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OST: Chapter 5

OST: Chapter 5. Cellular Manufacturing Group Technology. Introduction. Review of the introductory example Production and assembly of 4 parts (A, B, C, D) A: saw -> turn -> mill -> drill B: saw -> mill -> drill -> paint C: grind -> mill -> drill -> paint D: weld -> grind -> turn -> drill.

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OST: Chapter 5

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  1. OST: Chapter 5 Cellular Manufacturing Group Technology OST

  2. Introduction • Review of the introductory example • Production and assembly of 4 parts (A, B, C, D) • A: saw -> turn -> mill -> drill • B: saw -> mill -> drill -> paint • C: grind -> mill -> drill -> paint • D: weld -> grind -> turn -> drill OST

  3. Group Technology (GT) • Observation already in 1920ies:product-oriented departments to manufacture standardized products in machine companies lead to reduced transportation • Can be considered the start of Group Technology (GT):Parts with similar features are manufactured together with standardized processes  small "focused factories" are created as independent operating units within large facilities. • More generally, GT can be considered a “theory of management” based on the principle "similar things should be done similarly“ • "things" .. product design, process planning, fabrication, assembly, and production control (here); but also other activities, including administrative functions. OST

  4. When to use GT? • Pure item flow lines are possible, if volumes are very large. • If volumes are very small, and parts are very different, a functional layout (job shop) is usually appropriate • In the intermediate case of medium-variety, medium-volume environments, group configuration is most appropriate OST

  5. Cellular Manufacturing • Principle of GT: divide the manufacturing facility into small groups or cells of machines cellular manufacturing • Each cell is dedicated to • a specifiedfamilyof parttypes (or few “similar” families). • Preferably, all parts are completed within one cell • Typically, it consists of • a small group of machines, tools, and handling equipment OST

  6. Different Versions of GT • The idea of GT can also be used to build larger groups, such as for instance, a department, possibly composed of several automated cells or several manned machines of various types. • GT flow line (closest to flow shop) • classicalGT cell • GT center (closest to job shop) OST

  7. GT flow line • All parts assigned to a group follow the same machine sequence and require relatively proportional time requirements on each machine. • Automated transfer mechanisms may be possible. •  mixed-model assembly line (Chapter 4) fräsen (aus)bohren drehen schleifen bohren (Askin & Standridge, 1993, p. 167). OST

  8. classicalGT cell • Allows parts to move from any machine to any other machine. Flow is not unidirectional. • Since machines are located in close proximity  short and fast transfer is possible. (Askin & Standridge, 1993, p. 167). OST

  9. GT center • Machines located as in a process (job shops) • But each machine is dedicated to producing only certain Part families  only the tooling and control advantages of GT; increased material handling is necessary • When large machines have already been located and cannot be moved, or • When product mix and part families are dynamic  would require frequent relayout of GT cell (Askin & Standridge, 1993, p. 167). OST

  10. Cellular manufacturing • Group technology • Parts with similar features are manufactured • Small "focused factories" are created as independent operating units within large facilities. • Divide the manufacturing facility into small groups • Each cell is dedicated to a specified family or set of part types • A cell is a small group of machines, tools, and handling equipment • Since machines are located in close proximity  short and fast transfer is possible OST

  11. Cellular manufacturing • Often u-shaped for short transport • Often typical material flow OST

  12. Cellular manufacturing • Example with 3 workers • Also u-shaped OST

  13. Cellular manufacturing • Advantages: • Short transportation and handling (usually within cell) • Short setup times because often same tools and fixtures can be used (products are similar) • High flexibility (quick reaction on changes) • Clear arrangement, few tools/machines  easy to control • High motivation and satisfaction of workers (identification with “their" products) • Small lot sizes possible • Short flow times OST

  14. Cellular manufacturing • Howtobuildgroups? • Similiar parts (similiarprocessflow/machineusage, same materials,…) aregrouped • Visual inspection • Classificationandcodingbased on design andproductiondata (time consuming, nouniversallyapplicablesystemisavailable) • Production Flow Anlaysis (PFA), i.e. mathematicalmodels OST

  15. Production Flow Analysis • Many clustering methods have been developed • Can be classified into: • Part family grouping:Form part families and then group machines into cells • Machine grouping:Form machine cells based upon similarities in part routing and then allocate parts to cells • Machine-part grouping:Form part families and machine cells simultaneously OST

  16. Machine-part grouping • Construct matrix of machine usage by parts • sort rows (machines) and columns (parts) so that a block-diagonal shape is obtained OST

  17. Machine-part grouping • How can this sorting can be done systematically? • Various heuristic and exact methods have been developed. The simplest one is binary ordering, also known as “rank order clustering” or “King’s algorithm“ OST

  18. Binary Ordering • Example: 5 machines; 6 parts: • Interpret rows and columns as binary numbers • Sort rows w.r.t. decreasing binary numbers • Sort columns w.r.t. decreasing binary numbers OST 18

  19. Binary Ordering • Sort rows w.r.t. decreasing binary numbers • New ordering of machines: B – D – C – A - E 0101002 = 22 + 24 = 20 20 + 21 + 23 + 25 = 43 20 + 22 + 23 + 24 = 29 20 + 21 + 25 = 35 21 + 22 = 6 24 16 21 2 25 32 20 1 23 8 22 4 OST

  20. Binary Ordering • Sort columns w.r.t. decreasing binary numbers 24 = 16 23 = 8 • New ordering of parts: • 6-5-1-3-4-2 22 = 4 21 = 2 20 = 1 20+21+22=7 20+23+24=25 23 + 24 = 24 21 + 22 = 6 22 + 24 = 20 22+23+24=28 OST

  21. Result of Binary Ordering • No complete block-diagonal structure • Remaining items: 6, 5, and 3 produced in both cells • Or machines B, C, and E have to be duplicated • 2 groups: • Group 1: parts {6, 5, 1 }, machines {B, D} • Group 2: parts { 3, 4, 2}, machines {C, A, E} • Parts 1, 4, and 2 can be produced in one cell OST

  22. Repeated Binary Ordering • Binary Ordering is a simple heuristic  no guarantee that „optimal“ ordering is obtained • Sometimes a better better block-diagonal structure is obtained by repeatingthe Binary Ordering until there is no change anymore OST

  23. Example Binary Ordering (contd.) • After sorting of rows and columns: • No change of groups in this example OST 23

  24. Single-Pass Heuristic • Considering capacities (Askin and Strandridge): • All parts must be processed in one cell (machines must be duplicated, if off-diagonal elements in matrix) • All machines have capacities (normalized to be 1) • Constraints on number of identical machines in a group • Constraints on total number of machines in a group OST

  25. Single-Pass Heuristic - Example • 7 parts, 6 machines • Given matrix of processing times (incl. set up times) for typical lot size of parts on machines • Entries in matrix not just 0/1 for used/not used) • All times as percentage of total machine capacity • Maximal number of machines per cell:here at most 4 machines in a group • Not more than one machine of each type in a group OST

  26. Single-Pass Heuristic 1 1 2 2 1 2  = 9 machines OST

  27. Single-Pass Heuristic • At least 9 machines are needed • Not more than 4 machines in a group •  at least 9/4 = 2,25 groups, i.e. at least 3 groups • Step 1: acquire block diagonal structure e.g. using binary sorting • Step 2: build groups OST

  28. Single-Pass Heuristic • Step 1: • For binary sorting treat all entries as 1s. • Result: OST

  29. Single-Pass Heuristic • Step 2: • Assign parts to groups (in sorting order) • Necessary machines are also included in group • Add parts to group until either • the capacity of some machine would be exceeded, or • the maximum number of machines would be exceeded OST

  30. Single-Pass Heuristic table 1 D, C, A D (0,8), C (0,6), A (0,7) D (0,5), C (0,6), A (0,1) 1 D, C, A D (0,5), F (0,8), B (0,9) D, F, B 2 2 D, F, B D (0,1), F (0,5), B (0,9) D (0,1), F (0,1), B (0,6), C (0,5) 2 D, F, B, C 3 C, E C (0,7), E (0,5) C (0,7), E (0,1), F (0,8), B (0,7) 3 C, E, F, B OST

  31. Single-Pass Heuristic • Machines used: • One machine each of types: A, E • Two machines of types: B, D, F • Three machines of type: C • Single-pass heuristic of Askin und Standridge is a simple heuristic  not necessarily optimal solution (min possible number of machines) • Compare result with theoretical min number of machines OST

  32. Single-Pass Heuristic Maybe reduction possible?! OST 32

  33. BIP Model • Minimize total (or weighted) number of machines used when the number of groups is given • Previous example: • At least 9 machines necessary • Every group has at most M = 4 machines •  at least 3 groups (try 3) OST

  34. BIP Model ajk ... capacity of machine k needed for part j i  I ... groups (cells) j  J ... parts k  K ... machines M ... maximum number of machines per group OST

  35. BIP Model 1, if part j is assigned to group i 0, otherwise 1, if machine of type k is assigned to group i 0, otherwise = = OST

  36. BIP Model objective: constraints: each part must be assigned to one group respect capacity of machine k in group i not more than M machines in group i binary variables binary variables OST

  37. Solution • Optimal solution with 10 machines • Theoretical minimum number was 9 machines (not reached because of constraints) • Single pass heuristic used 11 machines OST

  38. Similarity Coefficients • Also a clustering method (machine grouping) • Define ni ... Number of parts visiting machine i nij ... Number of parts visiting machines i and j • Similarity coefficient between machines i and j Proportion of parts visting machine i that also visit machine j 38 OST

  39. Similarity Coefficients • Hierarchical Clustering Heuristic: • Calculate Similarity Coefficients (SC) for all combinations of machines • Group that combination leading to the highest SC. Stopping criteria: e.g. SC have to reach a given lower bound, only machines (no clusters) can be grouped, etc. • Update SC: e.g. maximum of the SC of the machines that are to be combined (this is some kind of lower bound, determining the new coefficients exactly could lead to higher values. e.g. A: 0 1 1 B: 1 1 0 C: 1 0 1 OST 39

  40. Similarity Coefficients • Machine-Part-Matrix: ni 3 3 4 4 2 2 40 OST

  41. Similarity Coefficients Calculate SC: ni 3 3 4 4 2 2 Combine: A-B 41 OST

  42. Similarity Coefficients • Bild Cluster und Update SC: 42 OST

  43. Similarity Coefficients • Dendogram: • Graphical illustrations of possible groupings per threshold 43 OST

  44. Graph Partitioning • Machines with common parts should be in same group • Graph illustrating common parts • Group forming can be seen as special case of graph partitioning OST

  45. Graph Partitioning • Given a graph with nodes and edges, find a partitioning of the node set into a (given) number of disjoint subsets of approximately equal size, such that the total cost of edges that connect nodes of different subsets is minimized. • NP-hard optomization problem • Various methods have been developed • Simple and well-known heuristic by Kernighan and Lin OST

  46. Kernighan and Lin • Input: A weighted graph G = (V, E) with • Vertex set V. (|V| = 2n) • Edge Set E. (|E| = e) • Cost cAB for each edge (A, B) in E. • Output: 2 subsets X & Y such that • V = X  Y and X  Y = { } (i.e. partition) • Each subset (group) has n vertices • Total cost of edges “crossing” the partition is minimized. OST

  47. Kernighan and Lin • Complete enumeration (brute force) is not possible (np-hard): • Try all possible bisections. Choose the best one. • If there are 2n vertices  number of possibilities = (2n)! / (n!)2 = nO(n) • For 4 vertices (A,B,C,D), 3 possibilities • 1. X = {A, B} & Y = {C, D} • 2. X = {A, C} & Y = {B, D} • 3. X = {A, D} & Y = {B, C} • For 100 vertices  5  1028 possibilities OST

  48. Kernighan and Lin OST

  49. 3 a b 1 4 2 2 c d 2 4 3 1 6 e f Kernighan and Lin • V(G) = { a, b, c, d, e, f }. • Start with any partition of V(G) into X and Y, e.g., • X = { a, c, e } Y = { b, d, f } • The cut value is the sum of all edge costs between the 2 sets: • cut-size = 3 + 1 + 2 + 4 + 6 = 16 • Try to improve this partitioning using KL OST

  50. Kernighan and Lin • For each node x  { a, b, c, d, e, f } compute the gain values of moving node x to the others set: Gx = Ex - Ix where Ex= cost of edges connecting node x with the other group (extra) Ix = cost of edges connecting node x within its own group (intra) • This gives: • Ga = Ea – Ia= 3 – 4 – 2= – 3 • Gc = Ec – Ic = 1 + 2 + 4 – 4 – 3 =0 • Ge = Ee – Ie = 6 – 2 – 3 = + 1 • Gb = Eb – Ib = 3 + 1 –2 = + 2 • Gd = Ed – Id = 2 – 2 – 1 = – 1 • Gf= Ef– If = 4 + 6 – 1 = + 9 OST

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