So far in this module, we have looked at the capacity as our lever of dealing with waiting time problems. We talked about creating staffing plans and we talked about pooling, as an elegant way of reducing waiting time. In all of this, however, we implicitly assume that customers will be served in the sequence in which they arrived. Why? Why would it be optimal for us as a service provider to serve customers in exactly the order they arrived? I can see that this makes practical sense in the supermarket, but, if you have the customers waiting in the call center, do you really want to serve the customer who called first, Sir? Well couldn't we find some more profitable way of messing things around a little bit? This is the idea of sequencing. Sequencing, or determining priority rules, is about defining who should be served first. And as we will see in this session, it's not always the one who came first. So remember we are dealing with a process flow diagram that looks something like this. Customers arrive and they are waiting in the area and ultimately going to see a server before they leave. The idea of triaging, or the idea of priority rules or sequencing based on some attribute, say we're going to introduce a tiny little step before the waiting room, where we going to determine the importance or the priority of a customer. We move people to the beginning of the line or we move people to the end of the line based on whatever attribute we like. The default attribute is we do nothing, and the only attribute that drives your position in the line is when you arrived. This is what's called, the First-Come-First-Serve rule. Our econ colleagues calls this FIFO, for first in, first out, when operations prefer first come, first served. The benefit of the First-Come-First-Serve rule is that it is easy to implement. Imagine a supermarket where you would try to implement some other priority rules than first-come, first-serve. Imagine you would sequence them based on the margin that they're bringing to the retail store. Do you think it is feasible to call the customer with the highest gross margin to the store, to the front of the line? It's going to be a mess. The other customers will also be irritated and find it unfair. Another benefit of the First-Come-First-Serve Rule, it is minimizing the variance of the waiting time. I hope this is intuitive. Customers have a certain amount of wait time depending on when they arrived. If we start moving some people to the front of the line, we have to bump other people to the back of the line. Anything we do against first-come, first-serve is going to spread out the distribution of the waiting time, leading to a higher variance. Now the alternative is what I alluded to in my supermarket example. Instead of basically prioritizing on when you came in, I can pick another attribute. The color of your hair, your gender, whatever attribute I like. From a business perspective, it makes more sense to prioritize profitable units. Imagine a bank where we have calls into a call center. It makes good sense to prioritize customers who want to open a new account or bring you business. If somebody however wants to just inquire about how much money there is on the account, you prefer to either automated it or move it to the back of the line. This is done in a hospital as well. Hospitals have, in the emergency room, a triage nurse, that identifies how important and how urgent the care is for that patient. If you have a gunshot wound, an open wound, or some other thing that needs to be dealt with immediately, you're going to jump the line and get served immediately. If you just have a minor headache, you might be in there for a couple of hours. One alternative way of sequencing customers is based on the shortest processing time rule. Let me illustrate the shortest processing time rule with the following example. Imagine there are four things I have to do, Tasks A, B, C and D. Now you see the processing times for A, B, C and D are layered. It takes me nine minutes to do A, ten minutes to do B, four minutes to do C, and eight minutes to do D. Now if I order them A, B, C, D, you see that B will have to wait nine minutes, C will have to wait nine plus ten equals 19 minutes, and D will have to wait for A, for B, for C equals to 23 minutes. So across our tiles, the total wait time is 51 minutes. Now imagine I resequence them. I do the shortest processing time activity first, which makes me start with C. D then has only to wait four minutes. If I do this, and I add up the waiting time across all activities, I have a total waiting time of 38 minutes. Now notice that, to state the obvious, I still have to do A, B, C, and D. And so the total time I'm going to spend and work on these tasks, is going to be the same, in no matter what sequence. However, the benefit here is that customer C gets served very quickly. Previously had to wait a long time and it makes more sense to have customer A wait for customer C, than the other way around. This is again the idea of what's called the SPT, the Shortest Processing Time Rule. Now in practice, a limitation of the shortest processing time rule, is that it is very hard to know the true processing times before you actually start the service. Imagine you are running some help desk, a physician's check in, or some information desk, and people know that you are following the shortest processing time rule. Well, they will have a strong incentive to claim that whatever they want from you will just only take a minute. For this reason, the SPT rule is most prominently used when you're dealing with either manufacturing jobs or with things in the digital world where you can easily predict the duration. Nevertheless, despite there's limitation it's sort of very useful thing to have in your toolbox. Whenever you see waiting time problems, like the ones that we discussed in this module, it is tempting to think about solving this problem through the management of appointment. After all, it seems that appointments are just all about matching supply with demand. If you remember our example of Doctor Toyota at the beginning of the module, Doctor Toyota was able to serve 80% utilization with absolutely no waiting time. The reason for this was that the patients were spread out nicely over time, and so that's really the dream of the appointment system. Unfortunately, there are two problems with appointment systems. The first one, is patients often don't follow their appointments. This is simply the idea of no shows and we have other variability in terms of patients arriving late. The second and much bigger design flow with appointment systems I would argue, is that it really solves the wrong problem. Appointment systems are great of keeping the population in the waiting room, no. So, if you have a set of patients here, and their waiting time, by giving out appointments, you might be able to reduce the time. However, that's solving, I would argue, is the wrong problem. Demand for care is not the number of people in the waiting room. Demand for care is people getting sick. And so, if I get sick and I want to see the doctor, I call doctor and the doctor tells me I only have an appointment next week from you, I'm still in a waiting room. I'm still in inventory. I'm just sitting in my bed at home. So what appointment systems really do is they shift inventory from the waiting room in the doctor's office, to people waiting for appointments. Now, this is arguably not a bad thing. I'd much rather spend five hours lying in my bed compared to sitting five hours in the waiting room. However, it really not doesn't solve the problem. For that reason you notice that in many parts of health care, the trend is moving away from appointments. The idea is open access, and to do today's work today, as opposed to pushing it out into the future. First come, first served, is a default in most waiting lines. Customers who arrived first, will get served first. While this is easy to implement, we saw in this session, that you often times can do better. We discussed the idea of the shortest processing time rule, which is based on the intuition, that it makes more sense to have somebody with a long processing time, wait for somebody with a short processing time, compared to doing it the other way around. We also discuss how you can use other attributes, than the processing time to give priority to certain groups of customers. For example, you might give priority to customers that have been doing a lot of business with you, or who are very profitable. And you might have customers that are not that profitable and will routinely eat up a lot of your capacity, you might send them to the back of the line. We've also discussed the pros and cons of appointment systems. This is a big topic in the field of healthcare and it's important to keep in mind that department systems have their strengths, they also have their weaknesses, and they fall short on their promise to match supply with demand.
