Please Note:
• Please include the details of your calculations so that graders can give you partial credit if not full credit.
• The data set included in this homework is also available in Excel format.

AlwaysCool.com is an online apparel company that produces and sells high-quality shirts. The firm’s production takes place in its Buffalo factory. Lately, the firm has faced some challenges in the marketplace, such as meeting demand and intense price competition.

The management suspects that these problems stem from the mismanagement of the production process in the factory. AlwaysCool.com needs your team’s help in analyzing its processes and driving some performance metrics.

The management provided the following pieces of information to your team. In the factory, the first step in the production process is cutting the shirt patterns. (A shirt pattern is a template that includes all components of a shirt, such as sleeves, cuffs.) The factory uses a new-generation computer-aided cutting machine that could cut as many as 50 layers of cloth at the same time. The factory’s current policy is to layout and cut 50 layers of cloth at a time. However, setting up the machine takes some time: it takes 2 minutes to roll out each layer of cloth on the cutting table. Once the fabric is laid out, regardless of the number of layers, it takes 100 minutes to cut all pieces of shirt patterns in all layers and remove them from the cutting table. Each layer of cloth includes 6 shirt patterns. For the cutting machine to be operated, 3 cutting-machine operators need to work simultaneously, and they need to be fully utilized. There are 3 cutting-machine operators.

After cutting, operations #1 through #12 need to be completed in the order given in Table 1. The processing times of each operation along with the number of workers that perform each operation are given in Table 1.

In operations #1 through #12, workers work in parallel, and a machine is assigned to each worker. The facility operates 8 hours a day.

Table 1. Operations #1 through #12

Operation Processing Time (minutes /shirt) Number of workers
1. Make collar 4.5 4
2. Make cuffs 3 3
3. Make sleeves 2.5 4
4. Make front 4.8 5
5. Make back 2.3 3
6. Attach collar 2.8 3
7. Attach sleeves 1.5 2
8. Attach cuffs 1.4 2
9. Hem buttons 2 3
10. Inspect 5 6
11. Iron 5.9 5
12. Fold, Package 2.5 6

All workers work for the entire 8 hours, and each is compensated hourly. The hourly pay for each type of worker is provided in Table 2.

Table 2. Hourly compensation of a worker

Type of Operation A worker’s compensation ($/hour)
Cutting 23
Make collar 24
Make cuffs 24
Make sleeves 27
Make front 38
Make back 37
Attach collar 21
Attach sleeves 22
Attach cuffs 22
Hem buttons 38
Inspect 39
Iron 35
Fold, Package 39

Based on this information, please answer the following questions.

(a) [15 points] What is the capacity of the cutting machine in terms of shirts/day? Please include your calculations to justify/support your answer.

Please see page 3 for questions (b) and (c).

(b) [35 points] (i) What is the bottleneck step in this process?
(ii) What is the process capacity in terms of shirts/day?
Please explicitly state your answers for both (i) and (ii), and please include the details of your calculations.

(c) [10 points] Based on your calculations in part (b) and additional data, your team has concluded that the facility’s capacity is ideal to meet the demand. The management is planning to let 3 workers go to reduce the production cost, but does not want the process capacity to be affected with that change. What is the most profitable way to implement such a change? Please justify your answer.