1. Analysis of flexible manufacturing systems
Bottleneck model
Part mix: the mix of various parts or product styles produced by
the system.
Pj: the fraction of the total system output that of style j
j=1, 2 ……P(the total number of different part styles)
Work station and servers: the FMS has a number of distinctly
work stations n including the load/unload stations.
Each workstation may have more than one server,
Means that it has two or more machines capable of performing
the same operations,
si = the number of servers per workstation i=1, …..n

2. Analysis of flexible manufacturing systems
Bottleneck model
Process routing: it defines the sequence of operations, the
workstations where operations are performed and the associated
process time.
tijk: the processing time that a production unit occupies a given
workstation server (without any waiting)
i : refers to the station
j : refers to the part or the product
K: refers to the number of the operation in the product process
plan

3. Analysis of flexible manufacturing systems
Bottleneck model
Work handling system: the handling system used to transport
parts with the FMS it can be considered as a special case of
workstations (n+1).
the number of carriers is analogous to the number of servers
Transportation time : the mean time required to transport parts
from one station to another one.
It can be more convenient to use average transport time for all
moves

4. Analysis of flexible manufacturing systems
Bottleneck model
Operation frequency: the expected number of times a given
operation in the process routing is performed for each work unit.
fijk: operation frequency for operation k in process plan j at station
i.

5. Analysis of flexible manufacturing systems
Bottleneck model
Average workload for a given station: the mean total time
spent at a station per part.
tijk: processing time for operation k in process plan j at station i.
fijk: operation frequency for operation k in process plan j at station
i.
pj: part mix fraction for part j.
Workload of handling station: the mean transport time multiplied
by the average number of transports required to complete the
processing of a part.
mean number of transports (nt) :

6. Analysis of flexible manufacturing systems
Bottleneck model
System performance measure:
a)Production rate of all parts,
b)Production rate of each part style,
c)Utilisation of the different workstations,
d)Number of busy servers at each work station.
These measures will be computed based on the assumption of:
The FMS is producing at its maximum possible rate. Which is
constrained by the bottleneck station in the system.
The bottleneck is the station with the highest workload per server.

7. Analysis of flexible manufacturing systems
Bottleneck model
System performance measure:
a)Maximum production rate of all parts (pcs/min),
S* number of servers at the bottleneck station
WL* is the workload at the bottleneck station
b) Maximum production rate of each part style (pcs/min),

8. Analysis of flexible manufacturing systems
Bottleneck model
System performance measure:
c) utilization of each work station Ui,
Average station utilization ,
Overall FMS utilization

9. Analysis of flexible manufacturing systems
Bottleneck model
System performance measure:
d) Number of busy servers at each workstation (BSi),
Example 19.5
Example 19.6

10. Analysis of flexible manufacturing systems
Bottleneck model
System performance measure:
d) Number of busy servers at each workstation (BSi),
Example 19.5
Example 19.6