solution

1. a furniture company that manufactures traditional Japanese furniture. The final assembly process is performed manually by 10 workers. Two main components C-I and C-II are required and fabricated with an equipment, TJ, on which setup times for the two components are 15 and 30 minutes, respectively, whenever switching manufacturing between C-I and C-II. The processing times for each unit of the two components are 4 and 1 minutes, respectively. One C-I and four C-II are required for each item of Furniture-A.

1. Furniture-A is very popular. Customers have to wait months in the order queue. F-Kyoto now runs batch sizes of 600 and 2400 for C-I and C-II, respectively. What is the capacity of TJ?
2. 10 minutes are required to assemble a Furniture-A. What is the capacity of assembly? Which is the bottleneck?

1. Customers are unhappy because they have to wait long periods to obtain a Furniture-A. The company comes to Doshisha Business School and hires you as a part-time consultant to improve the process capacity of producing items of Furniture-A. You cannot hire more workers because the current 10 workers are specialists with long-year experiences. It is difficult to find additional workers with those high skills. To match TJ with assembly process, you use the following “batch size formula” you learnt from Professor Yin’s course to decide the appropriate batch size for C-I and C-II.

But you are surprised that the answer is a negative number of -6.42857, gotten by (10/10 * 45)/(1-10/10 *8). Why does this formula not function?