1. MODELING AND ANALYSIS OF MANUFACTURING SYSTEMS Session 14 WAREHOUSING E. Gutierrez-Miravete Spring 2001

2. WHY WAREHOUSING? FOR PARTS DISTRIBUTION FOR SPARE PARTS PROVISIONING TO ASSEMBLE PRODUCT BATCHES PRIOR TO DELIVERY CRITICAL PART STOCKPILING FOR REGIONAL DISTRIBUTION FOR QUICK DELIVERY

3. WAREHOUSING SYSTEMS FACILITIES STORAGE RACKS QUALITY CONTROL RECEIVING DOCK STORE/RETRIEVE MANUFACTURING SHIPPING DOCK ACTIVITIES STORAGE INSPECTION UNLOADING + TRANSPORT + PARTS PREP. PACKING +

4. WAREHOUSE TYPES FULLY AUTOMATED MANUALLY CONTROLLED IN BETWEEN

5. WAREHOUSE COMPONENTS BUILDING SHELL STORAGE MEDIUM –PALLET RACKS TRANSPORT MECHANISMS –S/R MACHINES CONTROLS –DEDICATED STORAGE –OPEN STORAGE

6. WAREHOUSE DESIGN THE 85 PERCENT RULE STANDARD WAREHOUSE (F10.3) –RECTANGULAR BUILDING –I/O AT ONE END –TRAVEL ALONG AISLES DESIGN GOAL: TO MINIMIZE AVERAGE STORAGE/RETRIEVAL TIMES

7. WAREHOUSE DESIGN NUMBER OF STORAGE ROWS a NUMBER OF BAYS IN A ROW b WAREHOUSE LENGTH  a WAREHOUSE WIDTH  b NUMBER OF LEVELS n TOTAL NUMBER OF NEEDED STORAGE LOCATIONS K

8. WAREHOUSE DESIGN GOAL MINIMIZE  a/2 +  b/4 SUBJECT TO n a b > K

9. WAREHOUSE DESIGN SOLVE FOR a FROM THE CONSTRAINT, SUBSTITUTE IN THE GOAL FUNCTION THEN MINIMIZE WITH RESPECT TO b TO OBTAIN b* = (2  K/  n) 1/2 a* = (  K/2  n) 1/2

10. QUESTIONS WHAT IS THE LENGTH/WIDTH RATIO OF THE OPTIMAL WAREHOUSE? WHAT IS THE RATIO OF THE NUMBER OF STORAGE LOCATIONS ALONG THE WIDTH TO THAT ALONG THE LENGTH? Ex. 10.1, p. 333

11. QUESTIONS HOW TO DETERMINE THE HEIGHT OF THE OPTIMAL WAREHOUSE? WHAT IS THE CHEBYSHEV MEASURE TRAVEL TIME? MAX ( z/v z, x/v x )

12. QUESTIONS WHAT DETERMINES THE OPTIMAL WAREHOUSE SHAPE? CONSTANT TRAVEL TIME CONTOURS Figs. 10.4a, 10.4b, 10.4c WHAT IS THE APPROPRIATE RACK ORIENTATION? TRANSVERSE (Fig.10.3) VS LONGITUDINAL (Fig.10.5)

13. STACKING PATTERNS RACK STACKING BLOCK STACKING (Fig. 10.6) HONEYCOMB LOSS

14. LOCATION IN WAREHOUSES HOW TO ASSIGN INCOMING LOADS TO STORAGE LOCATIONS? WHAT IS THE EFFECT OF EXPECTED TURNAROUND OF THE LOAD? WHAT IS THE EFFECT OF DEDICATED VS OPEN STORAGE ON THE LOCATION DECISION?

15. DEDICATED STORAGE SIMPLIFIED CONTROL SIMPLIFIED STATUS CHECKING PRODUCT ORDERS FROM VISUAL INSPECTION LOW OCCUPATION LEVELS Ex. 10.2, p. 337

16. DEDICATED STORAGE PRODUCTS TO BE ALLOCATED TO STORAGE LOCATIONS N DIVIDE WAREHOUSE SPACE INTO M SQUARE ISOCAPACITY GRIDS EACH PRODUCT REQUIRES SOME GRIDS FOR ITS STORAGE NUMBER OF SHIPPING/RECEIVING PORTS P

17. DEDICATED STORAGE NUMBER OF TRIPS OF PRODUCT i THROUGH PORT p w ip DISTANCE FROM CENTER OF GRID j TO PORT p d pj TRAVEL COST PER PERIOD DUE TO STORAGE OF i IN j c ij GOAL: FIND THE SET OF GRIDS A i TO ASSIGN TO EACH PRODUCT i

18. DEDICATED STORAGE DECISION VARIABLE x ij GOAL MINIMIZE  i  j c ij x ij SUBJECT TO  j x ij = A i FOR ALL i  i x ij = 1 FOR ALL j

19. DEDICATED STORAGE PROGRAMMING PROBLEM IS ANALOGOUS TO TRANSPORTATION PROBLEM Ex. 10.3; Tables 10.4a, 10.4b, 10.5 WHAT HAPPENS IF ALL PRODUCTS USE ALL PORTS IN THE SAME PROPORTION?

20. DEDICATED STORAGE WHAT IS THE FACTORING ASSUMPTION? w ip = c i *w p –pp 340-341 Ex. 10.4, p. 341 –Table 10.6; Fig. 10.8

21. OPEN STORAGE COMPUTER CONTROLLED WAREHOUSES Ex. 10.5, p. 343 THROUGHPUT: THE NUMBER OF STORAGE AND RETRIEVAL REQUESTS THAT CAN BE HANDLED BY THE S/R MACHINE PER UNIT TIME

22. OPEN STORAGE RACK STRUCTURE FOR TRAVEL TIME CALCULATION (Fig. 10.9) X, Z HORIZONTAL AND VERTICAL LENGTHS OF STORAGE RACKS vx, vz HORIZONTAL AND VERTICAL SPEEDS OF S/R VEHICLE tpd FIXED TIME FOR PICKUP/DEPOSIT

23. OPEN STORAGE TOTAL SINGLE COMMAND TRIP TIME (Eqn. 10.8-10.10) T = v x Z 2 /(3 v z 2 X) + X/v x + 2 t pd Ex. 10.6, p. 344 DUAL COMMAND TRIP TIME (Eqn. 10.11) Ex. 10.7, p. 345

24. OPEN STORAGE CLASS-BASED STORAGE (OP) –EXPECTED LENGTH OF STAY IN STORAGE STORING COMPLEMENTARY ITEMS (OP) –LOCATING ITEMS WHICH ARE ORDERED TOGETHER NEAR TO EACH OTHER

25. ORDER PICKING PICKING SMALL ITEMS FROM A WAREHOUSE TO FILL ORDERS DESIGN PROBLEM –SHOULD PARTS COME TO PICKERS? –SHOULD PICKERS GO TO PART RACKS?

26. ORDER PICKING SYSTEM CONSIDERATIONS STORAGE HEIGHT THROUGHPUT VOLUME LEVEL OF COMPUTERIZATION PRODUCT WEIGHT DEGREE OF PRODUCT PROTECTION REQUIRED

27. ORDER-PICKING PROBLEM COMBINE CUSTOMER ORDERS INTO PICK LISTS THEN PLAN THE SEQUENCING OF VISITS TO STORAGE LOCATIONS IN EACH LIST

28. FORMING PICK LISTS KEY: BATCHING ORDERS INTO PICK LISTS C CARRYING CAPACITY OF S/R MACHINE K TOTAL NUMBER OF ORDERS Qk SIZE OF k-th ORDER CLUSTERING ALGORITHM

29. PICK LISTS QUESTION: HOW TO DETERMINE SIMILARITY BETWEEN ORDERS? S/R MACHINE PERFORMS CHEBYSHEV TRAVEL (Fig. 10.10)

30. PICK LIST CREATION FIND THE AREA OF TRAVEL REGIONS FOR ORDERS (Ex. 10.8) FIND INTERSECTIONS OF TRAVEL REGIONS (Ex. 10.9) FIND SIMILARITY COEFFICIENTS (E10.9) BATCH ORDERS INTO LISTS (Ex. 10.10)

31. PICK SEQUENCING LIKE TRAVELING SALESMAN PROBLEM SOLUTION TECHNIQUES –OPTIMIZATION –HEURISTICS (CLOSEST INSERTION PROCEDURE)

32. PICK LISTS Ex. 10.8, Table 10.8 Ex. 10.9, Tables 10.9, 10.10