Use the extended bottleneck model to solve problem 19.1 with the following number of parts in the system:
(a) N = 2 parts and
(b) N = 4 parts.
Also determine the manufacturing lead time for the two cases of N in (a) and (b).
Problem 19.1
A flexible manufacturing cell consists of two machining workstations plus a load/unload station. The load/unload station is station 1. Station 2 performs milling operations and consists of one server (one CNC milling machine). Station 3 has one server that performs drilling (one CNC drill press). The three stations are connected by a part handling system that has one work carrier. The mean transport time is 2.5 min. The FMC produces three parts, A, B, and C. The part mix fractions and process routings for the three parts are presented in the table below. The operation frequency fijk = 1.0 for all operations. Determine
(a) Maximum production rate of the FMC,
(b) Corresponding production rates of each product,
(c) Utilization of each machine in the system, and
(d) Number of busy servers at each station.

Partj Part mix p Operation Descriptio Stationi Process time tyx 0.2 Load 20 min 12 min Unload Load 8 0.3 30 min Unload Load 8 0.5 3 min 14 min Unload