Use the extended bottleneck model to solve Problem 16.3 with the following number of parts in the system: (a) N = 5 parts, (h) N = 8 parts, and (c) N = 12 parts. Also determine the manufacturing lead time for the three cases of N in (a), (b), and (c).
An FMS consists of three stations plus a load/unload station. Station 1 loads and unloads parts from the FMS using two servers (material handling workers). Station 2 performs horizontal milling operations with two servers (two identical CNC horizontal milling machines). Station 3 performs vertical milling operations with three servers (three identical CNC vertical milling machines). Station 4 performs drilling operations with two servers (two identical drill presses).The machines are connected by a part handling system that has two work carriers and a mean transport time = 3.5 min. The FMS produces four parts, A, B, C, and 0, whose part mix fractions and process routings are presented in the table below. The operation frequency fijk = 1.0 for all operations. Determine: (a) maximum production rate of the FMS, (b) utilization of each machine in the system, and (c) average utilization of the system, using the server average U,, Eq. (16.9).