Layout and Design

1. Layout and Design Introduction Fixed-position layout Job shop production I

2. Introduction Strategic decisions (location problems) Concretion and realization on tacticallevel (Layout and design, configuration) Operational decisions (operational planning) Layout and Design

3. Introduction • An efficient layout facilitates and reduces costs of material flow, people, and information between areas. • 4 concepts will be introduced here: • Fixed-position layout • Large, bulky workpieces (ships,…) • Job shop production (Process/Function-oriented production) • High variety, low volume • Cellular manufacturing systems • Individual products • Flow shop production(Object-oriented production) • Low variety, high volume cf. Heizer, J., Render, B., Operations Management, Prentice Hall, 2006, Chapter 9 cf. Francis, R., McGinnis, L., White, J., Facility Layout and Location: An Analytical Approach, Prentice Hall, 1992 Layout and Design

4. Introduction • 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 • Minimum equipment: • 1 weld • 1 grind • 1 saw • 1 turn • 2 mills • 2 drills • 1 paint cf. Heizer, J., Render, B., Operations Management, Prentice Hall, 2006, Chapter 9 cf. Francis, R., McGinnis, L., White, J., Facility Layout and Location: An Analytical Approach, Prentice Hall, 1992 Layout and Design

5. Drill Drill Weld Mill Paint Mill Turn Saw Stores Grind Assembly Workpiece Warehouse Introduction • 1. Fixed-postion layout cf. Heizer, J., Render, B., Operations Management, Prentice Hall, 2006, Chapter 9 cf. Francis, R., McGinnis, L., White, J., Facility Layout and Location: An Analytical Approach, Prentice Hall, 1992 Layout and Design

6. Introduction • 2. Job shop layout cf. Heizer, J., Render, B., Operations Management, Prentice Hall, 2006, Chapter 9 cf. Francis, R., McGinnis, L., White, J., Facility Layout and Location: An Analytical Approach, Prentice Hall, 1992 Layout and Design

7. Introduction • 3. Cellular manufacturing system cf. Heizer, J., Render, B., Operations Management, Prentice Hall, 2006, Chapter 9 cf. Francis, R., McGinnis, L., White, J., Facility Layout and Location: An Analytical Approach, Prentice Hall, 1992 Layout and Design

8. Introduction • 4. Flow shop layout cf. Heizer, J., Render, B., Operations Management, Prentice Hall, 2006, Chapter 9 cf. Francis, R., McGinnis, L., White, J., Facility Layout and Location: An Analytical Approach, Prentice Hall, 1992 Layout and Design

9. Introduction • Selection of layout: • Characteristic of workpiece • Variety of production • Volume of production • Combinations: • Components: job shop and/or Celluars sytems; assembly: flow shop system cf. Heizer, J., Render, B., Operations Management, Prentice Hall, 2006, Chapter 9 cf. Francis, R., McGinnis, L., White, J., Facility Layout and Location: An Analytical Approach, Prentice Hall, 1992 Layout and Design

10. Fixed-position layout • Workpiece too large or cumbersome to be moved trough its processing steps -> processes are brought to the product rather than otherwise. • Processes are arranged in the right sequence around the workpiece • Right processes at the workpiece at the right location in the right time cf. Heizer, J., Render, B., Operations Management, Prentice Hall, 2006, Chapter 9 cf. Francis, R., McGinnis, L., White, J., Facility Layout and Location: An Analytical Approach, Prentice Hall, 1992 Layout and Design

11. Fixed-position layout • Advantages: • Material movement is reduced. • Promotes job enlargement by allowing individuals or teams to perform the “whole job”. • Highly flexible; can accommodate changes in product design, product mix, and production volume. • Independence of production centres allows scheduling to achieve minimum total production time. cf. Heizer, J., Render, B., Operations Management, Prentice Hall, 2006, Chapter 9 cf. Francis, R., McGinnis, L., White, J., Facility Layout and Location: An Analytical Approach, Prentice Hall, 1992 Layout and Design

12. Fixed-position layout • Limitations: • Increased movement of personnel and equipment. • Equipment duplication may occur. • Higher skill requirements for personnel. • General supervision required. • Cumbersome and costly positioning of material and machinery. • Low equipment utilization. cf. Heizer, J., Render, B., Operations Management, Prentice Hall, 2006, Chapter 9 cf. Francis, R., McGinnis, L., White, J., Facility Layout and Location: An Analytical Approach, Prentice Hall, 1992 Layout and Design

13. Job shop production • High variety – low volume Rapid changes in mix or volume • „In-between conditions“ • Collection of processing departments or cells • Each containing a collection of machines processing similiar operations • Each product (group) undergoes a different sequence of operations • Different products have different material flows and are moved from one department to another in the appropriate sequence. • High degree of interdepartmental flow cf. Heizer, J., Render, B., Operations Management, Prentice Hall, 2006, Chapter 9 cf. Francis, R., McGinnis, L., White, J., Facility Layout and Location: An Analytical Approach, Prentice Hall, 1992 Layout and Design

14. Job shop production • Advantages: • Better utilization of machines can result -> fewer machines are required. • A high degree of flexibility exists relative to equipment or manpower allocation for specific tasks (break down,…) • Comparatively low investment in machines • The diversity of tasks offers a more interesting and satisfying occupation for the operator. • Specialized supervision is possible. cf. Heizer, J., Render, B., Operations Management, Prentice Hall, 2006, Chapter 9 cf. Francis, R., McGinnis, L., White, J., Facility Layout and Location: An Analytical Approach, Prentice Hall, 1992 Layout and Design

15. Job shop production • Limitations: • Longer flow lines are needed -> material handling is more expensive. • Production planning and control systems are more involved than for other layouts. • Usually, total production time is longer than for other layouts. • Due to the fact that jobs have to queue before being processed in a machine job comparatively large amounts of in-process inventory occur. • Comparatively high degree of (machine) idle time because machines have to wait until the subsequent job is finished with its foregoing process. • Space and capital are tied up by work in process. • Because of the diversity of the jobs in specialized departments, higher grades of skill are required. cf. Heizer, J., Render, B., Operations Management, Prentice Hall, 2006, Chapter 9 cf. Francis, R., McGinnis, L., White, J., Facility Layout and Location: An Analytical Approach, Prentice Hall, 1992 Layout and Design

16. Job shop production • Eliminiation of negative effects • Production planning (operational level) • Optimized machine allocation (tactical level) -> Assignment problems: • LAP (linear assignment problem) • QAP (quadratic assignment problem) Layout and Design

17. Linear Assignment Problem • Simplest optimization problem in intra-company location planning • Gegeben: nmachines (activities, workers) n potential locations (periods, projects) cij... cost of running maschine i on location j • Any machine can be assigned to any location • It is required to use all locations by assigning exactly one machine to each location • total cost of the assignments are to be minimized. Layout and Design

18. Linear Assignment Problem 3 machines, 4 locations and the following costs cij Machine 2 cannot be assigned to location 2 -> cost  Layout and Design

19. Linear Assignment Problem • If number of locations≠ number of machines: • Add dummymachines (-rows) or dummylocations (-columns) with costs 0 (this is always possible) Location with dummy machine -> location stays empty Layout and Design

20. Linear Assignment Problem • Formulation as TP: • Each LAP can be interpreted as special case of a TP with each supplier (=machine) having a capacity of 1 and each customer (= location) having a demand of 1. • Since, for the TP it is guaranteed (due to the special problem structure) that all decision variables are integer, we end up with a feasible solution for the LAP (n variables with value 1 and all others 0 (LAP: m=n basis variables; TP: m+n-1 basis variables) • TP: Layout and Design

21. Linear Assignment Problem 1 if maschine i is assigned to location j 0 otherwise xij= Cost: Constraints: = 1 für i = 1,...,n ... each machine is assigned exactly once = 1 für j = 1,...,n ... each location is allocated with 1 machine = 0 oder 1 für i = 1,...,nund j = 1,...,n Layout and Design

22. Linear Assignment Problem • In order to solve LAPs exactly we are going to make use of the following important problem characteristic: • it is always possible to reduce (or increase) all entries of any column or row by a certain value without changing the optimal solution (only the absolute costs change, the relation stays the same). We use this characteristic to generate the maximum number of 0 entries. • Example: • Optimal solution (column minimum method): A-I B-II C-III • Cost: 1+2+3=6 Layout and Design

23. Linear Assignment Problem • Cost reduction (Columns -> Rows): • The relation of assignment costs for each machine/locations does not change. • Optimal solution (column minimum method): A-I B-II C-III • (Reduced) cost: 0 • Reduced cost + reduction values: 0 + 6 = 6 (= Total assignment cost without cost reduction) -3 -2 -1 Layout and Design

24. Kuhn´s Algorithm • Kuhn´s algorithm • finds the exact solution • is based on adding/subtracting values to/from given cost factors in order to find the lowest opportunity cost (i.e. not-obtained profits) • 3 steps to be followed: • Cost reduction -> Generation of 0 elements • Try to determine the optimal assignment. If this is not possible draw the minimum number of lines necessary to cover all zeros in the matrix. • Adapt the cost factors in the matrix and return to step 2. cf. Heizer, J., Render, B., Operations Management, Prentice Hall, 2006, Chapter 15 Layout and Design

25. Kuhn´s Algorithm Step 1: Cost reduction • Subtract the smallest number in each column from every number in that column • Subtract the smallest number in each row from every number in that row. • We obtain a matrix with a series of zeros, meaning zero opportunity costs (at least one zero in each column and each row) • No cost reduction in columns already including zero elements Layout and Design

26. Kuhn´s Algorithm Step 2: Optimal solution? • Start with a column or row having as few as possible 0 entries • Frame one the 0 in this column/row and cross all other 0 in the corresponding column and row • Go on with the next column or row having as few as possible not-framed and not-crossed zeros. • And so on until all zeros are either framed or crossed. • If we are able to make a zero (reduced) cost assignment for all machines we found the optimal solution! • Otherwise we have to find the minimum arrangement of lines covering all zeros in the matrix. Layout and Design

27. Kuhn´s Algorithm • Example: • Step 1: Layout and Design

28. Kuhn´s Algorithm • Step 2: Optimal solution! Layout and Design

29. Kuhn´s Algorithm Step 2: If not draw the minimum number of lines covering all zero elements • Mark (for example „X“) all rows with no framed 0 • Mark all columns having at least 1 crossed 0 in a marked row • Mark all rows having a framed 0 in a marked column • Repeat until there is no column or row left to be marked • Mark each non-marked row and each marked column (shaded) with a continuous line. • -> this is the minimum arrangement of lines needed to cover all 0. If the number of lines is equal to the number of rows/columns, an optimal assignment is already possible. Layout and Design

30. Kuhn´s Algorithm Step 3: Adapt the cost factors • The smallest not-covered element is the new reduction value (a). • Subtract a from all not-covered elements in the matrix. • Add a to all elements covered by two lines. • Elements covered by 1 line remain unchanged. • Go on with step 2. Layout and Design

31. Kuhn´s Algorithm 13 7 0,5 0,5 6,5 -0,5 11,5 8,5 2 0 5  7,5 7,5 6 6 0 0 0 5,5 12,5 7,5 8,5 1,5 0 7 12 -4,5 -8 -8,5 -5 -5,5 12,5 6,5 0 0 6 11,5 8,5 2 0 5  7,5 7,5 6 6 0 4,5 + 8 + 8,5 + 5 + 5,5 + 0,5 K = 0 0 5,5 12,5 7,5 = 32 8,5 1,5 0 7 12 Layout and Design

32. Kuhn´s Algorithm No zero cost assignment! -> Find the minimum arrangement of lines covering all zeros. Layout and Design

33. Kuhn´s Algorithm -> Adapt the cost elements by adding/subtracting element a (minimum value of all not-covered elements) Layout and Design

34. Kuhn´s Algorithm 11 5 4,5 3,5 10 7  7,5 7,5 7 14 7 0 10,5 1 additional zero (assignment 5  2) increases the chance the find an assignment with total (reduced) costs of 0. a = 1,5 Layout and Design

35. Kuhn´s Algorithm Start again with step 2 until a zero cost assignment is possible! Optimal assignment! Total cost: sum of all reduction values (step 1 and 3): C= (4,5 + 8 + 8,5 + 5 + 5,5 + 0,5) + (1,5) = 33,5 Layout and Design

36. Kuhn´s Algorithm Some assignment problems entail, e.g., maximizing profit instead of minimizing cost. To convert a maximization problem to an equivalent minimization problem, we subtract every number in the original matrix from the largest single number in that matrix. Maximize the total profit! [„Cost“ = 20 - Profit] Layout and Design