moment. But, consider the example here of 12 patients spread out over 60 minutes, in less of an assembly line fashion. Moreover, look at the processing times for these 12 patients- some of them are longer, others are shorter. That's I think what most of us would mean with a more realistic set of processing times and arrival times. Now look what happens in this more realistic setting. Notice first of all, that our utilization has still remained at 80%. Of course after all the average time between two customers' arrivals is one customer every 5 minutes, 12 customers per hour, and the average processing time has remained at four minutes. Yet, despite this utilization. [SOUND] Of 80% you see that the picture changes dramatically. I notice 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 the 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 moment in times I might have three if not four patients in the practice. All of that better 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 time problems, the first thing you should think about is what can I do to increase the capacity of the resource? What we've done in our earlier discussion in the module on productivity analysis is a really good tool box to free up some capacity. We also talked about flexibility in making sure that we have the capacity available at the right time. However, we notice in this session, that often times 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 head first if the lake is deep, ten feet on average. Averages really only tell half of the story. For this reason in this module, we will focus a lot on variability, which is an important way to describe both the demand process and the supply process beyond the simple averages.
