PROBLEM:

Consider a popular coffee chain that has decided to introduce warm sandwiches and pastries to its menu.

The current system can be described as follows. Customers join a FCFS queue to place their order and then

proceed to the next counter to collect their completed order. Coffee customers can be divided into two types:

$1)$ Those that order a Regular coffee. These customers have an arrival pattern that follows an

exponential distribution with a mean of $2$ minutes and the processing time for their order follows

a uniform distribution with parameter values equal to $0\mathrm{.}5$ and $1$ minute.

$2)$ Those that order a Specialty coffee. Their arrival pattern follows an exponential distribution with

a mean of $4$ minutes and the processing time for their order follows a triangular distribution with

parameter values equal to $2,3,$ and $4$ minutes.

$3)$ The proposed system would allow customers to also purchase a sandwich$/$pastry with their coffee.

The process involves the employee selecting the item the customer wants then placing it in the oven

to heat it up$.$ Management estimates that the additional time to process a sandwich$/$pastry order

follows a triangular distribution with parameter values equal to $3,5,$ and $9$ minutes. They expect

the arrival pattern of customers wanting a sandwich$/$pastry will follow a lognormal distribution

with mean $5$ minutes and a standard deviation of $3.$ Since this is one of the best coffee places in the

world, management expects that every customer who purchases a food item will also purchase a

regular or specialty coffee.

A few additional issues that management would like you to consider are:

$1)$ In the fashion typical of these types of establishments, management feels that one employee at the

ordering station and two for preparing food$/$coffee is sufficient. In this setup, each food preparation

employee has their own workstation: Order Prep WS$1$ and Order Prep WS$2.$ The caf$$ has a

sophisticated computer system that directs each order $($and customer$)$ to the employee with the

shortest queue. If the two queues are the same, the computer will direct the order$/$customer to

Order Prep WS$1.$

$2)$ Management has done some research and studied past data and feels that customers will decide to

forgo their coffee or grande double soy mocha lattes and$/$or foccacia smoked ham with aioli

sandwiches if their waiting time exceeds three minutes $($which is typical for this type of industry$).$

They feel this translates into a customer balking when the sum of the order preparation queues for

WS$1$ and WS$2$ exceeds $12$ people.

SIMULATION OF BUSINESS SYSTEMS R$.$ YOOGALINGAM

$3)$ They expect that many of the customers will already be familiar with their drinks menu so the

ordering time for drinks only will follow a uniform distribution with parameter values $[1,1\mathrm{.}5].$ This

includes payment. On the other hand, with their sandwiches$/$pastries$,$ they expect the same type of

customer behavior they experienced when they first opened their establishment many years ago

$($i$.$e$.,$ a somewhat catatonic$-$like state while perusing the many options on the menu$).$ In any case,

they expect the coffee and food ordering process to follow a lognormal distribution with a mean of

$2$ minutes and standard deviation equal to $0\mathrm{.}5.$

$4)$ It has been several decades since some of the executives have taken a simulation course or any

course for that matter, so it would help if you animate the model $($entities$,$ resources$)$ for their

benefit.

$5)$ Many coffee establishments are now including a self$-$serve kiosk for customers who drop by for a

regular coffee. These customers would select their coffee from several choices of blends, dispense

it themselves $($assume this process follows a uniform distribution between $1\mathrm{.}5$ and $2\mathrm{.}5$ minutes$),$

then proceed to their own order counter to pay $($which takes half a minute$).$ Suppose approximately

$80\%$ of regular coffee customers can be diverted to this option and these customers will balk if the

queue at the kiosk exceeds $5$ people $($they really do not see why it should take so long to get their

coffee!$).$