Facility Layout 4 Computerized Block Layout Algorithms ALDEP

Facility Layout 4 Computerized Block Layout Algorithms: ALDEP, CRAFT, MCRAFT

Tarea: • Para la próxima clase, por favor resuelvan en parejas los siguientes problemas: – 6. 13 – 6. 18 – 6. 28 • Para entregar.

Computer-Aided Layout Methods Disadvantages: Advantages: • Lack human judgment • Rapid What-if Analysis • Lack qualitative aspects of Layout • Evaluate large number of alternatives

Automated Layout Design Program (ALDEP) Purpose: Generate many layouts Derived from CORELAP Dummy departments Separate Multiple Floor Capability

ALDEP data requirements Area of Departments REL Chart with A, E, I, O, U, X rankings Sweep width Minimum Closeness Rating (MCR) Ranking values: A = 64 O=1 E = 16 U= 0 I=4 X = -1024

ALDEP Facility Representation Discrete Representation Sweep Method

ALDEP Facility Representation Dept. size = 8 squares Facility width = 6 squares Sweep width = 1 square Dept. size = 14 squares Facility width = 6 squares Sweep width = 2 squares

ALDEP Facility Representation Dept. size = 8 squares Facility width = 6 squares Sweep width = 3 squares

ALDEP Procedure 1. 2. 3. Set MCR and sweep width. Choose first department randomly, add it to the first position of the Department Entry Order (DEO). Choose next department: a) b) c) d) 4. 5. 6. Choose department that has A REL with the last department in DEO. If none, choose department that has E REL with last department in DEO. Continue until MCR REL. If none, choose department randomly Repeat Step 3 until all depts. are in the DEO. Place departments in layout with DEO and sweep method, do not split if possible. Score layout with A-based objective.

ALDEP Example Step 1: • MCR = ‘E’ • Sweep Width = 2 Step 2: Select first department • Randomly choose 5 Step 3: Select 2 nd Department • No A’s with 5 • 1, 3, and 6 have E with 5: randomly choose 1 DEO: 5, 1

ALDEP Example Step 3 b: Select 3 rd dept. • 2 has A with 1, select 2 Step 3 c: Select 4 th dept • No A’s or E’s with 2 • Randomly choose 3 DEO: 5, 1, 2, 3, 4, 6 Step 3 d: Select 5 th dept • No A’s or E’s with 3 • Randomly choose 4 Step 3 e: Select 6 th dept • Last dept, choose 6

ALDEP Example Dept. DEO: 5, 1, 2, 3, 4, 6 Sweep Width = 2

ALDEP Analysis 2 Random selection does not produce the “best” layouts 1 4 Developed for Layout generation on mainframes and has become the basis for future algorithms. 3 5 6

Computerized Relative Allocation of Facilities Technique (CRAFT) Improvement Algorithm Discrete Representation From-To Matrix Distance-Based Objective Pairwise Exchange

CRAFT Algorithm 1. Determine the department centroids. 2. Calculate the inter department rectilinear distances. 3. Calculate the initial cost of the layout by multiplying the from-to matrix with the cost matrix. 4. CRAFT then considers all the possible two-way or three -way department exchanges and identifies the best “exchange”. 5. Update the layout and calculate the new department centroids. 6. The above procedure is repeated until no further reduction in the cost can be obtained.

CRAFT Example Find Centroids 1 2 4 5 7 8 6 3 Initial Layout Centroid Dept X Y 1 3 3 2 13 2 3 16. 5 8 4 9. 5 7 5 3 7 6 9. 5 11 7 1. 5 10 8 4. 5 10

Cost of the initial Layout dist 1 1 0 2 3 4 6 18. 5 2 8. 5 8 14. 5 0 11 0 14. 5 10 4 4. 5 0 7 0 8. 5 Fx. C 1 1 0 2 8 2 3 4 5 6 20 3 7 1 0 1 2 0 5 Cost = Distance x Reward 20* 18. 5 1* 16. 5 1* 8. 5 1* 4. 5 5* 10 1 0 7 0 2 0 + 2* 8. 5 + + 2* 14. 5 + + 2* 11 + + 10* 14. 5 + + 2* 8 = = 678. 5 2 0 10 8 2 5 8 0 0 4 Find Distances 16. 5 5 6 8 8. 5 0 4 8 7 0 3 6 5 Reward Matrix

Only equal areas or adjacent depts. are feasible exchanges fe as ib le Ex ch a ng e “Exchange 1 -3” Centroid Dept X Y. 1 13 2 2 3 3 3 16. 5 8 4 9. 5 7 5 3 7 6 9. 5 11 7 1. 5 10 8 4. 5 10 In “Exchange 1 -2” Centroid Dept X Y. 1 13 2 2 3 3 3 16. 5 8 4 9. 5 7 5 3 7 6 9. 5 11 7 1. 5 10 8 4. 5 10 … and so on… “Exchange 1 -4” Centroid Dept X Y. 1 9. 5 7 2 13 2 3 16. 5 8 4 3 3 5 3 7 6 9. 5 11 7 1. 5 10 8 4. 5 10

CRAFT exchanges centroids first Then calculates a new table of distances And then new layout costs All possible exchanges are evaluated The one with the most savings is selected And the centroids, distances and actual layout are updated

Exchange depts. 1 and 4 gives the most savings Exchange Centroids Dept X Y 1 9. 5 7 2 13 2 3 16. 5 8 4 3 3 5 3 7 6 9. 5 11 7 1. 5 10 8 4. 5 10 . Updated Centroids Dept X Y. 1 10 7 2 13 2 3 16. 5 8 4 3. 57 5 3 7 6 9. 5 11 7 1. 5 10 8 4. 5 10

Let’s calculate the cost of the layout after exchanging depts. 1 and 4 Cost = Distance x Reward 20* 7. 5 1* 16. 5 1* 11. 07 1* 4. 5 10* 5 + 2* 11. 5 + 2* 14. 5 + 2* 8. 43 + 10* 4 + 2* 7. 43 = + + = 355. 79 678. 5 – 355. 79 Savings = -------- = 47. 56% 678. 5

3 iterations take us to the final layout Exchange 1 and 4 4 2 Exchange 5 and 7 1 Exchange 5 and 8 7 8 5 6 Final cost = 345. 29 3

CRAFT Pros Evaluates MANY exchanges very quickly Initial layout can be captured accurately CRAFT Allows: • Flexible Department Shapes • Dummy depts. • Fixed Departments • Non-rectangular buildings Dummy

CRAFT Cons Results in Odd Department Shapes 4 Limited exchange options Greedy Algorithm => Local Optima CRAFT is path dependent: The starting layout makes a difference

MCRAFT (Micro-CRAFT) – PC Implementation • Similar to CRAFT, except it can exchange two non-adjacent departments • Layout formation technique that allows easy shifting of departments • Facility divided into bands • Layout formed by starting at the upper-lefthand corner of the building and sweeping the bands in serpentine fashion • Two way exchanges formed until no further improvement is achieved.

MCRAFT Limitations 1 • May be hard to fit the existing factory layout into bands • Band width assumed to be same for all bands • A fixed department may “float” when certain nonequal area departments are exchanged. 7 3 2 4 8 5 6