Boğaziçi UniversityDepartment of Management Information Systems

MIS 463 Decision Support Systems for Business

PROJECT FINAL REPORT

QUEUE SIMULATION FOR A CERTAIN FAST FOOD CHAIN

Project Team No: 12

ŞEBNEM ÇOPURGÖNÜL ZEYNEP SAVACI

ERDİ ŞEKERCİLERENES YILMAZ

Instructor: Aslı SENCER

İstanbul - December, 2015

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Table of Content I. INTRODUCTION.........................................................................................................................3

I.1 The Decision Environment...................................................................................................3

I.2 Mission of Project................................................................................................................4

I.3 Scope of Project..................................................................................................................4

I.4 Methodology.......................................................................................................................5

II. LITERATURE SURVEY.................................................................................................................5

III. DEVELOPMENT OF THE DSS....................................................................................................7

III.1. DSS Architecture...............................................................................................................7

III.2 Technical Issues.................................................................................................................8

III.3 Data Source and Flow Mechanisms.................................................................................10

III.3.1. Data Source and Structure.....................................................................................10

III.3.2. Data Flow Mechanisms..........................................................................................11

III.4. Model and Algorithms....................................................................................................12

III.4.1. Validation....................................................................................................................17

III.5. User Interface and Reports.............................................................................................19

V. ASSESSMENT..........................................................................................................................26

V.1. Project Plan.....................................................................................................................27

VI. CONCLUSION.........................................................................................................................30

REFERENCES...............................................................................................................................30

Appendix....................................................................................................................................30

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I. INTRODUCTION

I.1 The Decision Environment

In today’s rapidly changing world, time is an important factor for people and population of the world has exponentially increased. Although people have limited time, they have to wait in many queues such as shuttle queue, restaurant queue, a queue on traffic and so on. Particularly in metropolitan cities like Istanbul, since the population is so high, queues are getting longer. Then we decided to make a simulation to analyze and handle queues.

We tried to focus on a specific problem which is a queue problem in a certain fast food chain. If it is necessary to explain why we choose one of the fast food chains, we can say that many students and workers prefer to eat outside instead of prepare in their homes. Moreover, they decide to place to eat according to price and preparation times of foods to prevent money and time consuming. That’s why fast food restaurants are so common and their queues are so long. In brief, waiting queue in fast food restaurants is our daily problem not only for customers but also fast food chains. Since waiting time is too long, customer loyalty is decreasing.

To increase using time efficiency and customer loyalty, the certain fast food chain should handle long queues. Therefore, it should decide. To better understand, most of the people do not prefer to eat fast food in the morning so the fast food chain do not need to open many cash points. According to result of simulation, each regional director of the fast food chain decides to exact number of workers and number of cash points for each time period in a day. These kind of decisions are important to increase profit and supply demand of customers. Also it provides the fast food chain to schedule its workers in an efficient way. In every quarter of year, regional director of the chain should arrange number of workers and number of cash points. In decision period, simulation is repeated with different parameter values. Then results of simulations are compared. According to comparison, if necessary, regional director of the chain take action.

Deciding the number of workers and cash point can be seen easy however each new worker is cost for Chain Company. Therefore, regional director should want to be worked a few number of employee and serve more customers. Moreover, customer demand has fluctuations from month to month, from day to day. Even it changes in different time periods of day. All of these factors increases complexity of decision.

An important constraint of our real life problem is that it can be deduced that to supply customer demand, as many as possible employees should be worked in peak time. However, sometimes peak time takes just two hours so it is difficult to find part time employee to work for only two hours.

While our simulation system gives the results automatically to decide number of workers and checkouts, currently the fast food chains make decisions according to

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predictions and observations of chain’s supervisors. However, these kinds of decisions play a significant role on profit.

In fact, it is clearly stated the complexity of decision above. The complexity of decision brings along some risks. These risks definitely are cost for Fast Food Chain Company. Simulation techniques is not perfect method. It has handicaps. According to entered value of parameters like; service time, length of queue, the number of cash point, Chain Company may make recruitment. However, company may not need any recruitment in real time. These situation increases Chain Company cost.

We briefly try to state that scheduling employee efficiently according to their performance is difficult. At present time, this scheduling is made according to observation of supervisors. Trying different type working plan is risk and costly. To minimize the risk cost, our simulation project helps the companies.

I.2 Mission of Project

The mission of the project is to develop a simulation that gives as answer this question “What should be done for people waiting in queues in places where use the self-service system such as McDonald's or Burger Kings. “

Goals: To provide an opportunity for a manager of this kind of business to see what

decisions result in what consequences. To create a real time queue simulation that gives correct results in order to

increase the customer satisfaction because we can obtain some data from the simulation and the manager can use these for improving his business system.

To prepare sufficient reports for the user.

Objectives: Increase the reality of the simulation by using real data as base User will save time by going through the simulation with different parameters

hence he/she increase the business’ productivity Spreading the simulation into every fast food business in an area

I.3 Scope of Project

Since we live in an enormous city and people waiting in queues will be always a problem because of this we choose this subject and the aim of the project is simulating a queue in an enterprise relating to fast food. The system presently covers the only one business in an only one place. For example, we will simulate the McDonald's in Akmerkez. For now, the system will design for the fast food sector but the scope of the project can be expanded in the future for instance we can implement the system for banks, government offices, supermarkets, cinemas etc.

According to the former data, system takes the required parameters and starts to simulate. The administrator can change the parameters as he wants by considering the condition of his/her business organization. Moreover, by taking the result into account, system will prepare detailed reports. Due to the reports manager can use his/her

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employees efficiently. Namely by using simulation method we are going to show the results of the decisions that are taken by an administrator.

I.4 Methodology

We will use simulation technique which is imitation of some real thing, or a process. A simulation model is a mathematical model that calculates the impact of uncertain inputs and decisions we make on outcomes that we care about, such as profit and loss, investment return, efficiency, etc. In our model we will use this technique because our system is basically based on queuing and there is a lot of advantage. For example, designing, building, testing, redesigning, rebuilding, retesting for anything can be an expensive project. Simulations take the building/rebuilding phase out of the loop by using the model already created in the design phase. Most of the time the simulation testing is cheaper and faster than performing the multiple tests of the design each time. The other advantage is that  simulation is the level of detail that you can get from a simulation. A simulation can give you results that are not experimentally measurable with our current level of technology. Results such as surface interactions on an atomic level, flow at the exit of a micro electric thruster, or molecular flow inside of a star are not measurable by any current devices. The last crucial advantage of this is that the technique can tolerate complex systems where analytical solution is not available.

In many retail stores and banks, management has tried to reduce the frustration of customers by somehow increasing the speed of the checkout and cashier lines. Many banks, credit unions, and fast food providers have gone in recent years to a queuing system where customers wait for the next available cashier. We try to estimate cashier efficiency or average time of different cashier and how much queue will occur on the line. According to these information managers can decide how many cashier should I employ or which cashier should be used at specific period. To do this we need service time, arrival rate, service capacity and queue capacity of a company. We will take a fast food company’s bill to learn about service time and arrival rate at specific hours.

II. LITERATURE SURVEYSimulation is the most used and useful technique to make decision easily in

administrative level. The simulation used for a long time. Especially, stochastic activities, simulation is the best way to solve the problem. To better understanding, queue problems are the examples of stochastic activities. There are many examples of queue simulation system. One of the simulation examples is in the restaurants. Why do restaurants use simulation? Generally, the famous restaurants have long queues especially in night. Therefore many customers prefer to choose another free restaurants instead of waiting in queue. Managers of the restaurants do not want to lose these type of customers. Managers want to handle with queues. Thus, restaurants uses simulation models.

There is a study done by Ahsan, Islam & Alam (2014) for that purpose. Manager of busy restaurant would avoid customer loss. That study model use service time

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distribution and arrival time distribution for queueing factors. Model structured in Arena. The busy restaurant has longer queue length in night relatively to in day. They work a model with value obtained from database. Then simulation shows that waiting time in night is longer than waiting time in day. After that, they change model parameter values in order to decrease service time in night. They increase number of server which is number of waiter serve, in night and decrease the number of server in day. When they rework the simulation model with changed values. They found their desired results. They decrease the waiting time in night and waiting time in night is less than waiting time in day. In addition, after they validate simulation, they get positive result and they can use simulation to simulate any service system.

Another example is for bank teller manning (Hammond & Mahesh 1995). The data collection system of bank provide some information about average number of customer transaction for each time period. This information derived for day, week and month to find “bank standard” for transaction per customer and time per transaction (Hammond & Mahesh 1995). “The objective of the simulation model was to provide a simple method for testing new bank teller manning policies and to illustrate what may be expected under the policy.” (Hammond & Mahesh 1995, 1078). It is easy to have generated report on the number of transaction for each fifteen minute time interval during the work day from the Bank’s existing database system. Researchers rework the simulation model with different policies to test the effect of the manning policy on the Banking System. According to results of the simulation model, researchers claim that “the spreadsheet manning model provides a quick calculation of the approximate number of the full time tellers required to provide the desired service level.” ((Hammond & Mahesh 1995, 1080). This simulation is also for administrative level. Top manager and branch managers of Bank uses this findings when evaluating the performance of its branch banks.

Another famous example is toll station model (Günal 2012, 33-49). In this system, there are gate types which are TP, NP and KG, according to their payment type. %50 of all cars enters the TP gate, %30 enters the NP gate and others enter the KG gate. The queue changes depending on the hour in day. For example, at 7:00 am and 17:00 pm it will be busy, however, at 10:00 am or 21:00 pm it will be freest. The model try to calculate what is the effect of car delay on traffic, can we closed some gate in freest time, and should we expand the number of tape. As a result, with toll station simulation, some questions are answers by the result of simulation. For example, which station should be active, when it should be active and how many hours should be active. The model is figure 2.1.

Another interesting simulation is for emergency service (Günal 2012, 14-25). This model is more complicated than others. In this model, there are three types of patient. Types are called with color name which are red, yellow and green. Also this model is multi-channel. The patients come emergency service with ambulance or with different way (walking or private car). When the patient comes the service, he is registered by nurses in the system for first inspection. After inspection if necessary, some tests are done, then the second inspection made. End of the second inspection doctor decide which patient should be stay hospital and which not. These process takes

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a long time and all registering is done by nurses. The aim is shortening duration of the process. Simulation model is built with inter arrival time of ambulance, inter arrival time of other time of arrival, duration of first inspection duration of test, duration of second inspection, the rate of patient color, rate of patient who make test and rate of staying at hospital. Also number of nurses and doctors should be entered in the model as resources. Figure 2.2 is the system schema of emergency service model. According to report of the simulation, number of doctors should be increased. Thus, waiting time in queue decrease.

III. DEVELOPMENT OF THE DSS

III.1. DSS Architecture

We are try to eliminate the queues in fast food chain restaurant with simulation technique. We specify the certain fast food chain which is Burger King. Firstly, I mention about features of Burger King’s queue simulation system. Then, I mention about simulation input- output variables relationship. Finally, I mention our general simulation schema. The main feature is that queue simulation in Burger King shows stochastic activity. What is stochastic activity? According to Chance William A., there is an activity whose results do not predicted before. If the results of that activity change according to random values of certain parameters under uncertainty conditions. That type of activity is called stochastic activity. (p. 328) As the definition, results of our simulation problem is unpredictable and its results change according to month to month, day to day even hour to hour in a day. It can be understand above time is important for our simulation system. Therefore our simulation system is dynamic simulation system. Another and an important feature for queue simulation system like our model is service channel layout. Burger King Queue simulation has multi-channel and multi- queues layout. These channels work as a parallel way. Each cashier is a channel and there is a queue for each cashier.

An important point for simulation system is determining input parameters-variables and decision variables. We should know the difference between input parameters-variables and decision variables in order to determine. If we have the power to change the value of variable, that variable is the input parameter-variable. If we have not power to change, that is decision variable. For our Burger King Queue simulation system, queue capacity is decision variable. According to our group member observation, generally if the number of customer in queue reach a specific number in our observation, no one want to enter the queue. Whenever, the number of customer in queue is less than a specific number, then customer continue to coming. However, physically queue capacity might be a parameter variable. How many people might be enter the queue without leaving? This variable is related with capacity of place. The queue capacity can show variety from different Burger King Store. When look at the model, queue capacity is also evaluated as a parameter variable. Therefore, queue capacity is decision variable. Our main purpose of this project is decreasing waiting

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time and increase customer satisfaction. To achieve our purpose, we need some parameters. We think that which factors affect waiting time, then we specify these parameters. Arrival time, service time and number of cashier is directly affecting waiting time and customer satisfaction. After we enter the variables to model, model draws some results which are average waiting time and efficiency of cashiers and indirectly customer satisfaction and cost minimization.

When looked the system general perfective, we expect the system to show us the following consequence. When we decrease the arrival time, average waiting time and customer satisfaction should be increase. Furthermore, when we increase the service time, average waiting time should be increase or when number of cashier increase, average waiting time should be decrease. When service time decrease, cashier efficiency should be increase. If average waiting time increase, customer satisfaction decrease.

III.2 Technical Issues

To develop a simulation model several ways can be preferred

General programming languages Spreadsheets Some simulation software and simulation languages

Considering the scope of the project and what we want to do, we decided to develop our simulation model by using, the most popular simulation software, Arena.

For developing the simulation model. Some reasons underlies why we choose Arena as a simulator :

- Very easy to understand and to use- Simple but detailed graphical

interface- No syntax required- Input, output analysis- Some required animations- Detailed reports

This is the basic model of our simulation model which works with the similar logic of real model.

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These are the reports of the model above that are provided by Arena

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III.3 Data Source and Flow Mechanisms

III.3.1. Data Source and Structure

For Burger King Queue Simulation, we made an observation to collect some data. This data includes:

1. Arrival Time: When the customer queue up for purchasing the foods.2. The Number of (#) People in Queue: Which represents how many people are on

the line.3. The Number of People: Which exhibits for how many people a person, on the

queue, orders.4. Service Start Time: Which shows us starting time of service.

5. Service Finish Time: Which shows us finishing time of service.6. Total Service Time: That means how long service takes.

Besides, we gained some information by making calculation. First of all we defined three time intervals. These are 9 am- 12 pm for morning, 12 pm- 5 pm for afternoon and 5 pm- 9 pm for evening. We observed for first interval, there is no customer. Therefore, we decided to remove first time interval. We will make a queue simulation for two time intervals.

If it is necessary to mention our observations, we can say that the servicing time depends on the number of orders at the same time. For instance, if a person orders for two people, it takes approximately two minutes. However, if a person orders for four people, it takes almost four minutes. Moreover, density of customer is related to time. Especially for dinner times, the number of customer increases and definitely Burger King should arrange the number of cashiers according to customer’s density. In other words, defining the number of cashiers depends on time interval indirectly.

When we view all information, the most important result is mean of service time (average service time) which is nearly 2, 35. Moreover, it can be easily seen that service time is exponentially distributed.

One of the histograms demonstrating Inter Arrival Time which shows the time until another customer comes.

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Another histogram is for Service Time:

(For detailed information about data, look at the excel sheets which were attached on e-mail.)

III.3.2. Data Flow Mechanisms

We stated before our data exponentially distributed. We defined some statistical values to the system in order to use the model. We mentioned above we have 3 different time period. However we change the time periods a little bit according to results of data analysis. For the first period from 10:00 am to 12:00 pm, we defined inter arrival time exponentially distribution with the mean of 4 minutes. For the second time period from 12:00 pm to 14:00 pm, we defined inter arrival time as exponential distribution with the mean of 1.1 minutes and service time as exponential distribution with the mean 2 minutes. For the third time period from 14:00 pm to 23:59 pm, we defined inter arrival time as exponential distribution with the mean of 2,5 minutes and service time as exponential with the mean of 3,5 minutes. We obtained all this values from data analysis.

For the model working, two different values are needed. These are number of cashier and the replication number which is to specify how many times the model

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simulates. When the user start the simulation, system will ask the number of cashier and the replication number. After that simulation is going to start.

When the simulation starts, customers are assigned the cashiers randomly and serviced by using the appropriate distribution of time period. At the back stage, Arena makes some calculations. End of the simulation, average waiting time, average utilization, number of people served and in excel part we can see what if analysis. What – if analysis is shown in graphics.

III.4. Model and Algorithms

We are trying to simulate regular day of Burger King in Arena Simulation and Visual Studio. In arena there are different types of simulation model. Before the design the conceptual model, we have to decide which type of simulation we will use. The first step is deciding whether our system is static which time has no importance or dynamic which time has important role in model. Time is effective role for our system such as inter arrival time of customer and queue length, so our system will be dynamic simulation. The second step is to find our system is discrete which the system change is when an event occurs or continuous which are events are happening all the time. Our system will change when a customer arrives, otherwise it will be stable, and so our simulation model is discrete. Lastly, Is our system deterministic which is the model always give the same output for same input and there is no randomness or stochastic which include random variable so same input can give different output. Our system has random variable such as the number of customer arrives per minute, so our model is basically stochastic.

After deciding simulation type, the next step is determining input parameters, decision variable and output or performance. Input parameter is basically what we need from outside to run the model. For our project they are mean arrival time, mean service time, queue capacity and number of cashier. Decision variables are the input variable which can be manipulated such as number of cashier and maybe maximum queue capacity. Arrival time also can be thought decision variable because promotion can increase arrival rate but it is out of our project scope. Using input parameters and decision variable, there is possible outcomes to estimate average waiting time, customer satisfaction, utilization of employee, cost minimization and how much cashier should the company use. We will focus on cashier efficiency and how much cashier the company should use. If we have enough data we also calculate cost minimization.The input-out model for our simulation is following;

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Our model is user interacted DSS model so we need some input variable from user to run the system. There are two variables which are cashier number and run length. According to these variables, model will run and produce some input. After select variables, our model creates number of customer according to specific distribution system which shows variance during the different hours in day depending on variable we found via our data (exponential or nominal). The second step of the model is assign module. This module assigns different values for different process. One of them is k value which provides different customer arrival to create module by producing different arrival mean for customer according to hours in a day. The other is assigning time value for every customer when they arrived to find average waiting time of customers spends in the system. The third step of program is deciding module. This module determine that whether or not the next customer will enter queue or nor according to condition which is determined by observation. The conditions specify that if queue number greater than eight, the next arriving customer will not enter the queue. After that arrived customer will be distributed cashier according to queue number automatically because instead of adding new process for new cashier, we change the capacity of existence resource. This increases the efficiency of program. We also record some variable to obtain some statistical information via record module. Lastly, There are read-write module to connect excel file which is in the module file and save the every different cashier replication waiting time and customer loss so we can draw what-if analysis.

The codes in modules can be seen in the Model file which name model.backup that we send. Also we use VBA for creating user interface. You can click ALT+F11 on the model in ARENA to see our code for interface.

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We also assign some global and private variable that reflect some characteristic of our system. These variable will help us to get information from user so we can run the model according to what user wants such as number of cashier, max queue capacity , time if user want to simulate specific hour etc.; We have some resources which is cashier changing from 2 to 4 or 5. According to busy hour system model will determine how many cashier should work. For example, after the number of customer in queue, people do not want to come enter the queue. This means we will use customer. At this time model will suggest to open another cashier by comparing cost of cashier and the money we lost because of the number of queue. The model also examines the worker’s utilization by calculating leisure and working time in one day.

Lastly our model diagram is following. The diagram will have alternative such as 2 cashier or three or four and different model will produce different number of customer per minute according to specific hour in day.

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III.4.1. Validation

To measure validity of the queue simulation project, one sample t–test can be used. One sample t-test provides to compare statistically real mean according to collected data and simulation mean which is gained from simulation results. We tried to check the validity of waiting time when 2 cashiers are working and the number of customers who are served by two cashiers in two hours. To increase the confidentiality for validity testing, we run the system for 20 replications instead of 5 or 10 replications for both one sample t-test.

Firstly, we applied one sample t-test to see whether real mean of waiting time is equal to mean of waiting time according to simulation results or not for 2 hours period. Before starting with one sample t-test, we created two hypothesis which are:

H0: For waiting time, the mean of real data is equal to mean of simulation results.H1: For waiting time, the mean of real data is not equal to mean of simulation results.

By means of SPSS, we applied one sample t-test. We can reach the mean and standard deviation of data which is acquired from simulation. According to our real data, mean is 10,24 for waiting time, so test value is 10,24.

Figure: 1.1 SPSS Results for Waiting Time According To Simulation Results

When we look at the SPSS results, we can say that H0 is correct and accepted, since p value is bigger than significant level (we tested in %95 confidence interval, so significant level is 0,05).

0,483 > 0, 05 so, H0 should be accepted. This means that that there is no difference among means statistically for waiting time.

Our simulation system is valid in terms of waiting time for 2 cashiers in a given period which is 2 hours in afternoon.

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Moreover, we applied one sample t-test to see whether real mean of the number of customers who are served is equal to mean of the number of customers according to simulation results or not for 2 hours period. To begin with the one sample t-test, we again run our simulation system with 2 cashiers and 20 replications.

We created two hypothesis which are:

H0: For the number of customers who are served in 2 hours in afternoon, the mean of real data is equal to mean of simulation results.H1: For the number of customers who are served in 2 hours in afternoon, the mean of real data is not equal to mean of simulation results.

By means of SPSS, we applied one sample t-test. We can reach the mean and standard deviation of data which is acquired from simulation. According to our real data, mean is 106 for the number of customers, so test value is 106.

Figure: 1.2 SPSS Results for the Number of Customers who are served According To Simulation

When we look at the SPSS results, we can say that H0 is correct and accepted, since p value is bigger than significant level (we tested in %95 confidence interval, so significant level is 0,05).

0,168 > 0, 05 so, H0 should be accepted. This means that there is no difference among means statistically in terms of number of customers who are served in a certain period.

Our simulation system is valid in terms of the number of customers who are served by 2 cashiers in a given period which is 2 hours in afternoon.

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III.5. User Interface and Reports

Our simulation model has user-friendly interface because of this, to use the simulation you do not need to know any simulation terms or any simulation knowledge.

When you open up the simulation you will meet the screen below. This screen is the welcome page of the simulation. It includes some information about the project such as definition of the project, goals and objectives of the project.

Figure 4.1 Welcome Page

In this page you can see Start and Help buttons. When you click on the Help button you can learn how to start simulation and you can see what you should do in the next steps of the simulation interactively.

By using Back & Next buttons, you can roam between pages and you can go through the steps again .You can use the Start button whenever you want to start simulation.

If you click on the Start button directly, you should this yellow button in the arena default page.

Figure 4.3 Control Panel

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Figure 4.2 Buttons

And you will encounter the page below.

To start the simulation you should enter the two parameters Cashier Number and Run Length.Cashier Number determines how many cashiers are wanted to use in Burger King.Run Length is the replication number of the simulation. Namely how many times the simulation will be run.

You can enter the long values or maybe you want to stop the simulation. You should press the yellow part of this bar

Figure 4.5 Control Panel 2

When you click on this simulation will stop and you will face with the screen below. In this screen we have 3 buttons Stop, Continue and Restart.

With Stop button you can Stop the simulation permanently.With Continue button, you can resume the simulation.With Restart button you can go back to the beginning and enter different parameters.

When the simulation ends, this screen comes and asks to show the reports that are provided by arena.When you accept it, detailed reports about the simulation comes.

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Figure 4.4 Input Screen

Figure 4.6 Stop Screen

Figure 4.7 Results

We can see the results and all the statistic of our simulation by using the panel at left.

Figure 4.8 Reports

According to this simulation values (3 cashiers 5 replication), these results was gained.

Figure 4.9 Customer Waiting Time Report

According to this report (Figure 4.9), the average waiting time of a customer is 0.3669 (the whole day should be considered.) Maximum waiting time is 11.7190. The average time that a customer spent in Burger King is 3.8084 minutes.

274 Customer comes to the Burger King and get served in a day.

Figure 4.10 Number of Customer

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Figure 4.11 Resource Utilization

According to Resource Usage report (Figure 4.11) the rate of usage of the resources 0.3751. Since utilization is between 0 and 1 this system’s resources have worked almost 38% and resource capacity can be seen as Minimum Value 0.00, Maximum Value 3.00.

Figure 4.12 Queue Report

In Queue report (Figure 4.12) we can see this, a customer waits in queue average 0.3709 minute in a day and max waiting time in queue is 11.7190. The number of people waiting in queue is 0.1393(the whole day should be considered. ), maximum people waiting in queue is 8.

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Figure 4. 13 Time of Customer in System and Customer Loss

In Figure 4.13 shows that how many minutes the customer waits in the system. In this system each customer averagely waits 3.8263 minutes. There is also Customer Loss value. When the number of people waiting in queue passes over maximum queue length, the system losses 1.4 customer.

If you want to restart the simulation, you should stop the simulation permanently. To do this you should click on this yellow button

Figure 4.14 Control Panel 3

Otherwise you will encounter this error message.

Figure 4.15 Error Message

After you run the program for different cashier average waiting time will be recorded Excel file .You can see result for every run on Model Tables Sheet and you can see what if analysis in the same Excel sheet on What-if page.

CHARTS (What-if)

Following graphs show that changes in average waiting time, cost and customer loss according to cashier number.

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Average Waiting Time

2 3 4 5

0.5

1

1.5

2 Avarage Waiting Time

Series1

Figure 4.16 Average Waiting time According to Cashier Number

2 3 4 5

0.5

1

1.5

2

Series1

Figure 4.17 Average Waiting time According to Cashier Number

We cannot add one cashier because it was hard to read graph and it is meaningless. You can see that the biggest changes is between 2 and 3 cashier acording to waiting time.

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Cost

2 3 4 50

1000

2000

3000

4000

5000

6000Cost

Series1

Figure 4.18 Cost-Cashier Number

2 3 4 50

1000

2000

3000

4000

5000

6000

Series1

Figure 4.19 Cost-Cashier Number

You can see that cost increase in direct proportion to cashier number.

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Customer Loss

2 3 4 50.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00Customer

Loss

Series1

Figure 4.20 Customer Loss-Cashier Number

2 3 4 50.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

Series1

Figure 4.21 Customer Loss-Cashier Number

Normally, highest loss will occur with one cashier (It is 37 averagely) but we did not put it here. You can see that again the biggest change between two and three.

Moreover Program files have also Excel files. After run the simulation you can check the values by examining the Excel files.

V. ASSESSMENTWe applied our master plan one by one, which was announced in our project

proposal. All member completed their works in time, so we can say that we have high team power. For each responsibility, we finished them before their deadlines. Therefore, most probably, next time we would act like almost this time. However, when we were arranging deadlines of steps, we were not able to take into consideration that there could be some little changes on our model. It causes some delays according to our plan, but it did not cause some delays on main deadlines.

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V.1. Project Plan

We planned to meet regularly every week as we mentioned following table and finish the project before the deadline. As team members all live in different parts of the city, we planned to keep each other updated on online platform if we fail to meet face-to-face.

Meeting Place: Hisar Campus StudyMeeting Time: Friday at 09:30Coordinator: Gönül Zeynep SAVACI

Task Name Duration Planned Start Planned Finish

Actual Start Actual Finish

% Predecessors Resource Names

Project Preparation 21 days Wed 30.09.15 Wed 28.10.15

Wed 30.09.15

Wed 28.10.15

100

Determining Group Members

2 days Wed 30.09.15 Thu 01.10.15

Wed 31.09.15

Thu 01.10.15

100 Project Manager

Submit Project Group 1 day Fri 09.10.15 Fri 09.10.15

Fri 09.10.15

Fri 09.10.15

100 Project Manager

Searching Project Type 6 days Sat 10.10.15 Fri 16.10.15

Sat 10.10.15

Fri 18.10.15

100 System Analyst;Database

DesignerGroup Meeting 1 day Mon 19.10.15 Mon

19.10.15Mon

19.10.15Mon

19.10.15100 Business

Intellegence;Project Manager

Preparation Of Proposal 4 days Tue 20.10.15 Fri 23.10.15

Tue 18.10.15

Fri 23.10.15

100 5 System Analyst;Project Manager

Submit Proposal 1 day Mon 26.10.15 Mon 26.10.15

Mon 26.10.15

Mon 26.10.15

100 6 Database Designer;System Analyst;Business

Intellegence;Project Manager

Presentation 1 day Wed 28.10.15 Wed 28.10.15

Mon28.10.15

Mon28.10.15

100 7 Business Intellegence;System

AnalystAnalyze 40 days Thu 29.10.15 Wed Thu Wed 100

27

23.12.15 29.10.15 23.12.15Performing Preliminary

Investigation3 days Thu 29.10.15 Mon

02.11.15X Business Intellegence

Interviews with experts 2 days Tue 03.11.15 Wed 04.11.15

X Project Manager

Examining Similar Example

1 day Thu 05.11.15 Thu 05.11.15

Thu 05.11.15

Thu 05.11.15

100 Project Manager

Group Meeting 1 day Fri 06.11.15 Fri 06.11.15

Fri 06.11.15

Fri 06.11.15

100 Business Intellegence

Creating a Survey at Online

1 day Fri 06.11.15 Fri 06.11.15

X System Analyst

Preparing a Report Related to the Survey

1 day Mon 09.11.15 Mon 09.11.15

X Project Manager;System Analyst

Development of the Model

4 days Tue 10.11.15 Fri 13.11.15

Tue 10.11.15

Fri 13.11.15

100 Business Intellegence;System

Analyst

Preparation Of Mid-Report and

Presentation

7 days Sat 14.11.15 Sun 22.11.15

Sat 14.11.15

Sun 22.11.15

100 Business Intellegence;Project

Manager;System Analyst

Submit Mid-Report 1 day Mon 23.11.15 Mon 23.11.15

Mon 23.11.15

Mon 23.11.15

100 17 Database Designer

Presentation 1 day Wed 25.11.15 Wed 25.11.15

Wed 25.11.15

Wed 25.11.15

100 17 Business Intellegence;System

AnalystGorup Meeting 1 day Fri 27.11.15 Fri

27.11.15Fri

27.11.15Fri

27.11.15100 Business

Intellegence;Database Designer;Project

Manager;System AnalystData Collection and

Organization5 days Mon 30.11.15 Fri

04.12.15Mon

26.10.15Fri

30.10.15100 Database Designer

Group Meeting 1 day Sat 05.12.15 Sat 05.12.15

Sat 05.12.15

Sat 05.12.15

100 Business Intellegence;Database

Designer;Project Manager;System Analyst

28

Preparation Of Final Report

11 days Mon 07.12.15 Sat 19.12.15

Mon 07.12.15

Sat 19.12.15

100 Business Intellegence;Project

Manager;System AnalystSubmit Final Report

and Presentation1 day Mon 21.12.15 Mon

21.12.15Mon

21.12.15Mon

21.12.15100 23 Project Manager

Presentation 1 day Wed 23.12.15 Wed 23.12.15

Wed 23.12.15

Wed 23.12.15

100 Business Intellegence;System

AnalystDatabase Designing 7 days Thu 29.10.15 Fri

06.11.15Thu

29.10.15Fri

06.11.15100

Determining Tables and Relations

4 days Thu 29.10.15 Tue 03.11.15

Thu 29.10.15

Tue 03.11.15

100 Database Designer

Prepare database and optimize data

3 days Wed 04.11.15 Fri 06.11.15

Wed 04.11.15

Fri 06.11.15

100 27 Database Designer

Implementation 44 days Tue 20.10.15 Sun 20.12.15

Tue 20.10.15

Sun 20.12.15

100

Designing a Model 10 days Tue 20.10.15 Mon 02.11.15

Tue 20.10.15

Mon 07.12.15

100 System Developer

Combine Design and Function on Model

7 days Tue 03.11.15 Wed 11.11.15

Tue 03.11.15

Wed 08.12.15

100 System Developer

Test Model's Reliability (Unit, System etc.)

4 days Thu 12.11.15 Tue 17.11.15

Thu 12.11.15

Tue 17.11.15

100 Teste C;Tester A;Tester B

The Last Control of Overall Project

2 days Sat 19.12.15 Sun 20.12.15

Sat 19.12.15

Sun 20.12.15

100 Project Manager

29

VI. CONCLUSIONSimulation project about queue in a certain fast food chain works correctly, we

can reach the close results to real time from the simulation system. This means that the simulation system is valid. However, this system has some weaknesses. One of the most significant weaknesses is that the system is not user friendly. For example, when a person tries to stop and start to simulation, s/he has to use the buttons which belongs to Arena. User interface of our project is so weak because of our insufficient information about “Siman” and some difficulties to use Visual basic Language. Moreover, now we use the collected data, but in the future we will connect the simulation system to Burger King’s system. It provides to use real time data. Therefore, we will not need to collect data, it will happens automatically. Furthermore, deficiencies in user interfaces will be eliminated.

REFERENCES1. Ahsan, M., Islam, R., & Alam, A. (2014,) “Study of Queuing System of a Busy

Restaurant and a Proposed Facilited Queueing System”, IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE), vol 11, pp.31-35.

2. Günal, Murat M. (2012) “Benzetim Sistemi ARENA Laboratuar Notları”, Deniz Harb Okulu, Endüstri Mühendisliği Bölümü.

3. Hammond D. & Mahesh S. (1995) “A Simulation and Analysis of Bank Teller Manning”, In Simulation Conference Proceeding, 1995. Winter (pp. 1077-1080). IEEE.

4. Sarıaslan, H. (1986), “Sıra Bekleme Sistemlerinde Simulasyon(Benzetim) Tekniği” : A. Ü. Siyasal Bilgiler Fakültesi, Ankara.

Appendix

Data for Validation Test

We used data from below table to measure validation of waiting time by using SPSS.

# of Cashiers Results Replication #2 2,758 12 1,230 22 5,174 32 21,725 42 36,947 52 42,349 62 22,801 72 8,877 8

30

2 10,651 92 1,790 102 1,531 112 3,989 122 4,981 132 10,204 142 19,005 152 10,225 162 6,088 172 16,638 182 2,413 192 12,493 20

       mean 12,09

Appendix Table1: Simulation Results for Waiting Time

We used data from below table to measure validation of number of customers who are served in a certain period.

# of Cashiers # of people Replication #2 93 12 95 22 106 32 106 42 125 52 123 62 122 72 94 82 117 92 109 102 109 112 97 122 121 132 109 142 109 152 109 162 109 172 109 182 109 192 109 20

Appendix Table2: Simulation Results for Number of People who are served

Visual Basic Codes for Arena

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Arena ObjectsPrivate Sub ModelLogic_DocumentOpen() MainPage.Show 'when program open, it show the main pageEnd SubPrivate Sub ModelLogic_RunBeginSimulation() Simulate.ShowEnd SubPrivate Sub ModelLogic_RunEnd()RestartP.ShowEnd SubPrivate Sub ModelLogic_RunPause()Continue.ShowEnd SubMainPagePrivate Sub CommandButton1_Click()MainPage.hide 'Get rid of the User Form 'when the start button is 'clicked.Simulate.Label2.Visible = False 'it makes lable invisible if no errorSimulate.TextBox1.SetFocus ' it focus pointer to textbox field

End Sub

Private Sub help_Click()MainPage.hide 'Get rid of the User Form 'when the help button is 'clicked.UserGuide1.Show ' show the guide page 1End SubContinuePrivate Sub CommandButton1_Click()Dim m As Model 'Define variables used inDim s As SIMAN 'the VBA logic.Set m = ThisDocument.Model 'm is defined 'as this particular 'model.Set s = m.SIMANContinue.hide 'Get rid of the User Form 'when the Stop button is 'clicked.m.End 'End the model run.End Sub

Private Sub CommandButton2_Click()Dim m As Model 'Define variables used inDim s As SIMAN 'the VBA logic.Set m = ThisDocument.Model ' m is definedSet s = m.SIMAN 'as this particular 'model.Continue.hide 'Get rid of the User Form 'when the continue button is 'clicked.m.Go 'Continue the model runEnd Sub

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