Demand and Capacity Modelling in Healthcare Using Discrete Event Simulation

The NHS is right now confronting huge pressures relating to demand and capacity in radiology. The purpose of this research has been to provide information about MRI usage, details of operational aspects of MRI services, and to ascertain the planning intentions of NHS radiology services to keep up and create MRI capacity. The report expands on using Discrete Event Simulation (DES) to inspect and plan the utilisation of NHS hospital resources for the radiology department to help a 24 hr service that is available to outpatients which will help with diminishing patient waiting time, better resource usage, understanding the capacity and demand. Consequently, this research examines to adjust staff and resources with the demand of the MRI. The research was investigated using DES in various scenarios to find which resources are inactive; patients are treated slowly. DES helped in discovering resource utilisation and outpatient throughout the system. It additionally helped in distinguishing the bottlenecks in patient flow. The DES simulation results demonstrated that time for the outpatient in the system is less and more outpatients have been treated too. There is a higher level of outpatient patients leaving the system under 120 minutes. The report uncovered an MRI report interpretation time. Reception room time and MRI waiting room time are decreased significantly. It additionally exhibited with an expanded outflow of outpatients, resources, for example, MRI capacity and radiographer utilisation expanded.

The NHS is as of now confronting noteworthy pressures relating to demand and capacity in radiology. Generally, out of hours radiology services during late evenings, nights and end of the week used to be an on-call model. The government has, again and again, ensured the public a 24/7 health service. The rise in demand for radiology services brought unevenness among demand and supply. Here are a couple of issues in the radiology department as shown by [1] lop-sidedness makes Mondays busier when contrasted with different days of the week. In like way, [2] actualised Markov chains in planning different patients group coming at different arrival rate and confronted the problem of allocation of resources for the dynamic demand.
Another issue, at NHS Hospitals in the report [3] and [4], outpatient services, for example, radiology currently run day in and day out for inpatients and emergency; however, they are just accessible to outpatients between 9 am and 5 pm. [3] reports uncovered that around 8% of the outpatient missed their appointments and no show is an enormous issue. [5] clarifies that different patient groups such as inpatient, outpatient and the emergency patient are given different priority. The emergency patient is given more priority when contrasted with inpatient and outpatient. In like manner [6] states that disregarding random arrival of the patient can make the model off base.
At some of the time it is hard to incorporate all the aspects of the real problems in the simulation model. The issue which NHS is facing at the moment is an increase in patient waiting time and busier Mondays. This is due to the underutilization of the resources. This has further lead to randomness in-demand and mismatch between demand and capacity. According to [3] [7] prescribes assigning exclusive blocks to the process with the anticipated demand and assign pool blocks to the process with less predictable demand. Also, [9] contends that a separate process for emergency patient helps in decreasing cancellation and overtime. Furthermore, [10] states that more patients booked at the start of the hour and less at the end of the hour to absorb delays. Two patients are booked at the beginning of morning and afternoon sessions and remaining patients are booked at equal interval to avoid delays.
According to [11] report expresses that consultants should be on a staggered rota throughout the weekend and public holidays from 9 am to 8 pm. The weekday evening rota should be 5 pm to 8 pm. The support staff should be available for extended hours. The radiographer and radiologist time should not be wasted on administrative tasks. This will help improve the utilisation of high worth equipment, for example, MRI. Moreover, [4] report proposes that staff rota for radiographer and consultant to be 3 days for one week and 4 days for the following week.
[12] DES helps with foreseeing future demand using historical patient arrival rates. Additionally, [13] states DES helps in assessing poor outpatient flow. It uncovers that scheduling and capacity planning in healthcare helps with improving efficiency. Moreover, [14] and [15] suggest using DES modelling in healthcare for improvement and enhancement. Also [10] states DES underpins in modelling, outpatient in scheduling system, number of appointments, physician time and patient flow. [16] features that hospital expanded hours and opening on weekends encourages in improving access to hospital care. [17] diagrams that DES implemented hospitals in Sweden had improved the process quality. Moreover, [18] illustrates adjusting supply based on demand and time allocation for the activity assists in bringing balance. Likewise, [19] encourages to use DES for outpatient capacity planning, in healthcare. Similarly, [20] features DES to find the outpatient flow in healthcare. DES used for planning, testing and staff scheduling in a hospital facility with increased capacity. [21] claims that DES is used in an outpatient clinic with batch arrivals to take care of the no shows problem. The other solution, to give same-day appointment in which the patient is less likely for no show. In like manner, [22] states that overbooking helps in utilising healthcare resources for the no shows. Likewise, [23] highlights that outpatient cancellation and no shows can be settled using overbooking of the appointments, to amplify the utilisation of radiology capacity.
The objectives focused on solving the problem using DES to simulate the de-

Performance Measures
Key performance metrics KPI are occupancy rate, clinic utilisation, staff utilisation (radiographer, clerk, nurse), patient throughout time, average waiting time, diagnostic procedure count. [24] approves using DES for demand and capacity model which will assist in identifying the key performance indicator. The other KPI can be resources average use, percentage of the patient leaving the system is under 120 min.

Input
Input parameters shown in Figure 1 will be MRI service time, number of MRI, number of staff, patient process, patient arrival rate. As indicated by [25] [26] and Figure 1 and Figure 2(a) clarify that the process chart is imperative to understand the problem, objectives, input, and output of the system. It is separate from the simulation model. Likewise, [27] notices to use activity-based the diagram in healthcare for service delivery processes. Also, [28] proposes changing hospital process flowchart into the DES model which assists in analysing how much resources of the hospital are being utilised. Additionally, [29] features simulation assists in incorporating different customer arrival rates and service time for modelling without affecting the real system of the radiology depart-Open Journal of Modelling and Simulation ment. The process includes such as patient scheduling by the clerk, scanning by a radiographer and report interpretation by a radiologist. Figure 2(b) shows the methodology adopted for simulation.

Assumptions
• No travel time for any resources taken into consideration; • Preparation time is included in the waiting area time; • Patients are always coming in time; • Outpatient is coming with an appointment; • Emergency patient care given priority; • The lateness of staff is zero; • The capacity of 20 in the reception and waiting room queue; • The capacity of 25 in the MRI reading room queue; • Radiographer takes the patient from the waiting room; • Availability of resources (staff and machines)-90% of the time; • 3 shifts morning 9 am to 5 pm, evening 5 pm to 1 am and night 1 am to 9 am; • Figure 3 shows Radiographer morning 4 nos, evening 3 nos, night 2 nos; • Figure 3 Clerk morning, evening, night 1 no for each shift; • Figure 3 Consultant morning, evening, night 1 no for each shift; • We are not taking into consideration MRI report preparation time but considering consultant MRI report interpretation time; • Evening demand calculated from 50% of the total outpatient demand and Night demand calculated from 25% of the total outpatient demand; • Constraints are morning, evening, and night shifts.  [30] uncovered that DES results are better for nonlinear systems as compared with system dynamics and agent-based modelling (ABM). DES takes into consideration patient arrival rate, staff scheduling and resource constraints. In like manner, [31] clarifies that DES is used for operational and strategic purposes. It is likewise called a dark grey box, where clients can link different processes in the model easily. DES is the best solution to this problem. System Dynamics (SD) is good to see the holistic view and for this problem, a detailed view is essential consequently, DES is applied. [32] DES is in high demand in healthcare for resource planning, capacity estimation and evaluating alternatives. Key resources in healthcare are nurses, consultants, and physicians. Data for the simulation can be collected through primary sources such as survey and current records of the hospital. The other means of collecting data is secondary source such as a literature review.

Sources
Different service time is recommended for MRI. Moreover, [33] states that service time for MRI is 33.2 minutes with a minimum of 10 minutes and a maximum 120 minutes. Also, [34] states that around 55% patient goes to the preparation area and for the contrast, preparation time is a triangular distribution (3,4,5) and patient preparation in the MRI room is 6 minutes. MRI process time for changing room is Gamma (3.41, 0.86), setting patient and MRI machine is Gamma (2.08, 2.01), MRI scanning is Gamma (7.86, 2.67), after scan activities Gamma (1.66, 1.81). Furthermore, [35] states that MRI total process time is normal distribution (26.46, 20.47). Additionally, [1] states that service time for the critical patient is more as compared to the normal patient. As well, [36] states that an old patient scan takes more time as compared to the young patient as young are very responsive. In addition, [37] states service time using lognormal (4.15, 0.335) distribution.
The input parameters are listed in Table 1.

Assumptions
• Increased the standard deviation of MRI processing times for inpatient of 5 min and emergency patient of 10 min; • Warmup period of 4320 minutes (1/10 of the total run period); • Simulation run 1 month; • No of runs 20; • Figure 6 shows the precision with 20 runs; • Random Sampling 17.

Fitted Distribution
Different statistical distributions can be applied using Lognormal, Normal, Exponent, Gamma, Pearson V and Weibull. The input parameters are estimated and fitted using chi-square goodness of fit. Fitted distributions help the model incorporate the stochastic nature of the hospital system. In case, seasonal data is not available [37] suggests using Poisson distribution means static distribution for patient arrival. I had only daily data, so I divided it by 24 hrs and then by 60 min-get interarrival times in minutes. I have used Pearson V distribution for patient arrival time and the patient arrival during the morning, evening, night.
[38] highlights in the radiology department Pearson distribution is used. The input parameter fitted distributions type and value is given in Table 2. to check the normality of the patient arrival data and found P value less than 0.05 which means poor fit. I have tried to fit data using Chi-square goodness of fit and found P value greater than 0.05 which means each category has the same proportion.

Simul8
I have used Simul8 for the creation of the model.     & emergency patient is given a different route to access the MRI services. In this, a separate queue is given for inpatient & emergency. No-show problem of outpatient is resolved by overbooking shown in Figure 9(b) and Figure 9(c). Outpatient gave access for the reception and further going to the waiting room for MRI.

Run Length and Replication
To get precise and narrower confidence interval, I have run the simulation for one month with 46 replications for each scenario. I have used Simul8 to find the precision of 46 runs.

Output
Validation of the Model • The total demand in February 2018 for MRI scans was 2089 (historical data).
• Our model simulates a demand of approximately 1828 to 1930 scans, so is between 85% and 90% accurate in terms of demand. • Figure 10 display that outpatient flow of 8 hr, 16 hr, 24 hr was validated in Simul8 and there is an upward trend from 9 am to 5 pm for 8 hr. There is a rising trend from 9 am to 1 am for 16 hr and uphill trend for 24 hr.

Output Analysis
After running different scenarios, Figure 11 and Figure 12 and Table 4 show scenarios 9, 10, 11 gives the best result, throughout time for the patient in the system is less. More outpatients have been treated as well. There are a higher percentage of patients leaving the system in less than 120 minutes. Furthermore, in scenarios 9, 10, 11 approximate 1900 outpatient are treated with reasonable average time in the system. Figure 11 shows that scenario 8, more overbooking as compared to scenario 7, resultant to increase in average time in the system for inpatient and outpatient. Figure 12 shows that there is a trend to be seen with an increase in average time in the system for the outpatient results to a smaller number of outpatient being treated. Figure 12 shows that scenarios 4, 6 outpatient average times in the system dramatically shoots up due to slow processing at the MRI machine.
In Figure 13 elaborates that in scenarios 9, 10, 11 outpatient, inpatient &   emergency exit numbers are steady. The results are better as compared with scenarios 1, 2, 3, 4, 5, 6. The exit numbers of scenario 8 are more but adversely affecting the other KPIs. Therefore, scenario 8 was ignored. Additionally, more outpatients are treated in the system. Furthermore, in scenario 11, there is an upward slope which states the percentage of patients leaving the system has increased for the outpatients, steady for the emergency and inpatient. Table 5 shows statistical significance using one-way Anova and Tukey test to find the variation between different scenarios. Figure 14 shows that Report reading, Reception and MRI waiting room queue time is reduced dramatically.  Figure 13. Outpatients exit number.

Learn
The things I learnt in the model is that the scenarios in which resources are idle, patients are treated slowly. This model really helped in finding out resource utilisation patient throughout. It also helped in identifying the bottlenecks in patient flow. It also demonstrates with the increased outflow of outpatients, re-Open Journal of Modelling and Simulation sources such as MRI and radiographer utilisation increased. Waiting Room MRI Average queue time dropped from 17 min to 5 min. Outpatient exit average time in the system is reduced by 20 minutes in scenario 11. Also, I learnt to match demand with capacity in different hours.

Recommendations
We can also take into consideration that the cost as the KPI and agent-based modelling can be implemented for it, in which patient, radiographer, clerk, radiologist as a separate agent can be classified, and it takes a little bit more time to build. The hybrid model which is the combination of DES and agent-based modelling can also be applied for the planning and finding cost in healthcare.

Difficult to Model
• Gather more evidence for demand at night through a survey of family and friends. • DES is difficult to model interactions between the large diversity of staff.

Model Limitations
• Restriction only to MRIs, rather than the whole Radiology service.
• Using resources that are presumably shared with other scans or services.
• Only limited data from NHS, and lots of data taken from literature or assumed.
• Demand at night which has been assumed and needs more evidence to support it.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.