1. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 1 IE 368: FACILITY DESIGN AND OPERATIONS MANAGEMENT Lecture Notes #6 Computerized Methodologies for Facilities Layout

2. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 2 Computerized Layout Algorithms Objective  Understand how different quantitative concepts can be applied to generate layout alternatives Discrete and continuous departments Different algorithms

3. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 3 Computerized Layout Algorithms (cont.) CRAFT – Computerized Relative Allocation of Facilities Technique  Inputs From-To chart Cost matrix Initial layout  Objective Distance based  Department representation Discrete grids No shape restrictions

4. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 4 Computerized Layout Algorithms (cont.) CRAFT automatically implements a modified pairwise interchange method  Many details must be addressed CRAFT Algorithm 1.Start with an initial layout with all departments made up of individual square grids (Note: each grid represents the same amount of space) 2.Estimate the best two-way department exchange assuming department centroids exchange exactly  Departments i and j exchange  New centroid i = centroid j  New centroid j = centroid i  Only consider exchanging adjacent departments

5. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 5 Computerized Layout Algorithms (cont.) CRAFT Algorithm (cont’d) 3.Execute the exchange if the estimated cost of the best exchange in (2) is lower than the best cost found so far  The actual result of the exchange is problem-dependent 4.If the estimated cost of the best exchange in (2) is higher than the best cost found so far, stop  Else, go to 1

6. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 6 Example

7. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 7 Example (cont.)

8. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 8 Example (cont.)

9. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 9 Example (cont.)

10. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 10 Example (cont.)

11. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 11 Example (cont.)

12. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 12 Computerized Layout Algorithms (cont.) CRAFT – Additional notes  Dummy departments Can be fixed in location Can model irregular shapes, obstacles, extra space, aisles,…  CRAFT usually will not (for large layouts) find the global optimal solution Therefore, run CRAFT with different initial layouts  Today it is not necessary to approximate centroids due to availability of computing power  Adjacency does not always mean that departments can be exchanged and leave departments intact

13. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 13 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?

14. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 14 In-class Exercises (cont.) ABC A-- B C ABC A B C

15. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 15 In-class Exercise When CRAFT evaluates the exchange of departments, instead of actually exchanging departments, it only exchanges the centroids of departments a.What is the impact of this method if all departments are the same size? b.Given the data below (each square is 1x1), what does the evaluation of the exchange of depts. B and C indicate and what is the actual result?

16. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 16 In-class Exercise (cont.)

17. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 17 In-class Exercise (cont.)

18. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 18 Computerized Layout Algorithms (cont.) BLOCPLAN  Inputs Activity relationship chart From-To chart (if desired) Initial layout  Objective Adjacency based or distance based  Department representation Continuous Restricted to horizontal bands across the facility Maximum number of departments = 18 (in the software)

19. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 19 Computerized Layout Algorithms (cont.) BLOCPLAN automatically implements a pairwise interchange method  Can also accommodate manual exchange BLOCPLAN has a straightforward method of converting an activity relationship chart to a numerical rating  Default scale: A=10, E=5, I=2, O=1, U=0, X=-10  Can modify the scale if desired

20. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 20 Computerized Layout Algorithms (cont.) BLOCPLAN will also convert a from-to chart to an activity relationship chart

21. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 21 Computerized Layout Algorithms (cont.) BLOCPLAN also computes a Rel-Dist value for a layout, which is:  The f ij in the above equation are the relationship values

22. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 22 In-class Exercise 6.32 Suppose the following activity relationship chart and layout are given (each grid is a unit square)  Compute the efficiency rating  Compute the Rel-Dist value  A=10, E=5, I=2, O=1, U=0, X=-10

23. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 23 In-class Exercise (cont.)

24. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 24 Computerized Layout Algorithms (cont.) MULTIPLE – MULTI-floor Plant Layout Evaluation  Inputs From-To chart (if desired) Cost matrix Initial layout Lift data (if using for a multi-floor layout)  Objective Distance based  Department representation Discrete grid

25. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 25 Computerized Layout Algorithms (cont.) MULTIPLE automatically implements a pairwise interchange/exchange method  Can also implement a metaheuristic search procedure called simulated annealing MULTIPLE overcomes inflexibilities existing in other methods presented  CRAFT – Can only exchange adjacent departments  BLOCPLAN – Departments restricted to bands across the facility

26. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 26 Computerized Layout Algorithms (cont.) MULTIPLE also is applicable to multi-floor facility layout It overcomes extensions of other methods to multi-floor layout  CRAFT Department splitting occurs No consideration of lift locations Independent floor layout MULTIPLE allows for more departmental shape flexibility than BLOCPLAN and more department shape control than CRAFT MULTIPLE also can include facility constraints such as walls, fixed department locations, and obstructions in a straightforward manner

27. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 27 Computerized Layout Algorithms (cont.) Fundamental basis for the layouts generated by MULTIPLE  A space filling curve or hand generated conforming curve is used A space filling curve is a mathematical entity with a precise definition  MULTIPLE uses one type of space filling curve called a Hilbert curve Intuitively think of a space filling curve as a path traveled when moving from grid to grid in a layout The path will pass through the center of each grid and can only move to adjacent grids All turns in the path must be right-angle turns Used to reconstruct a new layout when any two departments are exchanged

28. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 28 Computerized Layout Algorithms (cont.) Example of a space filling curve

29. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 29 Computerized Layout Algorithms (cont.) Example of a hand generated conforming curve

30. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 30 Computerized Layout Algorithms (cont.) How does MULTIPLE use these curves to generate layouts?  With a curve established for a facility 1.Define a department layout sequence 2.Place the departments in the facility in department sequence along the curve, grid by grid

31. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 31 Computerized Layout Algorithms (cont.) Example

32. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 32 Computerized Layout Algorithms (cont.) Optimizing  MULTIPLE can implement a pairwise exchange/interchange algorithm All possible exchanges can be examined since the exchanges are exchanges in sequence position Exchanging departments of different sizes and the impact on the rest of the layout is handled by the space filling curve

33. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 33 Figure 6.32 (a) & (b)

34. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 34 In-class Exercise

35. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 35 Controlling Department Shape MULTIPLE incorporates a method to control department shape Let  P i denote the length of the perimeter of department i  A i denote the area of department i Overall principle  For a fixed department area, as the department shape becomes more irregular, its perimeter gets larger

36. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 36 Controlling Department Shape (cont.) Example – MULTIPLE represents departments as grids. is more irregular than P= 20 sides P= 12 sides

37. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 37 Controlling Department Shape (cont.) The minimum perimeter occurs for a department when it is square in shape  Assumes the department is non-circular, and represented as a grid made up of individual square units Let P i * = minimum perimeter occurring when department i is square If a square represents the ideal department shape, a normalized shape measure for a department can be constructed

38. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 38 Controlling Department Shape (cont.) Let Ω i = Normalized shape measure for department i Ω i ≤ 1.50 is recommended for MULTIPLE A separate upper limit for Ω i for each department can be specified  Exchanges resulting in Ω i ≥ upper limit are rejected

39. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 39 In Class Exercise Use layout options 1, 2, and 3 to fill in the information in the table (1) (2)(3)

40. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 40 Multi-Floor Facility Layout More common in older cities and buildings (e.g., Detroit) and in countries where land is very expensive Less flexibility of use of total facility space  A multi-floor building may have enough total space but may not be able to accommodate departments on different levels without splitting

41. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 41 Multi-Floor Facility Layout (cont.) Additional decisions/constraints  The number and location of vertical material handling devices  Restriction of certain departments to specific floors First floor restrictions due to floor loading capacity Ceiling heights Heat/chemical use and/or generation  Departments may have to be kept contiguous

42. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 42 Multi-Floor Facility Layout (cont.) Modified distance-based objective

43. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 43 Multi-Floor Facility Layout (cont.) Example Floor r Floor s Dept. i Dept. j Vertical Travel

44. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 44 Multi-Floor Facility Layout (cont.) Another heuristic approach 1.Assign departments to floors to minimize vertical travel distance. Can also be difficult, but for two or three floor and a small number of departments, this can be completed 2.Treat each floor’s layout as a single floor layout problem

45. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 45 Heuristics in Computer-Aided Layout The mathematical description or formulation of the layout problem is a mathematical specification of the optimization (IE 425) problem that a computer-aided layout algorithm (e.g., CRAFT, BLOCPLAN, MULTIPLE) attempts to solve

46. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 46 Heuristics in Computer-Aided Layout (cont.) Example for a simplified problem called the quadratic assignment problem (QAP)  Deciding what locations to assign to departments (or facilities). All departments can be located at any site

47. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 47 Heuristics in Computer-Aided Layout (cont.) The optimization problems that CRAFT, BLOCPLAN and MULTIPLE attempt to solve are more complicated due to department size considerations These problems share one common feature  They are very difficult to solve (find the best or a best solution with respect to the given objective function) Procedures exist but they can become so computationally expensive that all of the world’s computing power cannot solve them

48. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 48 Heuristics in Computer-Aided Layout (cont.) Example – MULTIPLE  MULTIPLE simplifies the layout problem by restricting layouts to be constructed in sequence on the space filling curve  MULTIPLE searches for the best or optimal sequence  Finding this sequence can also be very difficult as the number of departments increases Example – 25 departments. How many sequences?

49. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 49 Heuristics in Computer-Aided Layout (cont.) Example – MULTIPLE There are a lot of possibilities! 25! = 15,511,210,043,330,985,984,000,000 25! Pennies would cover the whole State of Texas to a height of over 6,000 miles (Hopp & Spearman 1996) There are 25! different schedules The first task has 25 choices, the second has 24 choices….

50. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 50 Heuristics in Computer-Aided Layout (cont.) MULTIPLE uses pairwise exchange as a method to find a good sequence  MULTIPLE also uses a search method called simulated annealing These search methods are called heuristics Heuristics are procedures whose objective is to find an optimal solution, but whose performance cannot be guaranteed CRAFT and BLOCPLAN are also using heuristic search procedures

51. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 51 Example Traveling salesman problem 1 2 5 N 7 3 4 6 … Distances from city i to city j are known. Find a minimum distance tour. A tour starts and ends at the same city and visits no city more than once.

52. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 52 Example – Traveling Salesman Problem Heuristic Nearest neighbor heuristic  From the starting city, successively move to the closest city not yet visited  The last link completes the tour

53. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 53 Starting in City 3, apply the nearest neighbor heuristic. Move to the closest city not yet visited Example – Traveling Salesman Problem Heuristic In-Class Exercise

54. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 54 For each city, apply the nearest neighbor heuristic. Select the best tour. Example – Traveling Salesman Problem Heuristic Improvement

55. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 55 Traveling Salesman Problem Heuristic

56. WINTER 2012IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT 56 Personnel Requirements General information on:  Parking  Restrooms  Your reading in Chapter 4 Food service Health service