PeloSpin $($PS$)$ makes quality bicycles to order, receiving customer orders online. Their most popular model is the

Torrent, which PS manufactures with the following process. First, John checks the order for consistency and

prepares instructions for the subsequent operations. When the process operates at capacity, John$$s utilization is

$40\%.$ Once John is done, the order moves to both Amit and Lance, who can work on their respective tasks in parallel.

Amit picks the correct frame from the inventory and spray paints the frame using PS$$s proprietary technology.

When the flow$-$balanced process operates at capacity, Amit$$s utilization is $100\%.$ When the frame is ready, Amit

passes it to final assembly and testing $($FAT$).$ Lance is in charge of wheel building and brake subassembly. Lance

selects and mounts tires and disk brake rotors on the wheels to order based on the customer$$s weight. When the

process operates at capacity, he is busy $60\%$ of the time. Once the wheels are ready, Lance passes them on to Beth,

whose tasks include assembling the shock absorbers and testing them together with the wheels on special

equipment. Beth requires $20$ minutes for these tasks and her utilization is $50\%$ when the process operates at

capacity. When done Beth passes the tested wheels and shocks on to the FAT. At the final assembly and test, there

are four equally competent workers: Britney, Tiffany, Avery, and Li$.$ When the frame, wheels, and shocks for a

customer order are all complete, one of these four workers takes these components and assembles them with

other parts $($handlebar$,$ saddle, etc.$)$ into the finished bike. $($That is$,$ only one employee works on a given bike at

FAT.$)$ When the process operates at capacity, the FAT resource pool$$s utilization is $80\%.$

a$)(6$ points$)$ Draw the process map

b$)(5)$ What is the theoretical capacity of the Torrent production process in bikes per hour in steady state

$$ namely, not the first few bikes assembled in the day? $($There is no missing information!$)$

c$)(5)$ What are the activity times for all the activities of the Torrent production process? $($in minutes$/$bike$)$

d$)(5)$ What is the theoretical flow time for a Torrent bike?

e$)(3)$ How will your answers to b$)$ and d$)$ change if activity times had variability?

For the following two questions, assume that the shop is open for ten hours from $8$ am to $6$ pm$.$ In addition,

assume that on a particular day, orders for $10$ bikes are waiting to be processed when the shop opens.

f$)(5)$ Can the store complete all ten orders by $6$ pm if there were no partially assembled bikes in the

process?

g$)(7)$ Draw an inventory buildup diagram for the number of partially assembled bikes in the store between

$8$ am and $6$ pm$.($Bikes that have started the process but have not finished yet$)$

h$)(5)$ Lance and John have the following argument. Lance claims that it is possible to simultaneously increase the

capacity and reduce the theoretical flow time of the Torrent bike production process simply by reducing the

activity time of a single $($carefully selected$)$ activity while keeping the process otherwise unchanged. John,

however, claims that this is not possible. Who is right and why?

i$)(8)$ Assume that Avery $($one of the people doing the final assembly and testing$)$ quits her job and no one replaces

her. What impact does this have on the theoretical flow time and the theoretical capacity?