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COMPUTERIZED LAYOUT_II

COMPUTERIZED LAYOUT_II. APRIL 2013. Layout Levels. From: http://www.strategosinc.com/facility_plan_levels.htm. Algorithmic Approaches ( i). • SLP is “ informal ” • Does not provide a formal procedure or algorithm for critical steps

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COMPUTERIZED LAYOUT_II

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  1. COMPUTERIZED LAYOUT_II APRIL 2013

  2. Layout Levels From: http://www.strategosinc.com/facility_plan_levels.htm Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  3. AlgorithmicApproaches (i) • SLP is “informal” • Does not provide a formal procedure oralgorithmforcriticalsteps • Algorithm: a precise rule (or set of rules)specifying how to solve some problem – Has an objectivefunction – Amenabletocomputerimplementation Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  4. AlgorithmicApproaches Types of input – Qualitative “flow” data (i.e. relationship chart) – Quantitative data (i.e. from-to chart, flow-between) – Both Classificationof algorithms – Based on objectivefunction • Distancebased • Adjacencybased – Format of layoutrepresentation • Discreterepresentation • Continuousrepresentation – Primaryfunction • Improvement • Construction Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  5. MeasuringFlow Quantitative Appropriate when large volumes of material/people move between departments From-tochart Flow-betweenchart Qualitative How important is adjacency to two departments? Often applied to the layout of office environments Activity relationshipdiagram(orchart) Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  6. Qualitative a. From-to- chart b. Flowbetweenchart If total flow is neededanddirection is not important. Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  7. Quantitaive

  8. Classification of Algorithms-LayoutRepresentation Format – Discrete • The area of each department is rounded off to the nearest integer number of grids. • A smaller grid size yields a finer resolution and gives more flexibility in departmentshapes, but • Results in a larger number of grids which complicates computations. Why? – Continuous • Does not use a grid • More flexible but more difficult to use • Usually limited to rectangular building and departments Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  9. Classification of Algorithms Construction-based – Develop ‘from scratch' and progressively build layout Construction algorithm Improvementalgorithm ALDEP CORELAP PLANET (Graph-basedmethods) CRAFT MCCRAFT MULTIPLE (Two-pairmethods) BLOCPLAN LOGIC MixInteger Programming Improvement- based – Start with an initial layout and try to improve it throughincrementalchanges Construction-based – Develop ‘from scratch' andprogressively build layout Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  10. ComputerizedLayoutAlgorithms Automated Layout Design Program (ALDEP) ALDEP is a construction type algorithm. This algorithm uses basic data on facilities and builds a design by successively placing the department in the layout. Computerized Relationship Layout Planning (CORELAP) This algorithm is based on Muthers’s procedure given in systematic layout planning. This computer algorithm was developed by R.C. Lee. Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  11. ComputerizedLayoutAlgorithms Computerized Relative Allocation of Facilities technique (CRAFT) A number of computerized layout programs have been developed since the 1970s to help devise good process layouts. Of these, the most widely applied is the Computerized Relative Allocation of Facilities Technique (CRAFT). • The main objective of the CRAFT is finding the optimal layout by interchanging the department pair wise accordingly total transportation cost is minimized. Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  12. Generating Layout Alternatives(Procedures) Procedures Construction procedures “Greenfield” layout, the layout of a new facility Improvement procedures Changes/ improvements to existing facilities Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  13. Computer-Aided Layout (cont.) Adistance-based objective functioncan be expressed as: An adjacency based objectivefunctioncan be expressed as: Usefrom-tochart as input data Userelationshipchart as input data Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  14. CRAFT-(ComputerizedRelativeAllocation of FacilitiesTechnique) • First computer-aided layout algorithm (1963) • The input data is represented in the form of aFrom-To chart, or qualitative data. • The main objective behind CRAFT is to minimize total transportationcost: • Improvement-typelayoutalgorithm Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  15. Distance • DistanceCalculations • Rectilinear distance from centroid to centroid • Euclidean distance from centroid to centroid Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  16. Centroids Rectilinear distance from A to B: D (AB) = 1.5 + 1 = 2.5 Rectilinear distance from B to C: D (BC) = (5-1.5) + (1+1.5) = 3.5 + 2.5 = 6 DistanceCalculations Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  17. Stepsin CRAFT 1. Start with an initial layout with all departments made up of individual square grids (Note: each grid represents the same amount of space) Calculate centroid of each department and rectilineardistance between pairs of departments centroids (stored in adistancematrix). • Departments i and j exchange • New centroid i = centroid j • New centroid j = centroid i • Only consider exchanging adjacent departments 2. Find the cost of the initial layout by multiplying the – From-To (flow) chart, – unitcostmatrix, and – From-To (distance) matrix Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  18. Steps in CRAFT 3. Improve the layout by performing all-possible two or threewayexchanges – At each iteration, CRAFT selects the interchange that results in themaximum reduction in transportation costs – These interchanges are continued until no further reduction is possible (If the estimated cost of the best exchange in (2) is higher than the best cost found so far, stop Else, go to step1) Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  19. CRAFT Properties • CRAFT only exchanges departments that are – Adjacent (share at least one common edge) – Haveequalareas • The actual size of cost reduction can beoverestimated or underestimated • Adjacency is a necessary but not sufficient criteria forswappingdepartments • Quality of final solution depends on the initial layout • Final solution may be locally optimal, not globally optimal Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  20. CRAFT Properties • Department representation • Discrete grids • No shape restrictions • Objective • Distance based Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  21. In-class Exercises Exchange departments 2 and 4 in the layout shown below. All departments are fixed except 2 & 4. If the flow from A to B is 4, A to C is 3, and B to C is 9, and all move costs are 1, what is the layout cost? Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  22. Weakness of CRAFT • It is not always possible to exchange two unequal size, adjacent departments without splitting the larger one. (adjacentandequalareas) • Centroid • Initialsolution_based • Discrete • Rectangularshape Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  23. Example Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  24. Example A - Rowmaterialstore B - Fabricinspectiondepartment C - Cuttingdepartment D -Sawingdepartment E - Finishingdepartment F - Washingdivision G - Ironingdivision H - Packagingdivision I - Finishgoodstore Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  25. Costmatrix • STEP 1 INPUTS • Initiallayout • Costmatrix (cij ) • Flowmatrix • Area of eachdepartment Transportation cost is among departments is Zero. So we got cost matrix based on that assumption Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  26. Example To compute the flow matrix we use no of movement between the departments Numbers of movements between the departments are given bellow. Flowmatrix Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  27. Example STEP 1Compute the centroids of the department in present layout • Calculationof centroids • A 26.59 54.77 • B 17.5 40 • C 10 17.5 • D 45.68 19.54 • E 60 50 • F 77.5 52.5 • G 77.5 40 • H 77.5 17.5 • I 92.5 30 Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  28. Example • STEP 1PREPARATION OF DISTANCE MATRIX • Initialsolution • Distancematrix Distancematrix Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  29. Example STEP 2CALCULATE THE PRESENT LAYOUT COST Initial cost matrix : Initial cost 119.3 + 108.64 +38.18 +68.68+ 181.36 +23.86 + 150 +377.2 + 537.36 +80 + 50 +180+110 = 2024.58 Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  30. Example STEP 3FIND THE POSIBLE INTERCHANGES A – B Commonboarder A – C Not possible A –D Commonboarder A – E Commonboarder A – F Not possible A – G Not possible A – H Not possible A – I Not possible B – C Commonboarder B – D Commonboarder B – E Not possible B – F Not possible B – G Not possible B – H Not possible B – I Not possible C – D Commonboarder C – E Not possible C – F Not possible C – G Not possible C – H Not possible C – I Not possible D – E Commonboarder D – F Not possible D – G Commonboarder D – H Commonboarder D – I Not possible E – F Commonboarder E – G Commonboarder E – H Not possible E – I Not possible F – G Commonboarder F – H Not possible F – I Commonboarder G –H Commonboarder G – I Commonboarder H – I Common board Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  31. Example STEP 3FIND THE COST OF INTERCHAGING DEPARTMENT Interchange A & B Distancematrix Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  32. Example Costmatrix Total cost = 119.3 + 97.28 + 52.5 + 60 + 170 +23.86 + 269.3 + 377.2 + 537.36 + 44.78 + 20 + 80+ 50 + 180 + 110 = 2191.50 Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  33. Example Interchange A & D Distancematrix Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  34. Example Costmatrix Total cost 243.2 + 108.64 + 44.68 + 52.28 + 67.72 +48.64+ 150 + 538.6 + 458.16 + 80 + 20 + 50 + 180 +110 Total costis 2151.92 Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  35. Example Interchange A & E Distancematrix Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  36. Example Costmatrix Total cost 262.5 + 89.48 + 38.18 + 27.5 + 100 +52.5 +150 +377.5 +430 +54.32 +212 +20 +50 + 180 +110 Total costis 2153.98 Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  37. Example Interchange B & C Distancematrix Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  38. Example Costmatrix Total cost 219.3 + 108.64 + 38.18 + 68.67 + 180.36 + 43.86 + 150 + 486.4 + 537.36 + 44.78 +20 + 80 +50 +180 + 110 Total cost2317.55 Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  39. Example Interchange B & D Distancematrix Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  40. Example Costmatrix Total cost 119.3 + 53.44 + 38.18 + 68.67 + 181.36 + 54.12 + 188.5 + 525 + 618 + 52.5 +80 +20 +50 + 180 + 110 Total cost2339.07 Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  41. Example Interchange C & D Distancematrix Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  42. Example Costmatrix Total cost 119.3 + 107.72 + 38.18 + 68.67 + 181.36 + 23.86 + 243.2 + 377.2 + 990 + 82.5 + 80 + 180 + 110 + 50 Total cost2651.99 Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  43. Example Interchange D & E Distancematrix Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  44. Example Costmatrix Total cost 119.3 + 108.6 + 38.18 + 68.67 +181.36 + 23.86 +150 +725 +537 + 44.75 + 240.88 + 50 + 180 +110 Total cost is 2577.6 Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  45. Example Interchange D & G Distancematrix Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  46. Example Costmatrix Total cost 119.3 + 108.6 + 38.18 + 54.32 + 181.36 + 23.8 + 150 + 900 + 330 + 27.5 + 80 +20 + 259.12 + 270.88 + 110 Total costis 2673 Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  47. Example Interchange D & H Distancematrix Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  48. Example Costmatrix Total cost 119.3 + 176.4 + 38.18 + 68.67 + 108.64 + 23.86 + 150 + 675 + 600 + 52.5 + 80 +20 + 50 + 418.24 + 229.12 Total cost is 2809.91 Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  49. Example Summary of approximate total cast due to pair wise interchanges Minimum value Prepared by: Asst.Prof.Dr. Nevra AKBILEK

  50. Example STEP 3COMPAIRING INITIAL COST AND INTERCHANGES Cost of the initial layout is 2024.58when comparing it with cost of interchanging departments, it is less than every interchanging cost. In the other words all interchanging costs are higher than the initial cost. Therefore, present layout can be considered as the optimal layout. Prepared by: Asst.Prof.Dr. Nevra AKBILEK

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