Unit Load Storage Policies

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1 Unit Load Storage Policies Marc Goetschalckx PASI 2013, Santiago, Chile 1

2 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

3 Storage Policies Overview: Introduction Introduction to Storage Policies 5

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

5 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

6 Block Stacking Operation With Counterbalanced Truck 8

7 Sainsbury s Grocery Distribution Center 10

8 Example: Walmart DC Pallet Rack 7-Aug-13

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

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

11 Empty Single-Deep Pallet Rack with Four Levels 15

12 ASRS Pallet Unit Load High-Rise Storage 16

13 Volkswagen Automated Finished Goods (Cars) Warehouse 17

14 Handling Units Example: Collapsible Pallet 18

15 Wine Barrels in a Rack 19

16 Container Port Overview (Hamburg Port Altenwerder) 20

17 Twin Yard Cranes (Hamburg Port Altenwerder Quay) 21

18 Amazon Forward Reserve Warehouse 7-Aug-13

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

20 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

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

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

23 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

24 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

25 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

26 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

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

28 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

29 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

30 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

31 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

32 Unbalanced Warehouse Size for Various Policies A B C D All Ded Sha

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

34 Storage Policy Size Ratio N DED 18, N a SHA 51

35 Perfectly Balanced Warehouse Size for Various Policies A B C D All Ded

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

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

38 Unit Load Warehouse P P P 1 57

39 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

40 Product Information (Factoring) Product A B C Characteristic Symbol p Storage Requirement q Pallets Received Monthly Through Door P3 e Pallets Shipped Monthly Through Door P1 e Door P2 e Total

41 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

42 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* * *25 = 50 g 13 = 0.375* * *15 = 40 61

43 Warehouse Factoring Distances P P 2 P 3 62

44 Locations Sorted by Increasing Distance P 2 P P 1 63

45 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

46 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

47 Demand Based Layout P C 2 3 C 50 50C 4 50C 5 50C 6 B A A C C 11 C 12 B A A A A 17 A 18 C A 20 A 21 A 22 A 23 A 24 C P 2 P 1 66

48 Total Travel Time for Demand Based Layout Total Travel = Sum of Product Travels T A = = 66,333 T B = = 12,900 T C = = 38,000 T = 66,333+12,900+38,000 = 117,233 %T = 0.8 % over 116,333 67

49 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

50 Inventory Based Layout P A 2 3 A 50 50A 4 50A 5 50A 6 A A A A C 11 C 12 A B B C C 17 C 18 A C 20 C 21 C 22 C 23 C 24 A P 2 P 1 69

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

52 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 = f B = 120/2 = 60 f C = 400/10 = 40 71

53 Product Turnover Dedicated Storage Layout (Factoring) P C 2 3 C 50 50C 4 50C 5 50C 6 C A A B B 11 C 12 C A A A A 17 A 18 C A 20 A 21 A 22 A 23 A 24 C P 2 P 1 72

54 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

55 Product Information (Non-Factoring) Product A B C Characteristic Symbol Storage Requirement q Pallets Handled Monthly Through Door P1 e Door P2 e Door P3 e Total

56 Product-Door Probabilities (Non-Factoring) Product A B C Characteristic Symbol Storage Requirement q Pallets Handled Monthly Through Door P1 e Door P2 e Door P3 e

57 Product A Expected Distances P 2 P P 1 77

58 Product B Expected Distances P 2 P P 1 78

59 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

60 Product Turnover Dedicated Storage Layout (Non-Factoring) P 3 1 B 2 3 C C 4 C B A A C 11 C A A A A 17 A A 20 A 21 A 22 A 23 A C 6 C C C C P 2 P 1 81

61 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

62 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

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

64 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 = 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

65 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

66 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

67 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

68 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 DED K p p p pk pk p C A I I C I B 92

69 Standard Deviation Zone Size Calculations q i 2 i A B C K 1 12, 2,10 q , , , pk 2 p, A B C 93

70 Zone Size Calculations 1 1 z N a, N N I z N N N 1 2 p p N k k space ratio % 94

71 2-Class Layout P P 2 P 1 95

72 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 g g

73 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 , ,970 77,048 38, ,018 % T 0.3 from 116,333 (optimal full dedicated) 1 97

74 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

75 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

76 Shared Storage Example: Frequency of Access Distribution Frequency of Access DOS COL DED Location 111

77 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

78 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

79 Duration of Stay Example: Product Schedule Information product daily reorder replenishment demand quantity day A B C D E F G H I Total

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

81 Duration of Stay Example: Layout with Expected Distances P 2 P P 1 119

82 Balanced Inventory Pattern Product Period A B C D E F G H I Total

83 Duration of Stay Example: Unit Load Duration of Stay Duration of Stay Arrival Period 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 B E H F I E F I 3 Total

84 Unit Load Duration of Stay Shared Storage Layout P P 2 P 1 122

85 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

86 Duration of Stay Example: Total Travel (Duration-Of-Stay) DOS z FOA g Travel Total

87 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 = T 4 = 4*255/4 = 255 T 8 = 4*175/8 = 87.5 T 12 = 4*150/12 = 50 T = = Space ratio = 19 / 29 = 66 % 125

88 Closest-Open-Location (COL) Storage P P 2 Only 19 best locations P 1 126

89 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 ( ) / / T ( ) T 3.8% vs DOS

90 Closest-Open-Location Performance Characteristics Space ratio = 19 / 29 = 66 % Zone z FOA g Travel Total

91 Duration of Stay Example: Two Class Product Turnover Product turnovers f p,,,,,,,, Product classes{{a,c,d,g},{b,h,e,f,i}} I A N A

92 Two Class Product Turnover: Size of Class 2 I 2 N N 2 2 B 2 2 E CL space ratio % 130

93 Duration of Stay Example: 2CL Warehouse Layout P P 2 P 1 131

94 Duration of Stay Example: 2CL Expected Travel g g T T T T 4.3% vs DOS

95 2 Class Performance Space ratio = 23 / 29 = 79 % a 0.95 Zone z f g g(a) Travel Total

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

97 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

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 Experimental Comparison Conclusions 137

99 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

100 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

101 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

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

103 May I answer any questions? 142

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