The Role of Discrete Event Simulation and Monte Carlo Simulation

The two most common types of simulation we encounter in our healthcare operations discussions are Discrete Event Simulation (DES) and Monte Carlo Simulation (MCS). As many healthcare operations practitioners are becoming acquainted with simulation, it may be helpful to discuss the differences between these approaches. In our book Simulation Solutions, Andrew Ganti and I discuss the application or framework for applying DES in some detail. Readers seeking more information can view our book, available on Amazon. In this article, we’ll discuss the role of DES and MCS in healthcare, focusing on their suitability for various hospital processes and requirements.

Logically, for those readers who aren’t familiar with these types of simulations, we’ll start with some definitions. Let’s begin with simulation, which Webster’s Dictionary defines as the imitative representation of the functioning of one system or process by means of the functioning of another, which is a complicated way of saying that we are using a computer to model or simulate a real-world process, such as a computer simulation of patients arriving at an Emergency Department. One of the advantages of simulation modeling is that the model “allows you to analyze systems and find solutions where methods such as analytic calculation and linear programming fail.”[1]

Next, let’s define Discrete Event Simulation. In DES, we model a process described by “events”. Each event is discrete, meaning the system changes only when an event occurs. So, our DES is a sequence of events that occur over time, and each event marks a change in the system's status. In a hospital Emergency Department, events may include patient arrival, triage complete, nursing assessment complete, treatment, etc. In this way, the basic structure of a DES model closely resembles a process map.

Some typical areas that we could apply DES:

• Hospital patient flow

• Manufacturing production lines

• Airport operations

• Call centers

• Supply chains

Finally, we define Monte Carlo Simulation (MCS). In MCS, we simulate a task, activity, or process step that exhibits variation or randomness. In DES, we simulate an entire process that may consist of several steps. In contrast, in MCS, we generally focus on a single step or an activity with a very limited number of steps. MCS is often used to assess the risk involved in a decision or the failure of a sequence.

"Monte Carlo simulation is basically the use of random sampling to obtain numerical results; in operations systems, those results are typically a system characteristic. The random samples from any type of distribution are combined in some manner (e.g., added, multiplied, or in some way mathematically transformed) in order to obtain an estimate."[2]

To expand on the definition, I think it is best illustrated through an example. One place I’ve used MCS is in assessing Discharge Team staffing. A Discharge Team, part of Environmental Services, is dedicated to cleaning the rooms of discharged patients. By having a dedicated team for this activity, patients’ waiting times in the Emergency Department are reduced. I first used MCS in a hospital in Michigan, where, looking at the Discharge Team staffing using average discharges, the staffing looked adequate, but we were having trouble getting discharged patients’ rooms cleaned in a timely fashion, resulting in patients waiting in the Emergency Department, which clogged that area and caused long wait times for patients who needed to be seen. While several factors could have been affecting the outcomes, we noticed that the number of “callouts” (employees calling out sick) fluctuated significantly. When someone calls out, they might be replaced in a few hours or, depending on availability, not at all.

We modeled the number of discharge beds that needed cleaning, which could also exhibit significant variation, and we modeled staffing, looking at the typical staffing level minus callouts. We used two different statistical distributions—one for the number of beds that would need discharge cleaning on a particular night and another for callouts—and combined these numbers, along with the average time to clean a discharge room, to determine how long it would take to clean the simulated discharged rooms. We then examined staffing increases in relation to the probability of callouts and the probability of a low or high number of discharges, and balanced staffing to ensure beds were cleaned in a timely fashion.

This is typical of MCS: we generally look at a task or event with a relatively simple mathematical formula. In my example, we have Number of rooms needing cleaning in a day (which has variability and is represented with a probability distribution) X Average Time to Clean a room / Staff available (which is variable and represented by a probability distribution x 7. We started with this simple formula, and as we explored the issues, it gradually became more complex as we added factors to account for how long it took to find a replacement for a callout and the chance that a replacement was not available.

But this simple formula showed us whether the Discharge Team could clean all the rooms within their shift, and we learned that with 1 callout, they could not. We also learned that in many cases, if the callout was replaced within two hours, the team still would not be able to finish their discharge cleaning within the shift. This was the key revelation – that discharge cleaning was highly dependent on having a full team at the start of the shift, and it was a hit-or-miss affair. Later, we refined our formula to determine when discharge cleaning would be complete and used that to understand the effects on the Emergency Department.

Some common applications for Monte Carlo Simulation are:

• Financial risk analysis

• Forecasting project completion times

• Reliability modeling

• Estimating probabilities in complex systems

A simple way to distinguish between these two techniques is:

• Monte Carlo: What might happen? (probabilities)

• Discrete Event Simulation: How does the system operate over time?

On the Kinetic Resolution website, in the Resource section, www.kineticresolution.com/resource, we have an Excel spreadsheet that further describes MCS and DES requirements and their suitability for key hospital processes.

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‍For those readers not very familiar with DES or MCS, this article explores the basic differences between these two techniques. The tables at www.kineticresolution.com/resource, should provide ideas for where to apply these techniques. Both Andrew Ganti and I consistently maintain that simulation is one of the most powerful and yet underutilized tools available to healthcare practitioners to improve patient flow and understand complex situations.

[1] Ilya Grigoryev, Anylogic7 in three days (Ilya Grigoryev, 2016),10

[2] Malcolm Beaverstock, Allen Greenwood, William Nordgren, Simulation: Modeling and Analysis using FlexSim, Fifth Edition (Utah: FlexSim Software Products, Inc., 2017), 236