Ashley Davis, Allison Pitt, and Emily Webelhuth

Modeling "Fox's Hole": The Simulation of a Campus Cafeteria

Senior Systems Engineering Design Project
Washington University, Spring 2008
Advised By: Dr. T. Eugene Day


Abstract

Computer simulation is often used to model the operations of complex systems. This paper describes the application of simulation to a campus eatery, Fox's Hole. Fox's Hole customers currently experience long wait times for service during the dinner hours. Simulation using MedModel© was used to model the current system, and thenadjustments to availability of resources were made in an effort to decrease the amount of time a customer spends in the system.

The possibility of a nearby eatery, Median Market, closing has been proposed by University administration. Should Median Market be closed, its customers would likely eat at Fox's Hole instead, thus increasing the volume of customers at Fox's Hole, thus putting additional stress on the system. The operation of Fox's Hole was then modeled taking into account the increase in the number of customers that would result from the closing of Median Market. Based on the results of this simulation, the current allocation of resources at Fox?s Hole would not be able to handle the increase in customers, causing the system to become unstable. Changes to the availability of resources were made in an attempt to bring stability to the system.

For both the current situation at Fox's Hole and the hypothetical case presented by the closing of Median Market, simulating various possible changes to each of the systems revealed well-defined adjustments to the allocation of resources that would improve customer experience by decreasing their time in the system.


Overview of Our Project

Introduction

A particular university campus eatery which will be referred to as ‘Fox’s Hole’, serves as the primary establishment for students living on campus to obtain meals. During peak times, Fox’s Hole is extremely crowded, and service times are long. Thus, there appears to be room for significant improvement in efficiency in terms of service times and server utilization. In addition to Fox’s Hole, there is another restaurant, which will be referred to as ‘Median Market’, very nearby to Fox’s Hole. Median Market is frequented by far fewer customers, and as a result, the university has considered closing it down. If Median Market were to be closed down, it would likely increase the number of customers at Fox’s Hole, thus potentially straining the Fox’s Hole system further. Simulation via MedModel©, a ProModel© product, was used to model the operations at Fox’s Hole. After modeling the operation of Fox’s Hole, taking into account the possible increase in customer volume that may result if Median Market were closed down, targeted adjustments to Fox’s Hole will be simulated in order to determine which changes improve efficiency.

Our Goal

The goals of this project are to (1) accurately simulate the operation of a university campus eatery, (2) determine modifications to the system that would improve performance in such ways as increased throughput and reduced customer wait time, and (3) assess the effect of an increase in the volume of customers to Fox’s Hole if Median Market was to be shut down.

Scope

Our simulation models Fox’s Hole during the peak dinner hours, 5:00pm to 9:00pm. We were interested in analyzing such aspects as waiting times for the individual food locations, average time spent in the entire system, aggregate throughput, utilization of the dining area, and utilization of other resources such as employees. We also gathered data on the number of people who frequented the secondary eatery to test the viability of shutting it down.

Methods

Raw data was collected by hand at Fox’s Hole from January to March. Data was collected on interarrival times, service times, resource behavior, and customer tendencies. The raw data was then fit to statistical distributions using StatFit©. Simplifying assumptions were made concerning resource availability, service models, and entity behavior.

The simulation was constructed using MedModel. While MedModel is typically used to simulate the operation of a medical facility, its flexible structure is conducive to the simulation of many types of processes. MedModel combines the intuitiveness of graphical programming with the flexibility hard coding.


Our Individual Contributions

Simulation Graphical Interface

Primary Designer: Allison Pitt

The intended users of this simulation are the designers of the model, and potentially Fox’s Hole management. We, the designers, intend to use the simulation to identify changes to the system that will improve efficiency and to determine the effect of an increase in the number of customers. Management could potentially use the model to predict the effect of day-to-day changes in the system (e.g. a cashier who calls in sick).

To make the simulation user-friendly, a graphical user interface was developed to represent the operation of Fox’s Hole. It allows the users to see a model of the system that is in an animated as opposed to a mathematical form, which will greatly increase its appeal to the non-technical managers. Users will be able to relate to an animation of the system far better than they would if the output was only numbers. For example, if a particular customer queue is getting very long, the user is able to quickly identify this as a bottleneck by simply watching the animation instead of having to look through several spreadsheets before identifying the problem.

Developing this animation required rough measurements of the dimensions of the eatery and the location of the furniture and appliances in order to make graphics in the model look like the real system. Appropriate graphical representations of various system elements (e.g. customers, employees, service locations, etc.) were chosen for incorporation into the animation. Path networks over which the customers and employees move from location to location were also created.

In addition, to allow the user quick modification location parameters, a graphical user interface was created that would allow user to change the number of resources and the capacity at a food station before the user runs the simulation in attempt to determine which changes should be made to the system to improve performance.

For further information about Miss Pitt's contribution to this project, feel free to email her at the following: alp1@cec.wustl.edu



Statistical Evaluation of Data

Primary Designer: Emily Webelhuth

After the raw data was collected, it needed to be organized and analyzed to become usable statistical data. We used the tool StatFit, a distribution fitting software, to help us with the task of converting the raw data into probability distributions that describe the possible paths of the stochastic processes within our model. These distributions and random processes direct the inner workings of our model, and needed to be reasonably reliable to produce realistic results. For more information on how we fit the distributions and the distributions used in our model, please refer to our attached paper at the bottom of this page.

For further information about Miss Webelhuth's contribution to this project, feel free to email her at the following: elw1@cec.wustl.edu



Simulation Processing Design

Primary Designer: Ashley Davis

Model Processing is devoted towards designing and implementing the logic which will recreate the flow of entities and resources in the system. This logic will provide the methods by which every customer and resource will be able to move on the path networks of the simulation, created by Miss Pitt, for every one of their desired actions, which follow the probabilities and distributions determined by Miss Webelhuth.

To simulate the arrival of customers into our model, I used the Beta distributions prepared by Miss Webelhuth under the following methodology. Arrivals were defined in MedModel via the Build Arrivals table. In the table, I specified the location where customers should arrive, the quantity of arrivals to be created at any one time, when the first of such arrivals are to be created, the frequency at which this quantity is produced, and the number of occurrences or total entities the arrival process will create in the model using these specificiations:

Once customers arrive at Fox's Hole, they will be routed around the model based on their personal preferences, which will be simulated by User-Defined Distributions entitled: WhatStation( ), WhatNext( ), and WhatExit( ). The WhatStation distribution will be used to route customers to a particular food station in the eatery. Then, once paying for their meal, customers will be routed to the exit, soda stations, or the dining area based on the output of the WhatNext distribution. Finally, those customers leaving the dining area will need to determine which exit they would like to leave from which will be simulated by the WhatExit distribution. The total processing of all customers follows the following flowchart.

For further information about Miss Davis's contribution to this project, feel free to email her at the following: aed2@cec.wustl.edu




Model Results and Modification Analysis

Present System Results

The model was run for 10 iterations representing 10 separate days' worth of data. Then the Utilization, Average Queue Time, Average Service Time, and Total Average Station Time were graphed for all the stations with service times that have statistical distributions. As seen in the graphs below, both Pasta and the Grill have utilizations that are hovering around 80%, and are therefore likely candidates to have the longest wait times. Our suspicions are confirmed when looking at the total station times. Because Pasta's long total station time is mainly due to the long wait in line, this is where our first improvement will be made. An improvement to the pasta station will also hopefully improve the percent of failed arrivals, which at times gets above 15%.

Modifications needed to Incorporate Median Market into Fox's Hole System

In adding Median Market arrivals to the present Fox's Hole system, the eatery became unstable. Thus, to make such a change manageable for customers and workers alike, the following modifications must be made to the amount of resources in the system: Additional Pasta and Grill Chefs, 5 Additional Grill Spaces, 4 Additional Tacqueria Oven Spots, and 2 Additional Cashiers. In making these changes, we found that the average time spent in the queue for any given station is not significant enough to cause any major problems. With these changes, Fox's Hole is now equipped to handle the additional customers who normally would have eaten at Median Market. For more information, please reference the figures below.

Fox's Hole with Median Market Arrivals: Queue Times and Failed Arrivals

Fox's Hole with Median Market Arrivals after Resource Allocation: Queue Times and Failed Arrivals


For Further Information about this Project

For complete information about this project please reference our complete write-up: Final Paper