MODELING AND ANALYSIS OFMANUFACTURING SYSTEMS

Session 14

WAREHOUSING E. Gutierrez-Miravete

Spring 2001

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

WAREHOUSING SYSTEMS

FACILITIES• STORAGE RACKS• QUALITY CONTROL• RECEIVING DOCK• STORE/RETRIEVE• MANUFACTURING• SHIPPING DOCK

ACTIVITIES• STORAGE• INSPECTION• UNLOADING +• TRANSPORT +• PARTS PREP.• PACKING +

WAREHOUSE TYPES

• FULLY AUTOMATED

• MANUALLY CONTROLLED

• IN BETWEEN

WAREHOUSE COMPONENTS

• BUILDING SHELL

• STORAGE MEDIUM– PALLET RACKS

• TRANSPORT MECHANISMS– S/R MACHINES

• CONTROLS– DEDICATED STORAGE– OPEN STORAGE

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

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

WAREHOUSE DESIGN

• GOAL

MINIMIZE a/2 + b/4

• SUBJECT TO

n a b > K

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

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

QUESTIONS

• HOW TO DETERMINE THE HEIGHT OF THE OPTIMAL WAREHOUSE?

• WHAT IS THE CHEBYSHEV MEASURE TRAVEL TIME?

MAX ( z/vz, x/vx )

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)

STACKING PATTERNS

• RACK STACKING

• BLOCK STACKING (Fig. 10.6)

• HONEYCOMB LOSS

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?

DEDICATED STORAGE

• SIMPLIFIED CONTROL

• SIMPLIFIED STATUS CHECKING

• PRODUCT ORDERS FROM VISUAL INSPECTION

• LOW OCCUPATION LEVELS

• Ex. 10.2, p. 337

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

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

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

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?

DEDICATED STORAGE

• WHAT IS THE FACTORING ASSUMPTION?

wip = ci*wp

– pp 340-341

• Ex. 10.4, p. 341– Table 10.6; Fig. 10.8

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

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

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

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

ORDER PICKING

• PICKING SMALL ITEMS FROM A WAREHOUSE TO FILL ORDERS

• DESIGN PROBLEM– SHOULD PARTS COME TO PICKERS?– SHOULD PICKERS GO TO PART

RACKS?

ORDER PICKING SYSTEM CONSIDERATIONS

• STORAGE HEIGHT

• THROUGHPUT VOLUME

• LEVEL OF COMPUTERIZATION

• PRODUCT WEIGHT

• DEGREE OF PRODUCT PROTECTION REQUIRED

ORDER-PICKING PROBLEM

COMBINE CUSTOMER ORDERS INTO PICK LISTS THEN PLAN THE SEQUENCING OF VISITS TO STORAGE LOCATIONS IN

EACH LIST

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

PICK LISTS

• QUESTION: HOW TO DETERMINE SIMILARITY BETWEEN ORDERS?

• S/R MACHINE PERFORMS CHEBYSHEV TRAVEL (Fig. 10.10)

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)

PICK SEQUENCING

• LIKE TRAVELING SALESMAN PROBLEM

• SOLUTION TECHNIQUES– OPTIMIZATION– HEURISTICS (CLOSEST INSERTION

PROCEDURE)

PICK LISTS

• Ex. 10.8, Table 10.8

• Ex. 10.9, Tables 10.9, 10.10