Models and Analysis of Manufacturing Systems

Models and Analysis of Manufacturing Systems

Review Models and Analysis of Manufacturing Systems 8/24/04 Paul A. Jensen Operations Research Models and Methods Copyright 2004 - All rights reserved Purpose of the course: Provide an understanding of problems and issues in manufacturing design Build flow models embodying the components of the manufacturing process Identify waste in the manufacturing process Use models to quantify waste Use operations research tools to analyze models and make decisions 2 The production system may be very complex R1 R2 R3 M1 M1 M1 M1 M1 M2 M1 M1 M3 M1 M5 M1 M4 M6 M7 M1 M2 Offices M1 M3 M1 M4 M5 V M1 M1 M6 Operations Machines Raw Materials Resources 3 The process model R1 R3 R2 11 5

1 12 6 2 Raw Materials Inventory Processing Operation 3 13 4 7 8 14 Inspection Delay 9 15 16 10 17 18 19 20 Finished Goods Inventory 4 Multiple products Product A R1 Product B Product C R1 R3 R2 4 1 5 2 6 3 R2 8 1 R3 4 1 2 2 9 3 5 3 4 A A 10

7 6 V 8 B 11 7 A V A 12 13 V C 5 Flow Analysis R2 R1 Grouping and waste And, OR, Proportion Nodes Cycles with and without waste Flow ratio Unit time Complex Networks 5 R3 3 1 6 2 A 7 4 A 8 6 Defects and Inspection R2 R3 R1 R2 R3 Operation 5 3 1 8 4 Defect Rate Scrap Rate

Flow Ratio 1 1 0.1 0 1.929 2 0.2 0 1.929 3 0 0.28 1.929 4 0.1 0 1.543 5 0 0.1 1.543 6 0.2 0 1.389 7 0 0.2 1.389 8 0.1 0 1.959 9 0.1 0 1.959 10 0.3 0 1.959 11 0 0.433 1.959 12 0.1 0

1.111 13 0 0.1 1.111 2 6 2 9 5 3 A A 7 10 6 4 11 7 A A 8 12 13 7 Work in Process WIP = Flow rate*residence time 10 1 3 2 Raw Delay 5 4 Oper. Delay 7 6 Inspect Oper. Delay 9 8 Delay Inspect Finished Material Goods Oper. 1 2

Time A Computing WIP 3 10 4 5 5 20 6 4 7 8 25 18 30 25 10 30 9 10 Total 5 117 min. Time B 10 10 20 12 15 min. Flow 1.272 1.272 1.272 1.272 1.272 1.111 1.111 1.111 1.111 1 132 11.573 8.3325 13.888 2.3146 56.778 23.146 9.2583

27.775 13.888 129.19 Ratio WIP A 5.3 WIP B 10.6 Oper. Evaluating WIP 1 2 WIP A Unit 2.65 10.6 10.6 21.2 3 5.3 20 4 2.65 20 2.12 12.72 5 10.6 20 6 2.12 20 7 11.573 20 8 8.3325 20 9 13.888 50 10 Total 2.3146 50 56.778 50 50 Value WIP

0 106 53 212 42.4 231.46 416.63 694.38 115.73 0 1871.6 value 8 Inventories Raw Materials Inventory Level s+Q TC =[ aK / Q ]+[ hQ /2] + hs 1 Lot size: Q *= 2 aK / h s Cycle time: t *= Q */ a . 0 0 Q/a 2 Q/a 3 Q/a 4 Q/a

5 Q/a 6 Time Q/a Finished Goods Inventory Level TC =[ aK / Q ] + [( p - a 2 apK ) hQ /2 p ]+ sh s+Q Lot size: Q *= /( p - a ) 10 Cycle time: t *= Q */ a . s 0 0 Q/a 2 Q/a 3 Q/a 4 Q/a

5 Q/a 6 Q/a Time 9 h Production in Lots Production and transfer lots Effects on machine capacity V T = T s + T p where T s = j t sj and Q T p = V j t pj j products products Effects on WIP Processing: Depends on the production and transfer lot Queuing delays: Depends on lot size 10 Variability Poisson and Nonpoisson Systems M1 M1 Queue

Operation with Delay s 1 0 Machine Station with Queue ( s r ) = n ( n ) =0 r -1 L q p s s = s r s +1 p 0 = (1 r ) 2 s !(1 r ) 2 ! s n r +

s s !(1 r ) 11 Queuing Networks 10 1 3 2 Raw Delay 5 4 Oper. Delay 7 6 Inspect Oper. Delay 9 8 Delay Inspect Finished Material Oper. Time X Goods 1 2 3 --- 5 4 5 --- 4 6 7 8 --- 12 --- --- 20 --- 9

10 5 min. Time Y --- 10 --- 12 15 min. Depends on machine assignment Depends on product demands Depends on operation times Depends on flow ratios 12 Material Movement Types of layouts Criterion for comparison The Craft method To From A B C D A E F G H 5 B 3 C 1 4 I J 1 9 1 Y 9 2 20 1 2 3 4 5 D A B

C D 6 1 E E 8 3 10 6 7 8 9 10 F F G H I 2 5 J G 6 0 0 10 20 30 40 50 X H 8 I J 13 Kinds of Problems Fixed machine assignments and capacities Fixed machine assignments and product mix Find the bottleneck Find the product mix Compute queuing delays, WIP, throughput time Select capacities (number of machines) Compute queuing delays, WIP, throughput time 14

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