Model Suggestions Based on Other Blogs



For this week, we have to review other similar projects and find possible improvements for our project. Consulting three different blogs, we have the following conclusions:

Our system could have one extra station, corresponding to the trash. It means that the client, after eating his meal, goes to the trash and leaves the table clean, before getting away HAMBURGER. The routing probability of this station is one when the client comes from the "Eating Area" station. There are not arrivals from other stations to the "Trash" station.
Blog:  http://hamburgueserias.blogspot.com/

The possible failures for our system are greater than we mentioned before. At the "Ordering" station, an additional set-up is that there is no more billing paper, and the cashier has to put it in the register.  Another possible failure is that there is no change for the client and the cashier has to ask to the other server for exchange some money. Finally, it can appear a failure when the product that the client wants to order is not available in the system. Thus, the client has to think about another product in the menu.
Blog: http://e9-restaurantes.blogspot.com/

For our system, it is possible that a client arrives to the system and decide not to get in because the place is crowded. The decision is based on the number of people in queue. If the queue is apparently long, then the client prefers going somewhere else.
Blog: http://fastproyectb3.blogspot.com/

The mentioned blogs were chosen according to the following reasons:

·         The systems are based on a fast-food restaurant, where the speed of service is mainly important to improve customer service. That’s why restaurants avoid making their clients to wait for so long in line. Thus, it is expected that the number of clients in queue is minimal.

·         The products that are offered are: hamburgers, salads, bakery products, French fries, and so forth.

·         There is optional for the client to go to a particular station, because it depends on his willingness. For example, a costumer who does not want to get sauces, sugar, salt, etc. Or there is the possibility that he wants his meal to-go.

·         Service takes place in two ways. First, there are people who take and deliver the order. Second, there is self-service for each client.

We hope you enjoyed our entry.

Thank you for reading us,

Nataly Patacón

Camila Fonseca

Fernand Malagón

Alejandro Moreno

PERFORMANCE MEASURES

This week we have to calculate performance measures for the restaurant HAMBURGER, but assuming that the distribution of the inter-arrival times and service times is exponential. This assumption is very important to apply Jackson’s theorem and modeling the system as a Jackson network.

Thus, by Jackson’s theorem, the arrival rates are calculated with the following expression:

The system of equations of the total arrival rates of HAMBURGER is:

 Looking at the graph schema, in “System Data” publication, the system of equations is simplified as it’s shown. 

We assume that our system satisfy Jackson’s suppositions (exponential inter-arrival times, exponential service times, infinite capacity for all stations and reached stable state λ_i<s_i*μ_i for all i stations). Then, the arrival rates found correspond to inter-arrival times distributed exponential. In order to calculate performance measures, we use network formulas, shown in the next table.

We hope you enjoyed our entry.

Thank you for reading us,

Nataly Patacón

Camila Fonseca

Fernand Malagón

Alejandro Moreno

SYSTEM DATA - TIMES DISTRIBUTION

Hello everyone!

This week we had to find the distribution of the inter arrival time and service time of each station. For this task, we applied goodness-of-fit test for each station service time and for the inter arrival time, by using an statistical software (Crystal Ball). The results are presented in the next charts.

The following graphs show the closest distribution found by the software. However, none distribution fitted perfectly to our taken times.

In order to find distributions, the following tables show how to calculate the mean and the variance for  each one. The results for the distribution of the service times, and the inter-arrival time, are shown in the second table.

Time Units in minutes.

Thank you for reading us!

Regards,

Nataly Patacón

Camila Fonseca

Fernand Malagón

Alejandro Moreno

SYSTEM DATA

Our job this week was visiting the system and taking some data. We had to register the arrivals and the service times for 100 entities.

Thus, we define the different routes that can follow an entity. 

A client who enters to HAMBURGER restaurant have to get into the line to arrive to the first station, which is "Ordering". Then, he has to wait his meal at the "Cooking and Delivering" station. 

From this last station he can leave the restaurant, or continue in the following routes:

- Go to the sauce station and leave de restaurant.

- Go to the sauce station and then to the "eating area".

When the client continues in the second route, he leaves HAMBURGER after he eats his meal at the fourth station "Eating Area". 

The typical route corresponds to: Ordering - Cooking and Delivering - Sauce - Eating Area - Exit.

The service time for each of the stations are in the graph schema. The summary of the data is at the following table:

                       

 

We hope you enjoyed our entry.

Thank you for reading us.

Regards,


Nataly Patacón
Camila Fonseca
Fernand Malagón
Alejandro Moreno

GENERAL DESCRIPTION OF THE SYSTEM

As we mentioned in our first blog entry, we are going to study a hamburger restaurant, which we are going to name "HAMBURGER". 
      
As a typical restaurant, HAMBURGER could have as many lines as cash registers. In this case, HAMBURGER has  two cash registers (which can be open or closed) but there is only one line to all the servers. Thus, this restaurant configuration is a single-line queue system. The queue discipline, for HAMBURGER, is FIFO, because anyone who comes first to the restaurant will be almost first served by the cashiers. But the client receives the order depending on the production time.
The servers work with cash machines, which have a programmed system. Failures of the cash’s system can appear. A usual failure is a human mistake. This is because the order does not get to the servers on the right way, so the costumer gets a wrong order. In restaurants, it is common to have electronic devices, which help the system to be faster. This devices show the number of order to the costumer, so that they can get for its meal.
      
The system has four stations. The first of all is "Ordering", because once customers have made the line and one of the servers is available, they can check out the menu, order, and pay to the cashier what they want to eat. Next, the client has to wait while the meal is ready to be delivered, which correspond to the second station. At this station, while the client is waiting, operators are responsible for the burger’s preparation. When HAMBURGER delivers the order, the client can go to "The sauce station" (third station), where he can get napkins, straws and sauces. This station can be considered as optional, because the entities decide to go or not to go. Finally, the client is ready to eat his meal at "the eating area" (fourth station). We can see the client leaving the restaurant when he has finished his meal.

      The population attending to eat at HAMBURGER corresponds to everyone who can afford this meal. We know that HAMBURGER has many restaurants in the city. So, we are going to study a restaurant located at a university. Thus, the entities correspond to the students, teachers, and administrative members of this institution. Those clients go to one station to another by walking. An important fact for this kind of restaurants is time, because this kind of food is called fast-food which means the queue time has to be the minimum. Costumers are looking for a good service without delays.
 

Thank you for reading us.
 
Regards,
 
Nataly Patacón 
Camila Fonseca
Fernand Malagón
Alejandro Moreno
 
 

Welcome message!

Welcome to HAMBURGER Blog!

We are attending Los Andes University and our major is industrial engeneering. The purpose of this blog is to show you the stages of our Final Proyect that we are doing for the course Probabilistic Models. We hope you will follow the blog during all the semester. We will do our best to make this blog interesting for you.

Regards,

Camila Fonseca

Nataly Patacón

Fernand Malagón

Alejandro Moreno