A machine shop has four machines of different types and must produce five different part styles during its 40 hours per week operation. The part-mix ratios, batch quantities, part routings, machines, servers, and production setup times and cycle times (in hours) are given in the table below for the part styles produced in the shop. Operation sequence for each part style is in the order of station number. Part styles are identified by letter and stations are identified by number. Determine the maximum production rate (determined by the bottleneck station) (pieces/hour, 3 decimal points). Part style (i) Part mix (pj) Batch quantity (Qb) Station Servers (i) (si) 1 2 3 4 3 3 2 2 A 0.23 TSUA 29 TCA 3.3 0.38 B 0.1 1.5 0.49 22 1.8 0.15 3 0.17 1.7 0.47 0.22 C 2.3 3.4 30 D 0.2 TsuB TcB Tsuc TCC TsuD TcD TSUE TCE 2.8 0.1 21 2.8 0.5 0.34 2.2 0.39 0.14 E 0.28 19 1.8 0.5 2.3 0.52 1.6 0.57

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section: Chapter Questions
Problem 59P
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A machine shop has four machines of different types and must produce five different
part styles during its 40 hours per week operation. The part-mix ratios, batch quantities,
part routings, machines, servers, and production setup times and cycle times (in hours)
are given in the table below for the part styles produced in the shop.
Operation sequence for each part style is in the order of station number. Part styles are
identified by letter and stations are identified by number.
Determine the maximum production rate (determined by the bottleneck station)
(pieces/hour, 3 decimal points).
Part style (j)
Part mix (pj)
Batch quantity
(Qb)
Station Servers
(i)
(si)
1
2
3
4
3
3
2
2
A
0.23
29
TSUA TCA
B
1.5 0.49
0.1
22
1.8 0.15 3 0.17
3.3 0.38
C
0.22
TsuB TcB Tsuc
1.7 0.47
30
2.3
3.4
TCC
D
0.2
21
2.8 0.5
0.39
E
0.28
TSUD TCD TSUE
19
0.34 2.2
0.14
2.8 0.1 2.3 0.52 1.6 0.57
TCE
1.8 0.5
Transcribed Image Text:A machine shop has four machines of different types and must produce five different part styles during its 40 hours per week operation. The part-mix ratios, batch quantities, part routings, machines, servers, and production setup times and cycle times (in hours) are given in the table below for the part styles produced in the shop. Operation sequence for each part style is in the order of station number. Part styles are identified by letter and stations are identified by number. Determine the maximum production rate (determined by the bottleneck station) (pieces/hour, 3 decimal points). Part style (j) Part mix (pj) Batch quantity (Qb) Station Servers (i) (si) 1 2 3 4 3 3 2 2 A 0.23 29 TSUA TCA B 1.5 0.49 0.1 22 1.8 0.15 3 0.17 3.3 0.38 C 0.22 TsuB TcB Tsuc 1.7 0.47 30 2.3 3.4 TCC D 0.2 21 2.8 0.5 0.39 E 0.28 TSUD TCD TSUE 19 0.34 2.2 0.14 2.8 0.1 2.3 0.52 1.6 0.57 TCE 1.8 0.5
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