A flexible manufacturing system is used to produce three products.

A flexible manufacturing system is used to produce three products. The FMS consists of a load/unload station, two automated processing stations, an inspection station, and an automated conveyor system with an individual cart for each product. The conveyor carts remain with the parts during their time in the system, and therefore the mean transport time includes not only the move time, but also the average total processing time per part. The number of servers at each station is given in the following table:
A flexible manufacturing system is used to produce three products.

All parts follow either of two routings, which are 1 ( 2 ( 3 ( 4 ( 1 or 1 ( 2 ( 3 ( 1, the difference being that inspections at station 4 are performed on only one part in four for each product (f4jk = 0.25). The product mix and process times for the parts are presented in the table below:

A flexible manufacturing system is used to produce three products.

The move time between stations is 4 min.
(a) Using the bottleneck model, show that the conveyor system is the bottleneck in the present FMS configuration, and determine the overall production rate of the system.
(b) Determine how many carts are required to eliminate the conveyor system as the bottleneck.
(c) With the number of carts determined in (b), use the extended bottleneck model to determine the production rate for the case when N = 8; that is, only eight parts are allowed in the system even though the conveyor system has a sufficient number of carriers to handle more than eight.
(d) How close are your answers in (a) and (c)? Why?

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