But with That, I'll Hand It Over to Dr. Benneyan There at Northeastern for the Presentation

Cancer Surgery Multi-Stage Scheduling and Related Scheduling Optimization Problems
Presenter: Dr. James Benneyan, Northeastern University
Recorded on: July 24, 2013

All right, welcome to CHOT Deep Dive webinar series. This is Nick Edwardson calling in from College Station. I'm the Assistant Director here at the Texas A&M site, but I'm joined here today with our Northeastern crew, led by Dr. Jim Benneyan. Jim's going to talk about today the Cancer surgery multi-stage scheduling project that was started over, I believe over a year ago, but has recently wrapped up.

Before we kick off, I wanna make a reminder to our members and those of you who have joined, two upcoming events, one, next month's webinar will be Led by doctor Eva K. Lee at Georgia Tech, the date for that is Wednesday August 28th, same time, 10pm Eastern, and she will be discussing the project on reducing surgical sight infections.

The second reminder I wanna make everyone aware of is our upcoming fall meeting will be October 17th and 18th on the campus of Northeastern. We've got some information and flyers already posted on our website but be checking back there frequently for updates. We'll send an email out to all of the members as well as soon as we have venue information and a schedule and an agenda, so look for that.

But with that, I'll hand it over to Dr. Benneyan there at Northeastern for the presentation.

> Thanks very much, Nick. Let me just do a sound check and make sure you can hear us okay.

> Sounds great.

> We're on a speakerphone. So, actually, I'll be presenting, but also presenting with me will be Serpil Mutlu, who's one of the PhD students, who's really been running the first project we want to summarize.

So as Nick mentioned I'm one of the CHOT co-directors really running the part of the CHOT program that's linked in Northeastern University, as most people know we have four universities currently involved, and what we wanna do is summarize this complex scheduling project we've been working on. Serpil, as a graduate student, has been working on together with M.D. Anderson, and I know John Terrell is on the phone from M.D. Anderson.

But more broadly, we wanna use this to illustrate this general approach to solving complex problems. So as I move to the outline slide, I'd like to just set the stage and give a very little bit of background about mathematical optimization, linear programming, things like that, and how they can be used to solve problems like the one Serpil will describe.

And then she'll get into this specific breast cancer surgery scheduling problem, which is really just one instance of general type of problem, a multi-stage problem where you have multiple resources you need to be co-available for the procedure at the same time. But then also illustrate the same general approach on onto other types of projects and problems we've been working on that take the same general approach, because what we're really hoping is to stimulate discussion about where else could we do this type of work, either this exact work or this type of work.

So hopefully we can leave some time at the end for some discussion. So, just by way of general background, you should be seeing a slide now that says Background. Scheduling is ubiquitous in health care, huge problem everywhere. Anywhere you have sort of complex sort of needs, resources, rooms, patients, providers, sort of like the airlines scheduling problem, who flies when where and on what equipment?

A lot of work has been done, of course, over the years, and a lot of that has taken this general approach of using some sort of optimization program, a set of equations to solve this complex problem. So, I think most people on the line are familiar with what linear programming is, but I know that we're actually capturing these web exes to archive as part of the CHOT library summary of projects, so let me just invest a minute in summarizing what's a linear program, what's an optimization program for others, who may view this later?

There are basically three components to this type of a program approach. There are Decision Variables, Objective functions, and Constraints. So Decision Variables are the things that we can change, we have control over. We can decide about who works when what room I work in, what class I teach, when I go home all these things that you can decide about.

There's something you can't decide about, but these are things that we can control. We'd like to set the values of the decision variables such that they maximize or minimize or optimize some sort of objective, some criteria, so that's called the Objective function, it's what we're trying achieve. We might be trying to achieve maximal profit, maximal throughput, minimal overtime, maximize quality-adjusted life years, you name it.

Maximize profit when you go to Vegas, maximize expected value of profit, maximize the variation in loss. You know, what's the objective. And then there are Constraints. Those are things that we can't change. Nobody can work, at least nobody I've met, in two places at the same time. We can't have two surgeries in the same room.

There's sort of physical constraints and then there's sort of some additive constraints, like if I'm employed to work 40 hours a week, the number of cases I'm assigned to can't exceed more than 40 hours. By example, if there are regulations about minimal amount of rest between resident rotations, somehow you have to represent that in a system of equations and constraints, you have to represent the Objective function as an equation.

And then you basically put all this stuff in a piece of software and ask it to operate, optimize the objective function for you, lots of complex algorithms. I don't mean to minimize that, but they decide on the values of the decision variables that will basically optimize the objective function.

So that's the basic idea of what a linear program is, or an optimization program. Some things aren't linear, sometimes you have non-linear. Sometimes you have integer programs because the decision variables are integers. With the exception of myself, you can't have one and a half people scheduled if I'm only half a person.

So, you can see in the right-hand column, an example having to do with primary care scheduling, basically when should each PCP work? Maybe you wanna maximize continuity, you'd have to describe that mathematically. And then there will be some constraints, maybe PCPs can't work more than four clinics in a week, things like that.

So, that's the idea of an optimization program. So now we wanna describe three examples and starting with this CHOT project having to do with basically multi-stage surgery and here having to do with breast cancer surgery. So I will introduce Serpil, my stellar PhD student who will describe this portion of her dissertation.

> Thank you Dr. Benneyan. So, in the first example I will talk about the breast cancer surgery application of the problem that we defined as co-availability problem. So in this schematic you can see that when a patient is going to have a to have a Breast Cancer Surgery then in general she also opt for a Reconstruction Surgery, which should happen at the same time with the breast cancer surgery.

So, that would require two critical resources, which are namely oncologic and plastic surgeons. But those two different resources have different schedules, and there are some constraints related to those schedules, which you should account for. There is a problem with finding those two resources available at the same time when you are trying to schedule this composite surgery, and what we are dealing here is this problem.

So, this co-availability problem is not specific to breast cancer surgery, actually. You can come across with similar situations in other cancer types, or some other health care areas, like mental health or chronic care. Because patients might have multiple morbidities, even for example, obesity, or patients might need multiple types of treatment, or patients might need treatments that require multiple specialists, which are all required resources that need to be co-available for meetings, consultations, or procedures in general.

So, here this slide shows how we place what we are doing, and where can we observe the problem. So, at the down part of this slide, you can see how scheduling the surgery requests happens. So the inputs to your system are surgery requests, surgeon availabilities, OR availabilities, or examine room availabilities.

And your schedulers do the daily short term schedules of ORs and clinics, and these feed into the feature schedules as well. So this is where we observe the difficulty in scheduling composite cases. What we are doing with our co-availability model is to get inputs and organize the schedules of the availabilities of surgeons with our model in order to solve this difficulty in scheduling composite cases.

But how we are doing it, as Dr. Benneyan mentioned before, we used lenient programming, and here is our model, created in order maximize total number of common time slots of teams that are defined. The teams composed of breast and oncologic surgeons, that will ease the scheduling flexibility for the schedulers.

So you can also see the constraints we considered, which are task requirements, set activities, for example, a standing meeting for a surgeon is a set activity that you should account for, or preferences of providers. Some surgeons might not be compatible with each other because of their technical aspect, technical skills, or there might be some coverage requirements, like that you might need at least two surgeons in the clinic in each session of the week.

And of course, the team assignments, and if you require a certain amount of those surgeon pairs, then we can also mention this into our model. And determining when each surgeon is working for what type of task in each session, we can maximize these common time slots of determined teams.

And this slide represents the parameters that we have belonging to the case study we did with MD Anderson Cancer Center and their breast clinic. So, in this problem instance, we have 13 breast surgeons and 18 plastic surgeons with different requirements related to breast surgeries. We also got the operating room availabilities, and we analyze the data in order to determine the specifics of the surgeries, and accordingly we include constraints and perimeters into our model.

And we obtained the results you are seeing in this slide. So, you are seeing two different schedules, current and optimal, which are showing the schedules of four related surgeons during the week days. These different patterns represent the tasks, and what we see here in the current schedule is that, for these related surgeons, there are only four times left that they are co-available in.

But when we solved our problem of our model and obtained the optimal solution you can see the increase in these circled time slots. So, the linear program gives us the optimal availability schedule for surgeons, and it's calculated at 94% increase in desired team co-availability assignments as a result of our model and approach.

> So, you're maximizing shared time that people who might be needed to work together, an oncology surgeon and a particular plastic surgeon. You're just maximizing, subject to the constraints of however much time I need to cover clinic, and be an administrator, and blah, blah, blah, that we're just co-available, so that when the scheduler comes along, magically, you and I are both free to do the work?

> Yes. So, instead of randomly created, or not considering the synchronization created with not considering the synchronization of the payers, instead of those schedules, we are arranging the schedules of each surgeon according to each other in order to make them available when there's a need for a composite type surgery.

> Okay.

> In order to test our results, and see what are the implications of our approach in a real setting, we created the stimulation model just to test it offline before implementing it. Actually, we tried two different scenarios, and here you can see the flow of one of them.

So here what we are doing is creating a type of surgery randomly, and also assigning them a random surgeon. But while we are doing it we used parameters you see in this table, which we obtained from the analysis of surgery data. Here you can see the graph for those.

And depending on the type of the surgery then doing the assignment as a real scheduler could do it. And we measure the performance after that to see the results. So here you see the result of the simulation models. So first graph shows the improvement in the average number of desired matches throughout the year.

And you can see the increase in the proposed solution compared with the current plan. And it's a 152% increase in these group team assignments. We also looked at the operating room utilization and waiting time of patients in order to see if our approach is creating any negative effect on the system in general.

But as you can see from the graph, no disruption related to those parameters are observed. That's it for the first example. Now for yours, Dr.

> Okay, thank you, Serpil. So that's one example of a fairly complex logistical problem, where you'd scratch your head for a long time and try to do the best you could with pen and paper representing it mathematically and trying to optimize something.

I want to describe another example and then at the end sort of have some discussion about. Because what you did is you developed this beautiful solution and then did a phase one test in simulation. And then how do we take this stuff and test it in the real world, of course?

And our colleague John from MD Anderson is on the phone, I think, so we could have some discussion at the end. Let me describe the second example which is same general approach, a different problem. And what's interesting about it is two things. It's more focused here on primary care, as opposed to inside of a large building.

And the objective function has less to do with efficiency and minimizing costs as it has to do with maximizing care continuity, which is one of the tenets of where we're going with patient centers, medical homes, things like that. And in this particular case we're looking at team-based care in family medicine.

So that's the whole idea, with an interest on care continuity. So this idea of coordinated teams and even subteams, which one of our healthcare partners, Cambridge Health, calls teamlets, is kind of illustrated in this slide, where you have your primary care physician, your PCP, primary care provider, but they work on a team.

And in this case the PCP may be an attending or a fellow, and they work on a team and have some first-, second-, third-year residents, maybe a nurse, maybe a medical assistant, a front office person and so on. But you're working in teams in general, and the idea is of course you'd like to see your PCP, but if you can't see the PCP who you're familiar with, second best is to see somebody on the team that you have some familiarity with.

Because there's great clinical literature that care continuity and seeing somebody you're familiar with leads to better outcomes, leads to better trusting relationships, better compliance with preventative health, wellness screening, mammography, colorectal, everything, less utilization of inpatient services in emergency departments. So if care continuity is the objective, then scheduling all these people becomes this complex exercise where the objective is now to maximize continuity.

So we'll describe that in a sec. You're looking actually at the blue team, team number 2, which they decomposed into three subteams which they call teamlets, and I'll come back to teamlets. So basically they have 12 subteams. And the conceptual approach, if you look at the left-hand side, you can sort of see this matrix with color coding.

R is resident and F is your PCP, basically. And this is just sort of a random schedule, and if any one of us called up and said, I'd like to come in tomorrow, being Thursday, if my PCP is on the peach team, there's nobody from that team who works tomorrow.

Doesn't work Thursday morning and doesn't even work Thursday afternoon. So I'm sort of out of luck. I need to either find another time I can come in or I have to be seen by somebody who's not familiar with me and I'm not familiar with them. So that's kind of the notion, and you can see, we call this poor coverage, and Tuesday morning there's really only coverage, in this example, by two of the four colors, two of the four teams.

That afternoon there's only coverage by three of the four. And on the right-hand side, this is a schematic cartoon that represents what one might consider optimal. Which is basically any session, morning or afternoon, no matter when you want to come in, you can see somebody on your team, no matter what the color is.