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Process Flow Analysis Goldratt: Balance flow not capacity 8/24/04 Paul A. Jensen Operations Research Models and Methods Copyright 2004 - All rights reserved Our Goal: For a single product Given: the process design Given: operation time and scrap rates at each operation Given: product demand Find: The flow in each operation and the total time required for each operation 2 To construct a model you must know the process The process is described by its operations R1 R1 R2 R2 R3 5 6 R3 3 1 2 7 4 8 A 3 The process model admits greater detail R1 R3 R2 11 5 1 12 6 2 Raw Materials Inventory Processing Operation 3 13 4 Inspection 14 8 Delay 15 9 16 10 7 17 18 19 20 Finished Goods Inventory 4 What happens to product flows at junctions? Do they assemble? Do they combine? Do they mix? Do they disassemble? Do they separate? Do they split? R3 R2 R1 5 6 3 1 2 7 4 8 5 “And” nodes model flows that assemble The flows are equal on all entering and leaving arcs Assembly Disassembly General Case fi A fk A A fh fj fh = fi = fj = fk 6 “Or” nodes model flows that combine The total flow in equals the total flow out Combining Flows Separating Flows General Case fi O O fk O fh fj fi + fk = fh + fj 7 “Proportionality” nodes model arbitrary combinations Input and output proportions are given Mixing Splitting 1 0.4 pi 0.6 P General Case fi 0.5 fk P P 1 pk 0.5 ph f h p j fj f i = xp i , f k = xp k f h = xp h , f j = xp j 8 All junction nodes must be specified in a process chart R3 R2 R1 5 6 3 1 2 A 7 4 O 8 9