Case Study: Italian Coffee House

MGT$4540/46412023-24$

You have recently started a new job as a junior operations manager in the 'Italian Coffee House', a large London based coffee shop chain. Your line manager has asked you to analyse the drink service process performance of one of the chain's London stores that is expecting increase in customer demand over the next four months. Your manager has provided you the information below on the store located at busy central London train station:

Customers arrive to the store as specified in Table $1$ below.

Table $1$: Customer interarrival times $($in minutes$)$

$\backslash$table$[[$Month$,$Customer interarrival time $($Exponential distribution$)],[1,$Mean $1\mathrm{.}7],[2,$Mean $1\mathrm{.}6],[3,$Mean $1\mathrm{.}5],[4,$Mean $1\mathrm{.}4]]$

The service process steps are:

i$.$ Barista takes customer order and payment at Service Counter. This follows normal distribution with mean of $1\mathrm{.}5$ minutes and standard deviation of $0\mathrm{.}2$ minutes. $50\%$ of the

$6$ customers order coffee, $40\%$ order tea and $10\%$ order hot chocolate.

ii$.$ Barista walks from the service counter to the drink station in order to prepare the drink. This follows normal distribution with mean of $10$ seconds and standard deviation of $0\mathrm{.}2$ seconds.

iii. Barista makes the drink ordered by the customer using either Coffee machine, Tea machine or Hot Chocolate machine. Making coffee follows normal distribution with mean of $2$ minutes and standard deviation of $0\mathrm{.}2$ minutes. Making tea follows normal distribution with mean of $35$ seconds and standard deviation of $0\mathrm{.}2$ seconds. Making hot chocolate follows normal distribution with mean of $1\mathrm{.}7$ minutes and standard deviation of $0\mathrm{.}2$ minutes.

iv$.$ Barista walks from the drink station back to service counter with the drink and hands the drink to the customer. This follows normal distribution with mean of $15$ seconds and standard deviation of $0\mathrm{.}2$ seconds. Most customers now leave the coffee store. However, $10\%$ of customers are unhappy with the quality of their drink and request the Barista to remake the same drink. In this case, the Barista walks back to the drink station $($this follows normal distribution with mean of $10$ seconds and standard deviation of $0\mathrm{.}2$ seconds$)$ and remake the same drink using the same drink machines and processing times as specified earlier $($joining the queue if the machine is busy$).$ After this the Barista takes the remade drink to the customer $($this follows normal distribution with mean of $15$ seconds and standard deviation of $0\mathrm{.}2$ seconds as before$).$ Again, there is $10\%$ chance that the customer rejects the drink and it need to be remade.

The store currently has the following resources continuously available: Three Baristas, two Service Counters, one Coffee machine, one Tea machine, and one Hot Chocolate machine.

Same Barista completes all steps of the service process, i$.$e$.$ takes the order and payment, makes the drink, and delivers the drink to the customer $($and if required remakes the drink$).$

When a customer arrives and if both Service Counter and Barista are available the customer will be served immediately, otherwise the customer waits in a single First$-$In$-$Firsts$-$Out queue.

Run the simulation for $1$ week i$.$e$.168$ hours with multiple replication runs. The system starts at time zero minutes with no products present and the machine$($s$)$ idle.