simulation project report

By: Jasmine SachdevaM No.: M10669285

Simulation Project in Arena

Optimization of Subway Outlet at UC Campus

ContentsObjective.................................................................................................................................................2

Current Process.......................................................................................................................................2

Problem and Counter Proposal..............................................................................................................2

Data Collection........................................................................................................................................2

Fitting Data..............................................................................................................................................3

Model Assumptions................................................................................................................................5

Model......................................................................................................................................................5

Model Results.........................................................................................................................................6

Model 2...................................................................................................................................................8

Output Analyzer......................................................................................................................................9

Process Analyzer...................................................................................................................................10

Conclusion:............................................................................................................................................11


Objective

To improve the effectiveness, productivity and sales of Subway by minimizing waiting time and maximizing the speed of service.This can be done by understanding how the customer wait times varies in different stages from the time they enter the queue till the time they receive their order.

Current Process

Customers enter Subway, wait in the queue or go to the first stage where they select the size and type of bread, meat, and cheese. Then depending if the customer chose to bake or not bake their bread, the customer goes through the second stage which is the oven. The customer then moves to the next stage to add veggies, meat and condiments. Once the sandwich is made, the customer moves to the billing counter after choosing additional chips and/or drinks. After this, the customer may or may not go to the soda machine to get their drinks.

Each stage has two resources except at the billing counter.

Problem and Counter Proposal

During lunch hours i.e. from about 10:00 AM to 2:00PM, there’s a longer queue at the order counter as well as the billing counter which leads to unsatisfied customers and a chance of people deciding not to go eat at a Subway because of the long waiting time.

Staffing the right number of employees at the right time and having the right person in the right place could solve the problem.

The restaurant can have an additional resource at the order counter or billing counter, which can make a significant difference in terms of waiting times and consequently customer satisfaction levels.

Data Collection

Permission had been taken from Subway to collect the data observe inter arrival and processing time. The time intervals were manually recorded for the following processes to get a rough estimate of entire system

Inter-arrival time of customers coming on a day Process time for choosing bread and cheese Process time for choosing vegetables and sauces


Process time for billing

Fitting Data

Arena’s Input Analyzer tool was used to fit the probability distribution to the data.

a. Customer Inter-arrival times

Following is the schedule of customers generally observed in a day. 10 AM to 2 PM and 7 PM to 9 PM have been observed as the peak rush hours.

9 - 10 AM

10-11 AM

11AM-12 PM

12 - 1 PM

1- 2 PM

2 - 3 PM

3 - 4 PM

4 - 5 PM

5 - 6 PM

6 - 7 PM

7 - 8 PM

8 - 9 PM

9 - 10 PM

22 42 47 48 50 9 19 11 27 9 47 36 10

b. Process time for Choosing bread and cheese

c. Toast

Distribution Summary

Distribution: Beta Expression: 0.33 * BETA(1.41, 1.64) Square Error: 0.004607

Chi Square Test Number of intervals = 16 Degrees of freedom = 13 Test Statistic = 17.4 Corresponding p-value = 0.196

Kolmogorov-Smirnov Test Test Statistic = 0.0481 Corresponding p-value > 0.15

Data Summary

Number of Data Points = 350Min Data Value = 0.5Max Data Value = 1.2Sample Mean = 0.829Sample Std Dev = 0.208

Histogram Summary


It was observed that the toasting time for bread is uniform between 0.33 mins (20 secs) to 0.66 minutes (40 secs), depending on the type of bread and the meat chosen.

UNIF (0.33, 0.66)

d. Process time for Choosing vegetables, sauces and condiments

Distribution SummaryDistribution: Gamma Expression: 0.11 + GAMM(.45, 4.23)Square Error:0.015364

Chi Square Test Number of intervals = 17 Degrees of freedom = 14 Test Statistic = 391 Corresponding p-value=0.496

Kolmogorov-Smirnov Test Test Statistic = 0.113 Corresponding p-value>0.01


Model Assumptions

• The two resources who take the order and prepare the sandwich are equally efficient and have the same service time.

• The time taken to use the soda machine has not been added in the model, since it doesn’t add to the queue time. The model has been simulated only till the billing counter.

ModelMy arena model has 7 modules as given below:

1. Arrival Module: The customer arrives at the restaurant and joinsxx a queue at one of the counters based on the length of the queue

2. Seize ‘Sub Resource’: The customer goes to one of the resource who is idle and orders his sub. The same resource prepares the sub for a particular customer.

3. Delay Module to choose bread, meat and cheese: The customer choose the type of bread, meat and the cheese and the Resource prepares the sub before toasting it.

4. Decision Module for Toast/No Toast decision: The customer can choose to toast or not toast his bread in oven.

5. Delay Module for Toasting bread in Oven: Bread is toasted in the oven. It takes 20 to 40 secs, depending on the type of bread, cheese and meat chosen

6. Delay Module to prepare the sub: The resource prepares the sub by adding vegetables, condiments and sauces.

7. Release ‘Sub Resource’: Once the sub is prepared, the resource is released to be seized by the next customer (or from the queue, if any).

8. Process Module for Billing Counter: When the sub is ready, customers from both counters move to a single billing counter.

Once the customer finalizes the order, he/she can choose to get a glass of soda/water if it’s part of the order. If the customer decides to get a glass soda/water along with his order, he goes to the soda machine and gets his glass filled. (This part is not included in the model)

Following is the outlay of the Arena model.


Model Results

The model was initially run for 50 replications and the number of replications required for a precision of 9% was calculated.

The model was finally run for 52 replications and the results obtained are as shown below.

A.

B.


C.

D.

The waiting time of customers in the queue are 5.07 mins for the billing queue and 2.58 for the Order queue.

Due to extreme rush in peak hours, even the average total time in system is 11 minutes which is quite high. Therefore, it is proposed to increase the resources. This is implemented in the second model.


Model 2

In this model, The Sub Resource and Billing Resource has been increased by one unit.

This model is run for a 52 replications and the results are as given below.

A.

B.

C.

D.

To check the authenticity of these results, it is important to analyze them statistically. This can be done by using the OUTPUT ANALYSER and PROCESS ANALYZER.


Output Analyzer

The Statistics to be checked are: Total Time spent by the Customer in the System, Average Wait Time in the Billing Queue and Average Wait Time in the Order Queue.

All of these are output statistics i.e. their results get stored in .DAT files specified by us. The Output Analyzer can be employed to perform T-Tests on the samples to determine the hypothesis:

H0: the means of the two samples of the statistic are same

Ha: the means of the two samples of the statistic are not the same.

We can use the files from both the models to compare the Means of these Statistics.

We reject Ho for all the three Responses, as we can’t say that there is a statistically significant difference in the means.


Process Analyzer

Following are the results obtained from the Process Analyzer:


From this chart and the result of the PAN we can say that, increasing both resources by one unit would be a better approach.

Conclusion:

After going through all the results, charts and graphs we can clearly see that reducing both resources by a unit would greatly decrease the wait time of customers, thereby decreasing the total time of customers in system.

Therefore, we can say that, using the Second model, i.e. by hiring an additional employee we can improve the customer experience by decreasing the wait time and hence further improve the reputation of subway.

So the final conclusion comes out to be that Model 2 is a valid and better approach. Hence two new employees can be hired by the restaurant.

References:

1. Simulation with Arena2. Data collected from Subway, UC

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