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Discrete Event Simulation of Sports Facilities at University of Cincinnati

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Simulation of Sports Facilities at University of Cincinnati Campus Recreation Center

By: Nikhil Shaganti MID: M07428499 MS- Business Analytics Carl.H. Lindner College of Business, University of Cincinnati

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Table of Contents
Acknowledgments………………………………………………………………….3 List of Figures……………………………………………………………...............4 Objectives of the study………………………………………………......................5 About UC Campus Recreation Center…………………………………….............. 5 Scope of Simulation……………………………………………………….............. 6 Data Collection  Fitting Distributions for Wait times…………………………………………8  Challenges Faced…………………………………………………………….9  Assumptions………………………………………………………………..10 Fitness Center Model…………………………………………………………….....9  Basic Model………………………………………………………………….9  Updated Model- More Realistic……………………………………………10 Swimming Pool Model……………………………………………………………13 Output Analysis…………………………………………………………………...14 Conclusion………………………………………………………………………...18 References………………………………………………………………………...19

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Acknowledgements
With sincere gratitude, I would like to express my special thank you to Professor Dr. W. David Kelton. This project would have never been completed without his direction, assistance, and encouragement.

I would also like to thank my parents, for their endless support during each and every one of my life’s endeavors.

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List of Figures
Figure 1. Triangular distribution observed in Input Analyzer for Fitness Center Wait times...………………………………………….. 8 Figure 2. Triangular distribution observed in Input Analyzer for Swimming Pool Wait times…………………………………………...8 Figure 3. “Assign” Module to choose second and third work out Dependently…………………………………………………………..11 Figure 4. Fitness Center- Updated Model in Arena...........................................................12 Figure 5. “Hold” Module to wait for empty lane………………………………...13 Figure 6. Swimming Pool Model in Arena………………………………………13 Figure 7. Different scenarios analyzed in Process Analyzer…………………….15 Figure 8. Box-Whisker plot in Process Analyzer showing statistical significance of utilizations across different models……………………16

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Objectives of the Study 1. Simulate a part of Fitness Center and Swimming pool at UC Campus
Recreation Center 2. To determine the current resource utilization, queueing status of these facilities and exploring options to improve.

About UC Campus Recreation Center
University of Cincinnati Campus Recreation Center (CRC) is ranked No.1 in the nation for its innovative design and facilities. The CRC is an impressive building, with over 200,000 square feet of recreation facilities. It has three pools, over 21,000 pounds of weights, a climbing wall, a suspended track, volleyball courts, basketball courts and many other sports facilities. With a heavy focus on swimming and other aquatic sports, the facility is a big bonus in Ohio’s extreme winter. University of Cincinnati has always placed a premium on impressive architecture, and the CRC is an example of this. UC’s facilities for student athletes are also impressive. The building is wedged into a tight spot between the football stadium (Nippert) and basketball stadium and was built when UC joined the Big East conference.

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Scope of Simulation
University of Cincinnati Campus Recreation Center is ranked the best in the Nation for its variety of facilities. So there is need for the management to constantly evaluate whether the facilities provided in the Recreation center are sufficient to maintain its status. Important factors while evaluation are resource utilization and queuing status. Like any other organization, even the sports facility must also maximize its resource utilization to maintain customer satisfaction and profitable functioning. One method of developing utilization strategies is to make use of the simulation modelling. With Simulation, one can easily evaluate the system under different scenarios. Using the software Arena, a simulation model can be created to replicate the characteristics and activities of fitness center and swimming pool. This allows the management to make correct decisions regarding the allocation of resources. An ideal model can also proposed based on number of resources which can be up to their optimum utilization.

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Data Collection
The data collection mainly involved recording number of students per hour and time they spent using the resources in Swimming Pool and Fitness Center. However, I have restricted myself to only few equipment in the Fitness Center namely Treadmills, Elliptical Trainers and Bikes to simplify the model and capture every scenario as in real world.

For arrival rates, I collected the data on three different days at five different timings. I extrapolated the data using statistical measures (mean and standard deviation) for a week and calculated the average. For this project, I used nonstationary Poisson process to create the entity arrivals. The reason behind choosing this type of schedule is to capture the varying arrival rates as in the real- world scenario. As we usually notice, there are certain peak timings in which people prefer to go for work out or a swim.

Timings: Fitness Center: 6 AM- 10 AM, 16 hours Swimming Pool: 6 AM- 8 PM, 14 hours Recreation Center usually operates at different timings during different days of the week. But for the scope of this simulation which is only one day, I considered most common timings among them.

Fitting Distributions for Wait times: The data collected for wait times have been fitted into a distribution using Input Analyzer tool in Arena. Best fit was observed to be triangular distribution.

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Wait times in Fitness Center:

Figure 1. Triangular distribution observed in Input Analyzer for Fitness Center Wait times

Wait times in Swimming Pool:

Figure 2. Triangular distribution observed in Input Analyzer for Swimming Pool Wait times

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Challenges Faced:  Due to time constraint, the amount of data collected is not really sufficient.  The data collected might not be the exact representative of the real world scenario as there are many factors which affect arrival rates like bad weather conditions, holidays etc.

Assumptions:  As the data is only collected at four different timings of a day, it is assumed that those are representative of the certain hours before and after that specific timing. This assumption does seem intuitive because of entity characteristics i.e. student. As students tends to work out more in a specific timings of the day due to schedule constraints.  It is assumed that the scheduled arrival rate is representative of all the days in a week, which might not be the case. Weekdays and Weekends usually have different arrival rates. In my data collection process, I collected data on 2 Weekdays and 1 Weekend. So, this might capture the total essence to some extent.  In real-world, most of the scenarios are based on decision making. E.g. choosing a lane in the swimming pool (or) equipment in the fitness center. So based on the amount of data collected, it is difficult to come up with an exact percentage of choosing an option in a scenario. So based on my limited observations and from a sense of human mentality, some decision percentages are assumed.

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Fitness Center Model
For the scope of this project, I have limited myself to only three equipment namely Treadmills, Elliptical Trainers and Bikes. This is because it gives a flexibility to capture the complex behavior of the system as closely as possible. Basic Model Basic Structure:  Students arrive. They chose one work out from the 3 available work outs. If the resource is available, they seize the resource immediately or else wait.  Student spends approximately 10-15 minutes in each workout. After the first work out they may or may not go for second and third workouts.  Then process repeats, and student leaves after certain time. Queuing is avoided in the updated model because in real- world that never really happens. Moreover, entities are divided into Male and Female. Decision percentages and arrival rates are kept different to capture reality. If an equipment is not available, the person tend to choose another work out. Key parts in Modelling:  Modelling the choice of work out is key in this simulation. As a student has to choose a work out from different work outs (which he hasn’t done before). Repeating work out never really happens in reality. Using the Modulus function we can achieve this.

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Figure 3. “Assign” Module to choose second and third workout dependently

Updated Model- More Realistic In the above model, the entities might experience some queue during peak timings. Queuing is avoided in the updated model because in real- world that never really happens. If an equipment is not available, the person tend to choose another work out. Moreover, entities are divided into Male and Female. Decision percentages and arrival rates are kept different according to gender to capture reality. This is because Female students are more likely to spend time in this area of Fitness center compare to male students.

Changes made:  Different arrival schedules are created for Male and Female Students. It is observed that distribution is 60:40 Female to male.
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 Students check if resource is available. If not, they skip and move on to next work out. They may or may not come back for again work out. The number of such students leaving is recorded.

Fitness Center-Final Model:

Figure 4. Fitness Center- Updated Model in Arena

Swimming Pool
Basic Structure:

 Students arrive. Initial delay of 1 minute for certain activities. If the lane is empty, they seize the resource immediately. But if there is someone already in the pool, they may or may not share the lane. If not sharing, then he/she waits for an empty lane.
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 Student spends about approximately 20 minutes in the pool and then leaves swim. Key Parts in Modelling:  The concept of sharing the lane and waiting for an empty lane. This can be achieved using “Hold” Module with “Scan for condition” option.

Figure 5. “Hold” Module to wait for empty lane

Final Model –Swimming Pool

Figure 6. Swimming Pool Model in Arena
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Output Analysis
Fitness Center At present, there are 36 Elliptical trainers, 24 bikes and 30 Treadmills in the Fitness Center.

For Basic Model (with queue),

The scheduled utilization of these equipments is found to be very low. Even if there was a possibility of queue, there was no wait time for the entity at all. So analyzing individual queue doesn’t make any sense.

For Updated Model (without any queue)

The updated model almost mimics the real-world scenario. In this case the scheduled utilization was found to be very less. Moreover, even the students leaving is found to be zero.

So this does not seems to be the best case. There is hardly any utilization of the resources. So it seems like recreation center is spending too much on the facilities which are not up to its optimum utilization.
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Analyzing the Updated Model using Process Analyzer:

Figure 7. Different scenarios analyzed in Process Analyzer

I have analyzed different scenarios using Process Analyzer. Management can make decisions keeping in mind two factors: - Increased resource utilization, - With not much increase in students skipping exercise due to non-availability I tried changing the values of number of equipments and analyzed the utilizations and skipping counters.

As in Scenario 4, we found the maximum utilization among the other scenarios but the number of students leaving due to non-availability of equipment has increased. So it is not a good sign. We can observe a utilization-No. Of students leaving trade-off. So we can see that Scenario 6 which has almost half of the resources when compared to present scenario, seemed to have almost doubled utilization. In addition, the students leaving are even less. So around 30 students skipping exercise due to resource non-availability is not a big concern to worry about. But this utilization-No. Of students leaving trade-off is subjective, and one that management can setup according to their decision. So PAN provides us this flexibility to analyze different scenario and choose the best one among them.

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Figure 7. Box-Whisker plot in Process Analyzer showing statistical significance of utilizations across different models

We can see that Scenario 6 is better than Present Scenario in terms of Scheduled utilization of the resources. But is it statistically significant? Yes, from the boxwhisker plot. According to PAN, Red scenarios are statistically significantly better than blues. 95% vertical confidence interval of utilization of each scenario is shown in the picture. The 95% confidence interval of Utilization in of Scenario 6 doesn’t overlap with that of Present scenario in any resource. This gives us a reasonable idea that both are very different and supports our PAN results.

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Swimming Pool At present, there are 6 beginner lanes and 10 expert lanes, in which each lane may or may not be shared.

From the above results, we can see that even when the utilization is very low, there is some queue which is observed. The waiting time for an empty lane is varying from 3.14 minutes to 21.47 minutes with an average of 5.41. This is the case when there is sharing of the lane which is not a best way to defend ourselves. So if the concept of sharing is not considered (or) with increase in arrival rates, then students may have to wait for longer time to get an empty lane. Moreover, we can see that utilization of Expert swimming lanes is around 0.1218 which is very low. These lanes are used for competitions, so it makes sense to have more-thanrequired quantity.

But management might want to take the empty lane queueing into consideration and increase the beginner lanes to provide more student- satisfaction. The model built is not a generalized one as we cannot vary the number of resources, analyzing output in Process Analyzer is not possible.

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Conclusion  The current utilization of the resources in Fitness Center is very low. Even with an allocation of half of the resources of that in present scenario, the utilization is around 0.5, which is almost 100% increment. So there is need for management to make decision regarding the same to maximize utilization and increase profitability keeping in mind student- satisfaction (Utilization- student leaving trade-off)  Even with the concept of sharing of the lane, which is not a usual thing, there is some queue observed to get an empty lane. This might turn into longer waiting times with increased arrival rates. So management might have to consider the same and take a step towards allocating more beginner lanes.

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References 1. Simulation with Arena, 6th Edition, W. David Kelton , Randall Sadowski, Nancy Zupick

2. “Use of Simulation Modeling in Sport Facility Resource Utilization”, Kevin Cross, The College at Brockport

3. Simulation Modeling and Analysis with Arena, Tayfur Altiok, Benjamin Melamid

4. “The 25 Most Amazing Campus Student Recreation Centers”, www.bestcollegereviews.org

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