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# Quantitative Modules: Essay

521 words - 3 pages

Quantitative Modules:
I Love Coffee (ILC) illustrate a waiting-line system. The Queuing theory is a very important aspect of operations at ILC, and plays as vital tool to ILC’s operations manager. I Love Coffee drive through, implements a queuing system with its customers, having customers wait in line for the product.
Characteristics of the waiting –line system at the I Love Coffee drive through. First using the arrivals or input in the systems of all the customers of (ILC) this will help build a database to better understand aspects of the ILC’s customers, such as the size or number of customers in given period of time, and certain patterns that emerge to help demonstrate a better understanding ...view middle of the document...

Additionally, to have a better quantitative understanding of the arrival rate with regards to the queuing theory, a discrete Poisson distribution can be established by the following:

x: 3 P(x)= Probability of 3 arrivals = 14.037%
y: 5
e:2.71828
Furthermore, another waiting-line characteristic with respect of the queuing discipline. ILC uses a first-in, first-out (FIFO) rule, with a basic queuing system design that involves a single-phase queuing system (M/M/1). This system operates with a Poisson arrival rate pattern, with an exponential service time pattern.
I Love Coffee drive through, is able to service hot caffeinated beverages at an average rate of 30 cups per hour, according to a negative exponential distribution. Customers wanting hot caffeinated beverages arrive at the drive through on an average of 18 cars an hour, moreover following a Poisson distribution, they are served on a FIFO from a very large population of possible customers, thus to have a better understanding of ILC’s queuing system:
Y: 18 cars arriving per hour
U: 30 cups served per hour
Ls= y/u-y = 18/12 = 1.5 cars in the system on average
Ws= 1/u-y = 1/30-18 = 1/12
= 5 min average waiting time in the system
Lq= y2/u(u – y) = 18^2/30(30-18) = 324/360 = 0.9 cars waiting in line on average.
Wq= y/u(u – y) = 18/30(30 – 18) = 18/360 = 0.05*60 = 3 min average waiting time per car.
P= y/u = 18/30 = 0.6*100 = 60% of the time the drive through is busy.
P0= 1 – y/u = 1 – 18/30 = 0.40 probability there are 0 cars in the system.

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