Go back to the year 2012 and Linsanity has arrived at XYZ. Jeremy Lin's record setting first five starts in the NBA has created a buzz in the media and a swarm of fans. There has been a spike in NBA League Pass subscriptions recently, and tickets to Knicks games at Madison Square Garden are going for a premium. Hoping to capitalize on this "Linsanity", a small jersey manufacturer that supplies New York City retail stores needs to ramp up production of Jeremy Lin basketball jerseys.

To produce a jersey, a sequence of three activities must be undertaken. The first step involves cutting fabric which takes 5 minutes per jersey. The second step involves embroidering 8 different pieces (lettering, numbering, logo, etc.) onto the jersey. Each of these pieces takes 45 seconds to embroider. Once all 8 pieces have been embroidered, the jersey moves to the final step where it is sewed together. This activity takes about 2 minutes per jersey. For simplicity, assume each order is for one jersey.

During the first week, the manufacturer employed one worker at each activity and ran the production process 8 hours per day, 5 days per week. The total number of jerseys ordered during the first week was 3200 jerseys, and Ron, the manager, noticed there was a fairly large backlog. He needs your help to figure out a cost effective plan for the upcoming weeks (weeks 2 through 4). His order projections are as follows:

Week Orders (jerseys)

Week2 3200

Week3 3600

Week4 4000

(i) During the first week, what was the process capacity (jerseys/week)?

(ii) What is his total backlog (number of jerseys ordered that have not been fulfilled) at the end of week 1?

(iii) Starting in week 2, Ron wants to increase the number of workers performing each activity to make sure he can produce jerseys fast enough to satisfy orders. Assuming that each worker is dedicated to a particular activity (no cross training), what is the minimum number of workers at each step in order to achieve no remaining backlog by the end of week 4? Note: Ron can only change the number of workers once at the beginning of week 2, and he must choose a whole number (i.e., 1, 2, 3, ...) of workers - no fractional workers.

For the remaining parts, assume you have the number of resources at each step that you computed in part (iii) for the final three weeks.

(iv) Draw an inventory build-up diagram of the jersey orders over all four weeks. Assume orders flow into the process continuously.

(v) At what point in time will the backlog finally be cleared?

(vi) What is the throughput of the process?

(vii) On average, how many days does an order wait in the backlog?

(viii) How many orders actually waited in the backlog?

(ix) Once the backlog has been eliminated, how long does it take for an order to go from arrival to fulfilled?