So far in this module, we have looked at capacity as our level 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 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 a supermarket, but, if you have the customers wait in a call center, do you really want to serve the customer who called first, sir? Or 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 declining 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 look something like this. Customers arrive, enter a waiting area, and then 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 is that we're going to introduce a tiny little step before the waiting room where we're going to determine the importance of a 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 accountant colleagues call this FIFO for first in, first out. We in operations prefer first come, first serve. The benefit of the first come, first serve rule is that it is easy to implement. Imagine a supermarket where you will try to implement some other priority rule than first come, first serve. Imagine you want to 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 cross 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. And that's the benefit of the first come first serve rule. It is minimizing, it's a variance of some waiting time. I hope this is intuitive. Customers have a certain amount of wait time depending on when they are 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 come 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 who we have calls into a call center. It makes good sense to prioritize customers who want to open a new account or bring you new business. If somebody, however wants to just inquire about how much money there is in the account, we prefer to either automate 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 things that need 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 over here. 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 nineteen minutes, and D will have to wait for A, for B, for C, equals to 23 minutes. So, across all tasks, the total wait time is 51 minutes. Now, imagine I resequenced 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, I notice that, to state the obvious, I still have to do A, B, C, and D and so the total time I am going to spend in 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 all know the true processing times before you actually start the service. Imagine you're running some help desk. A physician's check-in was some information desk and people know that you're 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 its limitations, it's still a 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 appointments. 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 don't often follow their appointments. This is simply the ideas 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 low. 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 the doctor and the doctor tells me I only have an appointment next week from you. I'm still in the 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 healthcare, 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 serve 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 oftentimes 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 discussed 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 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 appointment systems have their strengths, they also have their weaknesses. And they fall short on their premise to match supply with demand.
