DSOM $340$ Fall $2024$ HW$1$ Capacity Analysis

$1$

Please provide formulas, steps, or reasons to support your solutions.

Submissions with only the final solutions without any support will not be given

credit.

Due date: September $2$nd$,11$:$59$PM

Problem $1$: Sandwich Restaurant $(50$ points$)$

Consider the sandwich restaurant Which Wich. The process goes as follows:

$1.$ A customer enters the restaurant and grabs the sandwich bag corresponding to

the type of sandwich she wants $($chicken$,$ seafood, vegetarian, etc.$).$ She fills out

the list of ingredients she wants $($marked on the bag$)$ and gives the sandwich bag

to Adam $($who works at the cash register$).$ It takes a customer exactly $90$ seconds

to finish all the above steps after she$/$he arrives to the restaurant.

$2.$ Adam checks into the order and asks the customer what drink she$/$he wants,

which takes $15$ seconds; accepts the customer$$s payment, which takes $1$ minute;

and fills up the drink at the soda fountain for the customer, which takes $30$

seconds. Then Adam puts the sandwich bag on the $$order rack$$ above the

counter, which takes $15$ seconds.

$3.$ The order on the sandwich bag is then read by Bob who picks the bread, adds

the cheese and the meat and put the sandwich into a toaster oven. Altogether it

takes Bob $90$ seconds to finish this step.

$4.$ The sandwich stays in the oven for exactly $2$ minutes. The oven is small and can

hold only one sandwich at a time.

$5.$ Once the sandwich comes out of the oven, Bob $($the same Bob as in the above$)$

adds the rest of the ingredients to it $($mayonnaise$,$ vegetables, spices, etc.$)$

according to the order on the sandwich bag; then he takes the sandwich bag off

the order rack, puts the sandwich in the bag and takes it to the customer. In total,

it takes Bob $1$ minute to finish this step.

$6.$ When the sandwich is ready, the customer picks it up and leaves immediately.

Further, we make the following assumptions:

$$ The steps and times listed above are the same for all the types of sandwiches

that can be ordered and for all customers;

$$ Every customer orders a sandwich and a drink;

$$ There is an infinite amount of ingredients for the sandwiches so that the workers

never run out of ingredients;

$$ There is infinite space in the restaurant to put the bags above the counter or let

customers wait;

$$ There are infinite pens for the customers to fill out the order

Answer the following questions $($please provide the steps$)$:

$($a$)$ Draw a process flow diagram for this process. $(15$ points$)$

$($b$)$ What is the process capacity and where is the bottleneck? $(25$ points$)$

$($c$)$ What is the rush order flow time? $(10$ points$)$