1. Facility Design-Week12 Warehouse Operation Anastasia L. Maukar 1

2. Warehouse Functions Provide temporary storage of goods Put together customer orders Serve as a customer service facility Protect goods Segregate hazardous or contaminated materials Perform value-added services Inventory 2

3. Elements of a Warehouse Storage Media Material Handling System Building 3

4. Storage Media Block Stacking Stacking frames Stool like frames Portable (collapsible) frames Cantilever Racks 4

5. Storage Media (Continued) Selective Racks Single-deep Double-deep Multiple-depth Combination Drive-in Racks Drive-through Racks 5

6. Storage Media (Continued) Mobile Racks Flow Racks Push-Back Rack 6

7. Storage Media (Continued) Racks for AS/RS Combination Racks Modular drawers (high density storage) Racks for storage and building support 7

8. Storage and Retrieval Systems Person-to-item Item-to-person Manual S/RS Semi-automated S/RS Automated S/RS Aisle-captive AS/RS Aisle-to-aisle AS/RS 8

9. Storage and Retrieval Systems (cont) Storage Carousels Vertical Horizontal Miniload AS/RS Robotic AS/RS High-rise AS/RS (two motors) 9

10. Phoenix Pharmaceuticals German company founded in 1994 Receives supplies from 19 plants across Germany and distributes to drugstores $400 million annual turnover 10

11. Phoenix Pharmaceuticals 30% market share Fill orders in < 30 minutes 87,000 items 61% pharmaceutical, 39% cosmetic 11

12. Phoenix Pharmaceuticals (cont.) 150-10,000 picks per month Three levels of automation Manual picking via flow-racks Semi-automated using dispensers Full automation via robotic AS/RS 12

13. AVS/RS 13

14. RFID 14

15. Warehouse Problems Design Operational or Planning 15

16. Warehouse Design Location How many? Where? Capacity Overall Layout 16

17. Warehouse Design 17

18. Warehouse Design Layout and Location of Docks Pickup by retail customers? Combine or separate shipping and receiving? Layout of road/rail network Room available for maneuvering trucks? Similar trucks or a variety of them? 18

19. Warehouse Design (cont) Number of Docks Shipping and receiving combined or separated? Average and peak number of trucks or rail cars? Average and peak number of items per order? Seasonal highs and lows Types of load handled? Sizes? Shapes? Cartons? Cases? Pallets? Protection from weather elements 19

20. Model for Rack Design x, y are # of columns, rows of rack spaces a, b are aisle space multipliers in x, y directions 20

21. Model for Rack Design (Cont) In the relaxed problem, xyz=n x=n/yz The unconstrained objective is 21

22. Model for Rack Design (Cont) Taking derivative with respect to y, setting equation to zero and solving, we get 22

23. Rack Design Example Consider warehouse shown in figure 10.29 Assume travel originates at lower left corner Assume reasonable values for the aisle space multipliers a, b 23

24. Rack Design Example (Cont) Example 1: Determine length and width of the warehouse so as to accommodate 2000 square storage spaces of equal area in: 3 levels 4 levels 5 levels 24

25. Rack Design Example Solution Reasonable values for a, b are 0.5, 0.2 For the 3-level case, 25

26. Rack Design Example Solution (Cont) Previous solution gives a total storage of 24x29x3=2088 Due to rounding, we get 88 more spaces If inadequate to cover the area required for lounge, customer entrance/exit and other areas, the aisle space multipliers a, b must be increased appropriately and the x, y values recalculated 26

27. Rack Design Example Solution (Cont) For the 4 level and 5 level case, the building dimensions are 25x20 units and 18x23 units, respectively Easy to calculate the average distance traveled - simply substitute a, b, x and y values in the objective function For 3-level case, average one-way distance = 35.4 units 27

28. Warehouse Design Model 28

29. Model Assumptions 1.The available total storage space is known. 2.The expected time a product spends on the shelves is known. This is referred to as the dwell time throughout this paper. 3.The cost of handling each product in each flow is known. 4.The dwell time and cost have a linear relationship. 5.The annual product demand rates are known. 6.The storage policies and material handling equipment are known and these affect the unit handling and storage costs. 29

30. Model Notation 30

31. Model Notation 31

32. Model Notation 32

33. Model 33

34. Model 34

35. Spreadsheet Based AS/RS Design Tool 35

36. Spreadsheet Based AS/RS Design Tool 36

37. Block Stacking Simple formula to determine a near-optimal lane depth assuming goods are allocated to storage spaces using the random storage operating policy instantaneous replenishment in pre-determined lot sizes replenishment done only when inventory excluding safety stock has been fully depleted lots are rotated on a FIFO basis 37

38. Block Stacking (Cont) withdrawal of lots takes place at a constant rate empty lot is available for use immediately Let Q, w and z denote lot size in pallet loads, width of aisle (in pallet stacks) and stack height in pallet loads, respectively 38

39. Block Stacking (Cont) Kind’s (1975) formula for near-optimal lane depth, d 39

40. Block Stacking (Cont) E.g., if lot size is 60 pallets, pallets are stacked 3 pallets high and aisle width is 1.7 pallet stacks, then Verify optimality by checking the utilization for all possible lane depths (a finite number) 40

41. Block Stacking (Cont) Several issues omitted in Kind’s formula. Some examples What if pallets withdrawn not at a constant rate but in batches of varying sizes? What if lots are relocated to consolidate pallets containing similar items? 41

42. Storage Policies Random In practice, not purely random Dedicated Requires more storage space than random, but throughput rate is higher because no time is lost in searching for items Cube-per-order index (COI) policy Class-based storage policy 42

43. Storage Policies (Cont) Shared storage policy Class based and shared storage policies are between the two “extreme” policies - random and dedicated Class based policy variations if each item is a class, we have dedicated policy if all items in one class, we have random policy 43

44. Design Model for Dedicated Policy Warehouse has p I/O points m items are stored in one of n storage spaces or locations Each location requires the same storage space Item i requires S i storage spaces 44

45. Design Model for Dedicated Policy (Cont) Ideally, we would like However, if LHS < RHS, add a dummy product (m+1) to take up remaining spaces 45

46. Design Model for Dedicated Policy (Cont) So, assume that the above equality holds But, if RHS < LHS, no feasible solution Model Parameters f ik trips of item i through I/O point k cost of moving a unit load of item i to/from I/O point k is c ik distance of storage space j from I/O point k is d kj 46

47. Design Model for Dedicated Policy (Cont) Model Variable binary decision variable x ij specifying whether or not item i is assigned to storage space j 47

48. Design Model for Dedicated Policy (Cont) 48

49. Design Model for Dedicated Policy (Cont) 49

50. Design Model for Dedicated Policy (Cont) 50

51. Design Model for Dedicated Policy (Cont) Model is generalized QAP Can be solved via transportation algorithm No need for binary restrictions in the model 51

52. Design Model for Dedicated Policy - Example WH Layout 52 1234 5678 9101112 13141516

53. Design Model for Dedicated Policy - Example (Cont) 3 I/O points located in middle of south, west and north walls 4 items 53

54. Design Model for Dedicated Policy Example [f ik (c ik )] 54 123SiSi 1150(5)25(5)88(5)3 260(7)200(3)150(6)5 396(4)15(7)85(9)2 4175(15)135(8)90(12)6

55. Design Model for Dedicated Policy Example Solution (d kj ) 55 12345678910101 1212 1313 1414 1515 1616 15445433432232112 22345123412342345 32112322343345445

56. Design Model for Dedicated Policy Example Solution (w ij ) 56 123…1516 1162712721313...10031442 21020876996...12841668 3183013081361...19322559 4290824702650...18782675

57. Design Model for Dedicated Policy - Example Solution (Cont) 57 2332 2212 4441 4441

58. Design Model for COI Policy Consider special case of dedicated storage policy model All items use I/O points in same proportion Cost of moving a unit load of item i is independent of I/O point Define P k as % trips through I/O point k No need for the first subscript in f ik as well as c ik 58

59. Design Model for COI Policy (Cont) 59

60. Design Model for COI Policy (Cont) 60

61. Design Model for COI Policy (Cont) 61

62. Design Model for COI Policy - Solution COI model easier than Dedicated Model Rearrange “cost”, “distance” terms (c i f i /S i ), w j in non-increasing and non-decreasing order Match Item corresponding to 1 st element in ordered “cost” list with storage spaces corresponding to 1 st S i elements in ordered “distance” list 62

63. Design Model for COI Policy - Solution Second item with storage spaces corresponding to next S l elements, and so on … COI policy calculates inverse of the “cost” term and orders elements in non-decreasing order, of their COI values, thereby producing the same result as above 63

64. Design Model for COI Policy - Solution Arranging cost and distance vectors in non-increasing and non- decreasing order and taking their product provides a lower bound on cost function Above algorithm is optimal 64

65. Design Model for COI Policy - Example Consider dedicated policy example Ignore c ik and f ik data Assume all 4 items use 3 I/O points in same proportion pallets moved/time period are 100, 80, 120 and 90 cost to move unit load through unit distance is $1.00 Determine optimal assignment of items to storage spaces 65

66. Design Model for COI Policy Example Solution 66

67. Design Model for COI Policy - Example Solution Sort [c i f i /S i ] values in non-increasing order [60, 33.33, 16, 15], corresponding to items 3, 1, 2 and 4 Optimal storage space assignment Item 1 to Storage Spaces 2, 5, 7 Item 2 to Storage Spaces 1, 3, 9, 11, 14 Item 3 to Storage Spaces 6, 10 Item 4 to Storage Spaces 4, 8, 12, 13, 15, 16 67

68. Design Model for COI Policy Example Solution 68 2124 1314 2324 4244

69. Design Model for Random Policy Items stored randomly in empty and available storage spaces Each empty space has an equal probability of being selected Storage or retrieval may not be purely random, but we assume so for model 69

70. Design Model for Random Policy (Cont) Problem Definition Determine storage space layout so total expected travel distance between each of n storage spaces and p I/O points is minimized Sum of distances of each storage space from each I/O point is 70

71. Design Model for Random Policy- Solution Arrange spaces in non-decreasing order of the sum of above distances Pick the n closest storage spaces n depends upon inventory levels of all items n is less than that required under dedicated policy 71

72. Design Model for Random Policy - Example Determine storage space layout for 56 storage spaces in a 140x70 feet warehouse Random storage policy Minimize total distance traveled Each storage space is a 10x10 feet square I/O point located in middle of south wall 72

73. Design Model for Random Policy - Example (Cont) 73

74. Design Model for Random Policy - Example Solution Calculate distance of all potential storage spaces to the I/O point Arrange them in non-decreasing order 74

75. Design Model for Random Policy - Example Solution (Cont) Largest distance traveled is 70 feet Sum total distance traveled (2800) by number of storage spaces (56) to get average distance traveled = 50 feet 75

76. Design Model for Random Policy - Example Solution (Cont) 76

77. Travel Time Models For random policy, average distance traveled When number of storage spaces are large, calculating average distance can be tedious 77

78. Travel Time Models (Cont) If storage spaces are small relative to total area, approximate average distance traveled assume spaces are continuous points on a plane use the integral 78

79. Travel Time Models (Cont) We assume in previous integral that warehouse is in 1st quadrant only one I/O point (at origin and SW corner) distance metric of interest is rectilinear Previous integral can be easily modified if two or more I/O points distance metric is not rectilinear no restrictions on location of warehouse 79

80. Travel Time Models (Cont) Suppose designer interested in shape that minimizes travel time Then, depending upon number and location of I/O points, distance metric, warehouse shape can range from diamond to circle to trapezium !!! 80

81. Travel Time Models (Cont) Models minimizing construction costs and travel distance Consider following assumptions Warehouse shape is fixed - rectangle Warehouse area = A Construction cost is function of warehouse perimeter - r[2(a+b)] r is unit (perimeter) distance construction cost a and b are warehouse dimensions 81

82. Travel Time Models (Cont) One I/O point at origin and SW corner coordinates are (p, q) cost for each unit distance traveled = c Model 82

83. Travel Time Models (Cont) Optimal value of a and b, given that I/O point must be on or outside exterior walls, i.e., p $ 0 warehouse area must be A square units 83

84. Travel Time Models (Cont) Single command cycle Dual or multiple command cycles 84

85. Warehouse Operations Warehouse operational problems Sequence in which orders to be picked How frequently orders picked from high-rise storage area? Batch picking or pick when order comes in? Limit on number of items picked? If so, what is the limit? Operator assignment to stacker cranes 85

86. Warehouse Operations (Cont) How to balance picking operator’s workload? Release items from stacker crane into sorting stations in batches or as soon as items are picked? Order picking consumes over 50% of the activities in warehouse 86

87. Warehouse Operations (Cont) Not surprising that order picking is the single largest expense in warehouse operations Since construction and operation of AS/RS are very high,managers interested in maximizing throughput capacity 87

88. Order Picking Sequence Two basic picking methods Order picking Zone picking Consider this: An AS/R machine has two independent motors Movement in horizontal and vertical directions simultaneously 88

89. Order Picking Sequence (Cont) Time to travel from (x i, y i ) to (x j, y j ) 89

90. Order Picking Sequence Model 90

91. Order Picking Sequence Algorithms Construction Improvement Hybrid 91

92. Order Picking Sequence Algorithms (Cont) 2-opt 3-opt Branch-and-bound Simulated Annealing Convex Hull 92

93. Convex Hull Algorithm - Phase 1 Find x max and y max Delete points inside polygon formed by x max, y max and origin For each region, construct convex path between extreme points Sort points in regions 1 and 2 in ascending order of x- coordinate 93

94. Convex Hull Algorithm - Phase 1 (Cont) Sort region 3 points in descending order Starting with 1 st extreme point, compute V for three consecutive points i, i+1, i+2 V= (y i+1 -y i )(x i+2 -x i+1 )+(x i -x i+1 )(y i+2 -y i+1 ). Repeat until other extreme point is reached If V # 0, no convex hull with i, i+1, i+2 Otherwise, convex hull possible 94

95. Convex Hull Algorithm - Phase 1 (Cont) 95 y max x max Region 1 Region 3 Region 2 0

96. Convex Hull Algorithm - Phase 1 (Cont) Using some or all of the sorted points in regions 1, 2, and 3, three at a time, generate convex hull (sub-tour) Points not in sub-tour are considered in phases 2 and 3. If x max = y max following explanation still good 96

97. Convex Hull Algorithm - Phase 2 Insert points that maybe included in sub-tour without increasing cost Such free insertion points lie on a parallelogram with two adjacent points in the sub-tour as its corner 97

98. Convex Hull Algorithm - Phase 3 Insert points not included in the sub-tour in phases 1 and 2 using minimal insertion cost criteria greedy hull steepest descent hull If no points left for insertion in phase 2 or 3, phase 1 sub- tour is optimal 98

99. Simulated Annealing Algorithm Set S, z, r, T in, T= T in ; T fin = 0.1T in Randomly select points i and j in S and exchange their positions If new solution S' has z’< z, set S = S', and z = z’ Otherwise, set S= S' with probability e - d /T 99

100. Simulated Annealing Algorithm (Cont) Repeat Step 1 until number of new solutions = 16 times the number of neighbors Set T= rT. If T > T fin, go to Step 1 Otherwise return S, and STOP 100

101. TSP Software 101

102. Routing Problem 102

103. Multimedia CD for Distribution Center Design 103