WHY WAREHOUSING?

1. MODELING AND ANALYSIS OFMANUFACTURING SYSTEMSSession 14WAREHOUSINGE. Gutierrez-MiraveteSpring 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. FACILITIES STORAGE RACKS QUALITY CONTROL RECEIVING DOCK STORE/RETRIEVE MANUFACTURING SHIPPING DOCK ACTIVITIES STORAGE INSPECTION UNLOADING + TRANSPORT + PARTS PREP. PACKING + WAREHOUSING SYSTEMS

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/vz, x/vx )

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 wip • DISTANCE FROM CENTER OF GRID j TO PORT p dpj • TRAVEL COST PER PERIOD DUE TO STORAGE OF i IN j cij • GOAL: FIND THE SET OF GRIDS Ai TO ASSIGN TO EACH PRODUCT i

18. DEDICATED STORAGE • DECISION VARIABLE xij • GOAL MINIMIZE ij cij xij • SUBJECT TO j xij = Ai FOR ALL i i xij = 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? wip = ci*wp • 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 = vx Z2/(3 vz2 X) + X/vx + 2 tpd • 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