Gary's Gears is a production facility that produces metal gears. The first step is stamping, which happens at a press. There are two identical presses that operate simultaneously (gears can be stamped on either press). A press stamps one part at a time. It takes 1 minute to stamp a part, including loading and unloading. Before beginning a new batch of parts, there is a 20-minute setup involving die change. The batch size is 100 parts. In other words, after stamping 100 parts, the press must be set up again. The stamped parts are stored in a buffer area, called as the work-in-process (WIP) inventory rack. From here, the parts are taken to the furnace, where they are annealed (heat treated). Parts from different batches can be annealed together. To perform annealing, a boat (a type of fixture for holding stamped parts) loaded with parts is inserted into the furnace. While those parts are being annealed, newly stamped parts are loaded onto a spare furnace boat. Each boat can hold 70 parts. Once the boat is full, additional stamped parts are placed in the WIP inventory rack. After annealing is completed, the boat in the furnace is swapped with the boat outside the furnace and the next annealing cycle begins. Each annealing cycle takes a total of 30 minutes. The time to load and unload parts from a boat is very short, and can be neglected. The above system operates 8 hours a day, Monday through Friday. On Mondays, however, the furnace and both boats are cleaned. Thus, all parts stamped by the presses go straight to the WIP inventory rack on Mondays.

Questions

1. What is the throughput capacity of this system, in parts per week? In other words, how many parts can be processed per week?

2. What is the required buffer capacity of the WIP inventory rack?

3. What is the average inventory level in the WIP inventory rack (averaged over the factory operating hours)?

4. What is the system throughput capacity if the WIP inventory rack can hold only 500 parts?

5. What is the average number of factory operating hours that a part spends in the WIP rack in question 2? (Parts that do not wait in the WIP rack should be included in this average, and have zero waiting time by definition.)

6. What is the average number of factory operating hours that a part spends in the WIP rack in question 4? (Parts that do not wait in the WIP rack should be included in this average, and have zero waiting time by definition.)