There are two sample sizes for this work. For the observations of flow by severity index, a month of data from 2016, was randomly chosen using computer simulaton. Approximately 150,000 patients are seen annually at Kings County Hospital. A subsequent analysis (data not shown) demonstrated that there is relatively little month to month variation. However, since the database and data analysis programs were robust, a random month was chosen and the data from a spreadsheet file and was entered into the Online Staffing Optimization (OSO) software program of X32 Healthcare.

Subsequently, time measurements of 30 patients (10 for each of three severity index clusters) were followed on randomly chosen weekdays and randomly chose shifts for the analysis of minutes spent by patients in each area. These studies were planned by Xavier and Crane and were designed to focus on a single patient as they experienced the activities in the process. Different days and different shifts were sampled to avoid bias in the sampling. Three researchers timed the patients, Xavier and two Emergency Room residents, and care was taken to use the same methodology and to sample from all three shifts and each of the seven days (Data not shown).

In most hospitals, patients are triaged based on the Emergency Severity Index (ESI), a five-level emergency department triage algorithm that provides clinically relevant stratification of patients into five groups from 1 (most urgent) to 5 (least urgent) based on acuity and resource needs [14] .

Based on this system, we developed three resource-driven care flow cells (patients stratified by acuity and resource intensity) were created, thus allowing patients to be streamed to a resource driven flow cell [15] . Each of these flow cells have dedicated staff in a specific geographic area within the ED. This process of dividing patients into interconnected flow cells has reduced wait times and decreased motion for patients compared to a model that does not split patients into acuity stratifications [14] .

The high resource-driven flow cell involves patients triaged ESI 1 & 2. These patients are the most resource intense and are also allocated to a dedicated clinical team and geographic location. The medium resource-driven flow cell involves patients triaged as ESI 3. This flow cell is also staffed with a dedicated clinical team, including attending physicians, both emergency/internal medicine residents, nurses, a patient care technician, a clerk, and care managers to ensure this cell’s needs are met in a timely manner. The low resource-driven flow cell involves patients triaged as ESI 4&5. These low resource patients are typically “see and treat” and are allocated to a dedicated clinical team who only sees that type of patients. The team of providers for this flow cell includes a physician, an advanced practice provider, a nurse, a patient care assistant, and a clerk. This flow cell allows relatively “well” patients to be seen in a timely manner (Figure 1).

Figure 2 depicts the complex environment of patient flow through the health care continuum. Bottlenecks may occur: 1) within an area (internally within the ED itself), 2) between areas (internally within the hospital such as finding beds for admitted patients to either ICU’s or medical/surgical beds), and 3) with outside facilities such as Skilled Nursing Facilities (SNF) or discharge to home. Figure 3 depicts patient’s arrival into these treatment flow cells used for this study.

The authors observed care in the ED when they were not otherwise on duty. They defined flow cells and commenced with time observation studies. These were conducted by the first author and two research assistants who observed each of the key care team members: clerks, patient care assistants (PCA, equivalent to nursing assistants), nurses, and providers (including both Advanced Practice Providers and Physician Providers). Data were collected over all three shifts and over different days of the week. This time data was collected as de-identified data and this study was considered Internal Review Board exempt. Time observations (also called time studies) are important for accurately measuring the work load of each resource-driven flow cell. A time observation captures all the provider’s steps in the current state and the cycle time for each task separately. The procedures are outlined in the Crane text [16] .

After randomization of the day of the week and shift, the three researchers

followed patients carefully through all the steps in the ED. Ten patients were observed for each of the three severity index clusters. Data was collected on all the key care team members. The following materials and equipment were needed: stop watch, clip boards, a time-observation sheet, paper, and pencil.

Rather than resetting the stop watch to zero after each step, the time keeper announced the total elapsed time as the care team member performed each step. We calculated the individual time for each step excluding the wait times. The time recorder wrote the time for each process element on the time observation sheet. Data from the observation sheet was entered into a spreadsheet.

The Arrival Rate is the mean number of arrivals per unit time (usually per hour or per day). The Manual Cycle Time is equal to the time to complete the process minus any wasted time such as wait time The Service Rate is the mean number of customers that can be served at 100% utilization by each individual server per unit time (usually per hour or per day). After the time observations were completed, the cycle times were calculated for each key team member. The manual cycle times for each key care member are shown in Tables 1-3.

With the Manual Cycle Times known, the service rate can be calculated for each team members. A server’s service rate is typically calculated based on an hourly period by dividing 60 minutes by the MCT. Therefore, for the medium resource flow cell, the physician service rate is 1.83 patients per hour. In other words, if eight patients arrive per hour with three physicians on duty, only five patients can be seen per hour, meaning three patients are waiting every hour because the rate of arrival (eight patients per hour) exceeds the service rate (five patients per hour). Thus, for every hour the system runs this way, the queue length will grow an average of 3 patients; and assuming a steady state of arrival, about 72 patients will wait in a 24-hour period.

Queuing is a mathematical method of analyzing congestions and delays of waiting in lines or queues. Queuing theory is based on Poisson modeling. A thorough mathematic description can be found in this reference [17] . Ideally, queuing theory allows examination of every component of waiting to be served, including the arrival rate, service rate, number of servers, number of system places, and number of patients.

Queues are found nearly everywhere in healthcare. In the ED, we see queues on patient arrival at check-in; queues for triage; queues for providers; and queus for admission and discharge. For example, the first servers who patients encounter on entering an ED are a registration clerk followed by a nurse. When arrival rates are greater than the servers’ capacity or there is considerable variation in arrival patterns and/or service times, queuing occurs. This happens because the servers are still caring for patients who arrived earlier thus, the newly arriving patients must wait in a line.

To meet the facility’s goals as described in the True North Metrics [1] , X32 Healthcare’s Proprietary Online Staffing Optimization (OSO) tool was used. [18] The OSO tool is based on the use of Poisson Modeling and uses emergency department patient metrics, staffing inputs and volume information, and common emergency department statistical data to highlight demand versus capacity and hourly patient arrival distributions. The OSO tool can easily compare current and future staffing profiles, thus allowing teams to effectively allocate resources to reduce bottlenecks and better meet patient demand.

Theoretically these models can be used to understand the demands made of clerks, patient care assistants, nurses, advanced practice providers, and physicians by both hour of the day and day of the week. This information can then be compared with the current staffing levels to identify inefficiencies and create an optimal schedule for each service group. Our ED sees 140,000 patients annually.

We randomly chose a month of data between October of 2016 and October of 2017 for part of the analysis and a random week of data for the staffing analysis.

Cost analysis is critical to operations analysis. To recognize the necessary improvements, cost must be considered. In this analysis, we based calculating the reimbursement lost on patients who left without being seen and compared that with the increased costs of staffing flexibly to meet the actual demand. These calculations were made on widely acknowledged salaries for various figures on the patient care team: clerks, patient care assistants, nurses, advanced practice providers, and physicians. The hourly rates pertain to urban areas in the Northeast.

The roles of each care team member were identified and mapped before the time

observation data was collected for ten patient encounters in each flow cell over randomly selected days and all three shifts. The aggregated data was computed and is shown in Tables 1-3, stratified by the Emergency Severity Index. As expected, the time spent in each area almost always increases as ESI decreases (i.e. as acuity increases).

We calculated manual cycle times and service rate for each of the three severity index cells for clerk, patient care assistants, nurses, advanced practice providers, and physicians. Examining the data in this way allows one to see how many staff of each type are needed per hour to keep up with the demand. Table 4 shows the manual cycle time and hourly service rate by each care team member stratified by the severity index of the flow cell.

The flow changes over each hour and as patients remain in the ED, they remain in a bed that cannot be used for another patient. To determine the queuing effect on patients arriving at our busy ED by hour of the day and day of the week, data was entered into the Queuing Flow Simulator developed by Ms. Clay and Dr. Noon. Figure 4 shows that the length of stay through the physician queue, as estimated by discrete event simulation, varies throughout the day and ranges from less than one hour to over five hours for some patients.

In Figure 5, the red bars represent patients in the high and medium resource- driven cells, and the green bars represent patients in the low-acuity resource-driven

cells. The lower acuity demand is highest Monday through Thursday with peak arrival between 9 a.m. and 12 p.m. and lowest arrival between 11 p.m. and 6 a.m. Except for noted lower volumes, the high acuity and low acuity demands show a similar pattern of arrival. The patient demand will translate into provider workload for each given segment, which is discussed in more detail in the section in the following staffing analysis.

Table 5 shows the current patient metrics used in the model. These values are averages from a month of data chosen randomly between October 2016 to October 2017 provided by our internal scheduling software. Although 2016 and 2017 data was selected for this analysis, the data for the previous five years is based on 150,000 patient visits annually.

The percentile value in the third column of Table 5 compares these metrics with the EDs in the Centers for Medicare and Medicaid Services’ (CMS) database. For example, consider the length of stay (LOS) discharged value of 255. The percentile score of 1.51% indicates that 98.49% (100% - 1.51%) of emergency departments in the CMS database have shorter length of stay. Our observations suggest that our patients have long length of stays and wait times. Furthermore, the increased length of stay requires more nursing time.

Figure 6(a) shows the direct care nurse-resource demand based on the data in

the input module in OSO. The y-axis displays total demand (in number of nurses needed), and the x-axis is the hour of the day and day of the week. The red line profile represents the current nurse staffing based on the scheduled nurse assignments, using 0.9 patients per hour as the nurses’ service rate. The above analysis reveals the following: 1) the demand for nursing resources far exceeds capacity during the week days; 2) on weekends, the demand almost matches the current staffing profile; and 3) there is excess capacity on the night shift.

The new analysis created by our model is shown in Figure 6(b); ideal staffing would be represented by the blue line. The new schedule adds nurse capacity during the days to fully meet the demand. It also removes hours from the overnight periods and allocates hours to necessary time segments. To achieve this new schedule, an additional 225 weekly hours would have added to this model.

Figure 7(a) shows the advanced practice provider resource demand. These providers primarily work in the low acuity unit so that workload is governed by the percent of ESI 4 and 5 inputs. The y-axis displays total demand (in number of APPs needed), and the x-axis is the hour of the day and day of the week. The red line profile represents the current APP staffing levels. Based on the current schedule, which was entered into the OSO staffing model, we used the APP’s current productivity of one patient per hour as the service rate for the low-re- source flow cell.

The above analysis reveals the following: 1) a spike in unmet demand from 11 a.m. to 3 p.m. on most days; 2) a mismatch in demand and capacity, leading to excess capacity on the front end and resulting in waste; and 3) a significant amount of unmet demand on the back end possibly leading to patients’ leaving without being seen due to long waits. Figure 7(b) shows the ideal schedule.

When this schedule was created, more consideration was given to shift lengths and start times. Shift lengths are 10 or 12 hours because of contractual constraints, making it difficult to truly optimize staffing to meet the demand. However, the new schedule has some excess capacity that could be used for patient activities such as positive culture follow-ups and post-discharge follow-up calls. A better-fitting scheduling profile could be obtained by allowing these providers to work eight-hour shifts.

Figure 8(a) shows the physician workload, which is governed by the percent of ESI 1, 2, and 3 inputs. Furthermore, any low acuity advance practice provider leftover demand not covered rolls over to physicians and is included in the physician-demand chart. The y-axis displays total demand (in number of physicians needed), and the x-axis is the hour of the day and day of the week. The red line profile represents the current physician staffing levels based on the actual schedule and is then entered the OSO staffing model. The model uses 2.4 patients per

hour as the physicians’ high resource flow cell service rate and 2.7 patients per hour as the medium resource flow cell service rate.

This analysis shows the following: 1) the provider resource in staffing is not aligned with demand with too much capacity on the front end; 2) the demand for physicians far exceeds capacity almost daily, likely leading to increased number of patients who leave without being seen as well as long waits to see a provider; and 3) excess capacity is noted during night shifts. The new proposed schedule better aligns physician resources to meet demand (see Figure 8(b)).

In the staffing-to-demand analysis, significant gaps in staffing for advanced practice provider and nursing were observed. To align patient demand with adequate nursing resources, 225 additional hours would be added when creating the recommended profile; 205 hours were added to APP role and 15 hours were added to physician hours. The resulting costs can be viewed as salary/hour of additional time minus increased revenue from having less or no patients leaving without being seen.

For example, a nurse’s average pay rate of $47/hour in New York State and is equivalent to 225 * 47= $10,575 increase in cost. An advanced practice provider pay rate of $70/hour is equivalent to 205 * 70 = $14,350 increase in cost. A physician’s pay rate of $200/hour is equivalent to 15 * 200 = $3000 increase in cost.

Considering these changes ($10,575 + $14,350 + $3000), the new weekly cost is $27,925 more than the current model, almost $1.5 million annually.

In the current model, the APP service rate is one patient per hour, accounting for the need to increase hours to meet demand; however, if we benchmarked APP at two patients per hour service rate, we would decrease the weekly hours by 285, equivalent to a 285 * $70 = $19,950 decrease in weekly cost.

Let us assume that current rate of patients who leave without being seen is about 8%. If we assume each discharged patient represents an average charge of $250, an additional revenue of $2.8 M can be generated with this new staffing-to-demand model, thus increasing the ED’s profit margin.