# Use the extended bottleneck model to solve Problem 16.3 with the following number of parts in the…

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).

Problem 16.3

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).