Unit Load Storage Policies

Unit Load Storage Policies Marc Goetschalckx marc.goetschalckx@isye.gatech.edu PASI 2013, Santiago, Chile 1

Instructor Information Born in Belgium Georgia Tech Total research career in logistics, material handling, facilities design, supply chains Material Handling Research Center & CICMHE Supply Chain Engineering (Springer 2011) Educational interactive software (TSP, VRPB, block layout) Soccer, tennis, photography, beer & wine 2

Storage Policies Overview: Introduction Introduction to Storage Policies 5

Warehouse Operations Flow Path Schematic (FFN) Receiving Sharp et al. 1991 Cross Docking Storage Full Pallet Picking Case Picking Item Picking Sortation Packaging Shipping 7-Aug-13

Definitions Storage Policy Set of rules that determine where to store arriving SKUs in a warehousing system Unit Load A collection of materials that can be transported, stored, and controlled (managed) as a single unit Examples Vast majority of discrete goods 7

Block Stacking Operation With Counterbalanced Truck 8

Sainsbury s Grocery Distribution Center 10

Example: Walmart DC Pallet Rack 7-Aug-13

Forward-Reserve: Restocking with Reach Truck Restock: Person remains on floor, forklift & reach truck Forward 7-Aug-13

Forward Reserve: Order Picking on Higher Levels Order Picking: Person in cab travels up, Order picking truck 7-Aug-13

Empty Single-Deep Pallet Rack with Four Levels 15

ASRS Pallet Unit Load High-Rise Storage 16

Volkswagen Automated Finished Goods (Cars) Warehouse 17

Handling Units Example: Collapsible Pallet 18

Wine Barrels in a Rack 19

Container Port Overview (Hamburg Port Altenwerder) 20

Twin Yard Cranes (Hamburg Port Altenwerder Quay) 21

Amazon Forward Reserve Warehouse 7-Aug-13

SKUs (Products) Classification Bulk Storage Liquids, gases, dry bulk Discrete Units Storage Unit Loads Free standing Rack supported Loads of different sizes 25

Warehousing Storage Objectives: Back to Basics Minimize the expected travel time & cost for given input-output operations Minimize MH equipment and personnel Variable (marginal) costs Minimize the required storage space for given stored inventory Minimize capital investment Fixed costs 28

Storage Policies Overview: Unit Load Storage Policies Introduction to Storage Policies Unit Load Storage Policies 29

Unit Load Main Principle to Maximize Storage Capacity Use the Cube by utilizing the height of the warehouse and keeping it filled 33

Unit Load Main Principle to Minimize Travel Time Place unit loads that generate the highest frequency of access in locations with the lowest expected access time 34

Warehousing Storage Objectives Minimize the Expected Travel Time Minimize MH Equipment and Personnel Min f t j j j Minimize the Required Storage Space Minimize Capital Investment Min N 36

Occupancy Gantt Chart: Rack Based Direct Access J 1 I 1 I 9 J 2 I 3 I 7 J 3 I 4 I 8 J 4 I 5 I 2 J 5 I 10 I 6 Time Periods 37

Unit Load Storage Formulation Single command, Direct Access min M i1 j1 c x s. t. x 1 i j1 x N M i1 ij N ij b x i ij ij ij { 0, 1} 1 j 38

Occupancy and Constraint Matrices B A [ ] L NM b i L NM 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 I I I.. I B 0 0.. 0 0 B 0.. 0.......... 0 0 0.. B O QP O QP 39

Vector Assignment Formulation Neither AP nor 3DAP nor BPP Consecutive ones in occupancy matrix B Block diagonal structure of constraint matrix Integrality property not satisfied 41

VAP Conclusions Very large integer optimization problem Very tight LP relaxation Efficient sub problem and problem size indicate decomposition Very small gap for Lagrangean relaxation upper bound Highly primal and dual degenerate Acceptable penalty for primal heuristic 44

Dedicated vs. Shared Storage Policies: Product Dedicated Product Dedicated Storage Policies Static Simple Space inefficient (maximum) Unconstrained replenishment max N q si I N DED p p pt MAX t p p 45

Dedicated vs. Shared Storage Policies: Product Shared Product Shared Storage Policies Dynamic Requires inventory map Simple (COL) or complex (DOS) Space efficient N SHA max t R S T p I pt U V W 46

Unbalanced Warehouse Size for Various Policies 18 16 14 12 10 8 A B C D All Ded Sha 6 4 2 0 1 6 11 16 21 26 31 36 41 46 51 56 47

Storage Policy Size Ratio Storage Policy Size Ratio a N 051., N DED 49

Storage Policy Size Ratio N DED 18, N 16 16 a 0.89 18 SHA 51

Perfectly Balanced Warehouse Size for Various Policies 16 14 12 10 8 A B C D All Ded 6 4 2 0 1 6 11 16 21 26 31 36 41 46 51 56 52

Perfect Balanced Storage Space Ratio for Shared Storage Policies N DED 16, N 10 10 a 0.625 16 SHA 54

Storage Policies Overview: Unit Load Storage Policies Introduction to Storage Policies Unit Load Storage Policies Product Based Storage Policies 56

Unit Load Warehouse 1 2 3 4 5 6 P 2 7 8 9 10 11 12 P 3 13 14 15 16 17 18 19 20 21 22 23 24 P 1 57

Safety Inventory for Product Turnover Based Storage Safety inventory si aded to replenishment order size q to compute locations required Safety and cycle replenishment order size q determined by supply chain factors Fp Fp f p N q si p p p 58

Product Information (Factoring) Product A B C Characteristic Symbol p Storage Requirement q 12 2 10 Pallets Received Monthly Through Door P3 e3 400 60 200 0.500 Pallets Shipped Monthly Through Door P1 e1 300 45 150 0.375 Door P2 e2 100 15 50 0.125 Total 800 120 400 59

Factoring Condition All products have identical probability mass functions for the selection of input/output points (docks) F e p p k pk p p p pk k pk e pk F p 60

Travel Independence If factoring condition is satisfied: expected travel time is independent of the product stored in location g p d j k kj k g 1 = 0.375*80+0.125*60+0.500*25 = 50 g 13 = 0.375*60+0.125*80+0.500*15 = 40 61

Warehouse Factoring Distances 1 50 2 50 P 1 3 50 4 50 5 50 6 57.5 7 42.5 13 40 19 42.5 20 42.5 21 42.5 22 42.5 23 42.5 24 50.0 8 42.5 14 40 9 42.5 15 40 10 42.5 11 42.5 12 50.0 16 40 17 40 18 47.5 P 2 P 3 62

Locations Sorted by Increasing Distance 1 2 3 4 5 6 50 50 50 50 50 57.5 7 8 9 10 11 12 P 2 P 3 42.5 13 42.5 14 42.5 15 42.5 16 42.5 17 50.0 18 40 19 40 20 40 21 40 22 40 23 47.5 24 42.5 42.5 42.5 42.5 42.5 50.0 P 1 63

Three Dedicated Storage Policies Fast and furious Fast movers closest to the door Small is beautiful Small inventory closest to the door But higher turns beats them all Frequency of access ratio of demand rate divided by maximum inventory Fastest turning closest to the door Short stays closest to the door 64

Demand Based Layout Commonly Called Place Fast Movers Closest to the Door Products Ranked by Decreasing Demand or Operations F A = 800, F C = 400, F B = 120 Assigned to Locations by Increasing Expected Travel Time 65

Demand Based Layout P 3 1 50C 2 3 C 50 50C 4 50C 5 50C 6 B 57.5 7 8 9 10 A A C C 11 C 12 B 42.5 42.5 42.5 42.5 42.5 50.0 13 14 15 16 A A A A 17 A 18 C 40 40 40 40 40 47.5 19 A 20 A 21 A 22 A 23 A 24 C 42.5 42.5 42.5 42.5 42.5 50.0 P 2 P 1 66

Total Travel Time for Demand Based Layout Total Travel = Sum of Product Travels T A = 2 800 41.46 = 66,333 T B = 2 120 53.75 = 12,900 T C = 2 400 47.50 = 38,000 T = 66,333+12,900+38,000 = 117,233 %T = 0.8 % over 116,333 67

Inventory Based Layout Commonly Called Place Low Inventory Products Closest to the Door Rank Products by Increasing Number of Required Locations q B = 2, q C = 10, q A = 12 Assign to Storage Locations by Increasing Expected Travel Time 68

Inventory Based Layout P 3 1 50A 2 3 A 50 50A 4 50A 5 50A 6 A 57.5 7 8 9 10 A A A C 11 C 12 A 42.5 42.5 42.5 42.5 42.5 50.0 13 14 15 16 B B C C 17 C 18 A 40 40 40 40 40 47.5 19 C 20 C 21 C 22 C 23 C 24 A 42.5 42.5 42.5 42.5 42.5 50.0 P 2 P 1 69

Total Travel Time for Inventory Based Layout Total Travel = Sum of Product Travels T A = 2 800 48.54 = 77,667 T B = 2 120 40 = 9,600 T C = 2 400 41.75 = 33,400 T = 77,667+9,600+33,400 = 120,667 % T = 3.7 % over 116,333 70

Frequency of Access Sort and Locate Products by Decreasing Frequency of Access to Locations with Expected Distance f p Fp Fp N q si p p p f A = 800/12 = 66.66 f B = 120/2 = 60 f C = 400/10 = 40 71

Product Turnover Dedicated Storage Layout (Factoring) P 3 1 50C 2 3 C 50 50C 4 50C 5 50C 6 C 57.5 7 8 9 10 A A B B 11 C 12 C 42.5 42.5 42.5 42.5 42.5 50.0 13 14 15 16 A A A A 17 A 18 C 40 40 40 40 40 47.5 19 A 20 A 21 A 22 A 23 A 24 C 42.5 42.5 42.5 42.5 42.5 50.0 P 2 P 1 72

Total Travel (Factoring) Total travel = sum of product travels T 2 p T p 2 f q g 2 f g 2 F g p p jz p p p p p p j p p T A = 2*800*41.46 = 66,333 T B = 2*120*42.5 = 10,200 T C = 2*400*49.75 = 39,800 T = 66,333+10,200+39,800 = 116,333 73

Product Information (Non-Factoring) Product A B C Characteristic Symbol Storage Requirement q 12 2 10 Pallets Handled Monthly Through Door P1 e1 300 6 100 Door P2 e2 100 24 240 Door P3 e3 400 90 60 Total 800 120 400 75

Product-Door Probabilities (Non-Factoring) Product A B C Characteristic Symbol Storage Requirement q 12 2 10 Pallets Handled Monthly Through Door P1 e1 0.375 0.050 0.250 Door P2 e2 0.125 0.200 0.600 Door P3 e3 0.500 0.750 0.150 76

Product A Expected Distances 1 2 3 4 5 6 50 7 50 8 50 9 50 10 50 11 57.5 12 P 2 P 3 42.5 13 42.5 14 42.5 15 42.5 16 42.5 17 50.0 18 40 19 40 20 40 21 40 22 40 23 47.5 24 42.5 42.5 42.5 42.5 42.5 50.0 P 1 77

Product B Expected Distances 1 2 3 4 5 6 34.75 7 39.75 8 44.75 9 49.75 10 54.75 11 60.75 12 P 2 P 3 28.75 13 33.75 14 38.75 15 43.75 16 48.75 17 54.75 18 30.25 19 35.25 20 40.25 21 45.25 22 50.25 23 56.25 24 39.25 44.25 49.25 54.25 59.25 65.25 P 1 78

Product Storage Assignment Formulation (Non-Factoring) min 2 i s.. t x q si i j x i ij x 0 j 1 i ij ij ij i i ij f g x j service requirement capacity naturally integer 80

Product Turnover Dedicated Storage Layout (Non-Factoring) P 3 1 B 2 3 C C 4 C 5 34.75 52.75 45.75 38.75 31.75 7 8 9 10 B A A C 11 C 12 28.75 42.5 42.5 40.75 33.75 13 14 15 16 A A A A 17 A 18 40 40 40 40 40 19 A 20 A 21 A 22 A 23 A 24 42.5 42.5 42.5 42.5 42.5 C 6 C 29.75 C 31.75 C 35.25 C 40.25 P 2 P 1 81

Total Travel (Non-Factoring) Total Travel = Sum of Product Travels T 2 T 2 f q si g p 2 f g 2 F g p jz p p T A = 2*800*41.46 = 66,333 T B = 2*120*31.75 = 7,620 T C = 2*400*38.05 = 30,440 T = 66,333+7,620+30,440 = 104,393 p p p p p p p pj p p 82

Product Turnover Class Based Storage Pure product dedicated is very space inefficient 3 to 5 classes based on frequency of access Dedicated space for each class Inside class use random (RAN) or closest open location (COL) Shared storage policy inside a class 83

Turnover Based Class Storage Policy Class space determined by simulation Class space estimated based on service level statistics 84

Classes based on Frequency of Access Sort and aggregate products by decreasing Frequency-of-Access f p Fp Fp N q si p p p f A = 800/12 = 66.66 f B = 120/2 = 60 f C = 400/10 = 40 sequence[a,b,c] 2 classes {{A,B},{C}}, but {{A},{B,C}} may be better alternative 85

Inventory Measures and Relationships iq=ci+si ci=q/2 miq=2ci+si=q+si Inventory Average Cycle Inventory Average Cycle Inventory Safety Inventory Time 86

Inventory Distribution Middle of Period Withdrawal Probability of i units of inventory is distributed [0,q]+si, nearly uniformly except two extreme periods q q i E i sii 2 2 q 2 i Var i 12 Inventory 1 Time 2 qi 12 2 87

Zone K Size Determination Based on Service Level a qp I I si pk pk 2 K p p K pk 2 p Z I z K K K L NM P x x z O QP a pk q 2 p 2 12 91

Average Zone Size Calculations q [12, 2,10] N N 24 I I q 2 si I 1 2 MAX 6,1,5, I 12 I I A, B I I 6 1 7 5 DED K p p p pk pk p C A I I C I B 92

Standard Deviation Zone Size Calculations q 2 2 2 i 2 i A 2 2 2 2 B C K 1 12, 2,10 q 2 12 2, 12.167, 12 12 2 2 10 2 0.5, 8.500 12 12 pk 2 p, 12.167 0.500 12.667 3.559 2 2 A B 2 8.500 2.915 2 C 93

Zone Size Calculations 1 1 z N a, N 0.95 1.65 N I z N N N 1 2 p p 7 1.653.559 7 5.87 12.87 13 5 1.652.915 5 4.81 9.81 10 N 13 10 23 k k space ratio 23 24 96% 94

2-Class Layout P 3 1 2 3 2 2 2 4 2 5 2 6 50 50 50 50 50 57.5 7 8 9 10 1 1 1 1 11 1 12 42.5 42.5 42.5 42.5 42.5 50.0 13 14 15 16 1 1 1 1 17 1 18 40 40 40 40 40 47.5 19 1 20 1 21 1 22 2 23 2 24 42.5 42.5 42.5 42.5 42.5 50.0 2 2 2 P 2 P 1 95

Average Travel Time for Each Zone T k T k 1 Tk 2 Fp gz 2 Fp g j pz k pz N k k jz k 5 40 8 42.5 540 g1 41.54 13 13 242.5 47.5 7 50 482.5 g2 10 10 96

Travel Time (Random inside 2 Zones with Spillover) T 2 F g 1 g pzk T T T 1 2 a a k p z z 2 800 120 0.9541.54 0.0548.25 292041.87 77,048 1 2400 0.9548.25 0.0557.5 10 240048.71 38,970 77,048 38,970 116,018 % T 0.3 from 116,333 (optimal full dedicated) 1 97

Modeling Extensions (Research) Number of classes and product partitions Skewness of the frequency of access (turnover) distribution Dual command Quadratic programming Warehouse layout/configuration Problem size (10K SKUs, 20K unit locations) and dynamic (8 periods) 98

Storage Policies Overview: Unit Load Storage Policies Introduction to Storage Policies Unit Load Storage Policies Product Based Storage Policies Unit Load Based Storage Policies 99

Shared Storage Example: Frequency of Access Distribution Frequency of Access 1 0.9 0.8 0.7 0.6 0.5 0.4 DOS COL DED 0.3 0.2 0.1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Location 111

Duration of Stay Shared Storage Observations Exploits that first and last unit load in batch are different Cross docking (DOS = 0) Minimizes both storage space and travel time for a perfectly balanced warehouse Very constrained perfectly balanced replenishment pattern n p (t) 114

Perfectly Balanced Warehouse Balanced = Minimum Space n ( t) n ( t) t in out Perfectly Balanced = Minimum Space and Minimum Time n ( t) n ( t p) t, p p p z n ( i) p p i1 p 115

Duration of Stay Example: Product Schedule Information product daily reorder replenishment demand quantity day A 1 4 3 B 0.25 2 2 C 1 4 2 D 1 4 1 E 0.25 3 3 F 0.25 3 7 G 1 4 4 H 0.25 2 6 I 0.25 3 11 Total 5.25 29 117

Duration of Stay Example: Statistics Product dedicated required storage space = 29 Total daily demand rate = 5.25 Warehouse size = 24 locations 118

Duration of Stay Example: Layout with Expected Distances 1 2 3 4 5 6 50 50 50 50 50 57.5 7 8 9 10 11 12 P 2 P 3 42.5 13 42.5 14 42.5 15 42.5 16 42.5 17 50.0 18 40 19 40 20 40 21 40 22 40 23 47.5 24 42.5 42.5 42.5 42.5 42.5 50.0 P 1 119

Balanced Inventory Pattern Product Period A B C D E F G H I Total 1 2 1 1 4 1 2 3 2 3 19 2 1 2 4 3 1 2 2 1 3 19 3 4 2 3 2 3 1 1 1 2 19 4 3 2 2 1 3 1 4 1 2 19 5 2 2 1 4 3 1 3 1 2 19 6 1 1 4 3 3 1 2 2 2 19 7 4 1 3 2 2 3 1 2 1 19 8 3 1 2 1 2 3 4 2 1 19 9 2 1 1 4 2 3 3 2 1 19 10 1 2 4 3 2 3 2 1 1 19 11 4 2 3 2 1 2 1 1 3 19 12 3 2 2 1 1 2 4 1 3 19 120

Duration of Stay Example: Unit Load Duration of Stay Duration of Stay Arrival Period 1 2 3 4 5 6 7 8 9 10 11 12 zone 1 D C A G 1 2 D C A G 2 3 D C A G 3 4 D C, B A, E G H F I 6 5 0 6 0 7 0 8 B E H F I 4 9 0 10 0 11 0 12 E F I 3 Total 19 121

Unit Load Duration of Stay Shared Storage Layout P 3 1 3 4 5 6 5012 2 50 50 50 50 57.5 7 8 9 10 4 4 8 8 11 8 12 42.5 42.5 42.5 42.5 42.5 50.0 13 14 15 16 1 2 2 3 17 3 18 40 40 40 40 40 47.5 19 4 20 4 21 4 22 4 23 3 24 42.5 42.5 42.5 42.5 42.5 50.0 12 8 12 P 2 P 1 122

Duration of Stay Example: Total Travel (Duration-Of-Stay) Total Travel = sum of Duration-Of- Stay zone travels Frequency of Access (FOA) 2 * for storage and withdrawal access 4 * for withdrawal access (1/p) only T T 2 f z g 4 p p p p p p p 1 p F HG jz g p j I KJ 123

Duration of Stay Example: Total Travel (Duration-Of-Stay) DOS z FOA g Travel 1 1 1.0000 40.00 160.00 2 2 0.5000 40.00 160.00 3 3 0.3333 40.83 163.33 4 6 0.2500 42.50 255.00 5 0 0.2000 0 0.00 6 0 0.1667 0 0.00 7 0 0.1429 0 0.00 8 4 0.1250 43.75 87.50 9 0 0.1111 0 0.00 10 0 0.1000 0 0.00 11 0 0.0909 0 0.00 12 3 0.0833 50.00 50.00 Total 875.83 124

Duration of Stay Example: Duration-Of-Stay Performance T 1 = 4*40/1 = 160 T 2 = 4*80/2 = 160 T 3 = 4*122.5/3 = 163.33 T 4 = 4*255/4 = 255 T 8 = 4*175/8 = 87.5 T 12 = 4*150/12 = 50 T = 160+160+163.33+255+87.5+50 = 875.83 Space ratio = 19 / 29 = 66 % 125

Closest-Open-Location (COL) Storage P 3 1 50 7 1 1 1 1 42.5 13 40 19 1 42.5 2 50 8 1 42.5 14 40 20 1 3 50 9 1 1 1 1 1 1 1 1 1 1 1 1 42.5 42.5 15 40 21 42.5 4 50 10 42.5 16 40 22 42.5 5 50 11 42.5 17 40 23 42.5 6 57.5 12 50.0 18 47.5 24 50.0 P 2 Only 19 best locations P 1 126

Closest-Open-Location Travel Time Random access to any used location Overall expected travel distance N T Ti Ti 4gfiqi 4ri g 4ri g j N i j1 g (540 1042.5 47.5 350) /19 822.5 /19 43.29 T 443.29 (4150.25) 909.08 T 3.8% vs DOS 875.83 127

Closest-Open-Location Performance Characteristics Space ratio = 19 / 29 = 66 % Zone z FOA g Travel 1 19 0.2763 43.29 909.08 2 5 0.0000 51.50 0.00 Total 909.08 128

Duration of Stay Example: Two Class Product Turnover Product turnovers 1 1 1 1 1 1 1 1 1 f p,,,,,,,, 4 8 4 4 12 12 4 8 12 Product classes{{a,c,d,g},{b,h,e,f,i}} I 1 4 4 2 8 2 2 A 4 2 12 1.50 N 1 1 2 4 A 6 2.45 8 1.652.45 8 4.04 12.04 13 129

Two Class Product Turnover: Size of Class 2 I 2 N N 2 2 B 2 2 E 2 2 2 2 2 33 2 6.5 2CL 2 2 12 0.50 3 2 12 0.917 20.5 30.917 3.75 1.94 6.5 1.651.94 6.5 3.20 9.70 10 13 10 23 space ratio 23 29 79% 130

Duration of Stay Example: 2CL Warehouse Layout P 3 1 2 3 2 2 2 4 2 5 2 6 50 50 50 50 50 57.5 7 8 9 10 1 1 1 1 11 1 12 42.5 42.5 42.5 42.5 42.5 50.0 13 14 15 16 1 1 1 1 17 1 18 40 40 40 40 40 47.5 19 1 20 1 21 1 22 2 23 2 24 42.5 42.5 42.5 42.5 42.5 50.0 2 2 2 P 2 P 1 131

Duration of Stay Example: 2CL Expected Travel g g T T 1 2 1 2 5 40 8 42.5 13 540 13 41.54 242.5 47.5 7 50 10 482.5 10 48.25 44 0.9541.54 0.0548.25 4 4 41.87 669.98 41.25 0.9548.25 0.0557.5 41.2548.71 243.56 T 669.98 243.56 913.55 T 4.3% vs DOS 875.83 132

2 Class Performance Space ratio = 23 / 29 = 79 % a 0.95 Zone z f g g(a) Travel 1 10 0.4000 41.54 41.87 669.98 2 13 0.0962 48.25 48.71 243.56 3 1 0.0000 57.50 0.00 Total 23 913.55 133

Shared Storage Policies: Comparison Summary Comparison criteria Space, travel time, information requirements, implementation simplicity Policy Space Space Travel Time Time DOS 19 875.83 COL 19 0% 909.08 3.8% 2CL 23 21% 913.55 4.3% 134

Not Perfectly Balanced Systems Static Greedy Heuristic Sort by Increasing Departure Time Adaptive, Dynamic Heuristic Combine DOS into classes z p p E n p Remedial Action for Full Classes 135

Storage Policies Overview: Unit Load Storage Policies Introduction to Storage Policies Unit Load Storage Policies Product Based Storage Policies Unit Load Based Storage Policies Experimental Comparison Conclusions 137

Unit Load Storage Policy Conclusions Unit load systems are very common Single or dual command cycles Two main objectives: storage space, total travel time Three planning problems Strategic sizing Tactical storage policy Operational storage & retrieval sequence 138

Conclusions (2): Three Types of Storage Policies No information (RAN, COL) Space efficient, simple storage, retrieval with inventory map, medium travel efficiency Product Turnover Information (DED, 2CL, 3CL) DED: space inefficient, simple xcl: good tradeoff between space, travel, and simplicity Unit Load Time Information (DOS, 2TZ, 3TZ) DOS: theoretical best, but not practical xtz: tradeoff not as good as xcl in practice 139

Research Questions Easier Do more than three classes make a difference? Does dual command make a difference? Do aisle configurations make a difference? Harder Does this apply to deep lane, block stacking (not rack supported)? When to relocate? Extensions to container ports 140

Unit Load Storage Policy Conclusions Savings magnitude depends on replenishment pattern, # products, product correlations Data requirements indicate automated warehouses or WMS 141

May I answer any questions? 142