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WAREHOUSE & DISTRIBUTION SCIENCE
Release 0.89
www.warehouse-science.com
John J. BARTHOLDI, III
Steven T. HACKMAN
The Supply Chain and Logistics Institute
School of Industrial and Systems Engineering
Georgia Institute of Technology
Atlanta, GA 30332-0205 USA

First draft: May 22, 1998; revised August 20, 2008 1
Copyright c 1998”“2008 John J. BARTHOLDI, III and Steven T. HACKMAN
.All rights reserved. This material may be freely copied for educational purposes
”but not for resal” as long as the authors names and the copyright notice appear
clearly on the copies. The authors may be contacted at
john.bartholdi@gatech.edu or
steve.hackman@isye.gatech.edu.






















































































Contents
Preface I
0.1 Why this book . . . . . . . . . . . . . . . . . . . . . . . . . . . . I
0.2 Organizations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
0.3 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
0.4 But first. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

I Issues, equipment, processes
1 Warehouse rationale 1
1.1 Why have a warehouse? . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Types of warehouses . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Material flow
9
2.1 The fluid model of product flow . . . . . . . . . . . . . . . . . . . 9
2.2 Units of handling . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Storage: “ Dedicated “ versus “ Shared “ . . . . . . . . . . . . . . . 10
2.4 The warehouse as a queuing system. . . . . . . . . . . . . . . . 16
2.5 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3 Warehouse operations 21
3.1 Receiving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 Put-away . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Order-picking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3.1 Sharing the work of order-picking . . . . . . . . . . . . . . 25
3.4 Checking and packing. . . . . . . . . . . . . . . . . . . . . . . . 26
3.5 Shipping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.7 More . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.8 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4 Warehouse management systems 31
4.1 Receiving and shipping . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Stock locater system . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.3 Menu of features . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.4 The market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.5 Supply Chain Execution Systems . . . . . . . . . . . . . . . . . . 33
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.6.1 The ugly . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.7 More . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5 Storage and handling equipment 35
5.1 Storage equipment . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.1.1 Pallet storage . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.1.2 Bin-shelving or static rack . . . . . . . . . . . . . . . . . . 39
5.1.3 Gravity flow rack . . . . . . . . . . . . . . . . . . . . . . . 39
5.2 Conveyors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.3 Sortation equipment . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.5 On the lighter side . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.6 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

II Layout 45
6 Layout of a unit-load area 49
6.1 Labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6.1.1 Storage locations . . . . . . . . . . . . . . . . . . . . . . . 51
6.2 Location of receiving and shipping . . . . . . . . . . . . . . . . . 52
6.3 Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.3.1 Stack height . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.3.2 Lane depth . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.5 More . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.6 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

7 Layout of a carton-pick-from-pallet area 71
7.1 Some strategies for carton-picking . . . . . . . . . . . . . . . . . 71
7.1.1 Pick from floor stack . . . . . . . . . . . . . . . . . . . . . 71
7.1.2 Simple pick from pallet rack . . . . . . . . . . . . . . . . . 73
7.1.3 Forward- or fast-pick areas . . . . . . . . . . . . . . . . . 73
7.1.4 Building a new fast-pick area . . . . . . . . . . . . . . . . 80
7.2 Sortation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
7.4 More . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.5 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83











8 Layout of a piece-pick-from-carton area 87
8.1 What is a fast-pick area? . . . . . . . . . . . . . . . . . . . . . . 87
8.2 Estimating restocks . . . . . . . . . . . . . . . . . . . . . . . . . . 89
8.3 How much of each sku to store in the fast-pick area? . . . . . . . 90
8.3.1 Minimizing labor to maintain a forward pick area . . . . . 91
8.3.2 Two commonly-used storage strategies . . . . . . . . . . . 94
8.3.3 Comparison with optimal . . . . . . . . . . . . . . . . . . 95
8.3.4 Differing costs per restock . . . . . . . . . . . . . . . . . . 98
8.3.5 Minimum and maximum allocations . . . . . . . . . . . . 99
8.3.6 Reorder points and safety stock . . . . . . . . . . . . . . . 99
8.4 Which skus go into the fast-pick area? . . . . . . . . . . . . . . . 99
8.4.1 Selecting skus to minimize labor . . . . . . . . . . . . . . 102
8.4.2 Stocking to equalize space or restocking frequencies . . . 104
8.4.3 Further comments on the model . . . . . . . . . . . . . . 105
8.5 Additional issues . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.5.1 Storage by family . . . . . . . . . . . . . . . . . . . . . . . 106
8.5.2 Accounting for safety stock . . . . . . . . . . . . . . . . . 107
8.5.3 Limits on capacity . . . . . . . . . . . . . . . . . . . . . . 108
8.5.4 Accounting for on-hand inventory levels . . . . . . . . . . 108
8.5.5 Setup costs . . . . . . . . . . . . . . . . . . . . . . . . . . 109
8.6 Limitations of the fluid model . . . . . . . . . . . . . . . . . . . . 109
8.7 Size of the fast-pick area . . . . . . . . . . . . . . . . . . . . . . . 111
8.7.1 How large should the fast-pick area be? . . . . . . . . . . 111
8.7.2 How can the fast-pick area be made larger? . . . . . . . . 113
8.8 Multiple fast-pick areas . . . . . . . . . . . . . . . . . . . . . . . 114
8.9 On the lighter side . . . . . . . . . . . . . . . . . . . . . . . . . . 115
8.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
8.11 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

9 The geometry of slotting 125
9.1 Case orientation and stack level. . . . . . . . . . . . . . . . . . . 125
9.2 Packing algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 126
9.2.1 Next Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
9.2.2 First Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
9.2.3 More on packing algorithms . . . . . . . . . . . . . . . . . 129
9.3 Other issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
9.4 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

III Order-picking 135

10 Pick-paths 139
10.1 The problem of pick-path optimization. . . . . . . . . . . . . . . 139
10.2 Heuristic methods of generating short pick paths . . . . . . . . . 140
10.2.1 Path outlines . . . . . . . . . . . . . . . . . . . . . . . . . 142
10.2.2 Product placement . . . . . . . . . . . . . . . . . . . . . . 145






10.3 Pick-path optimization . . . . . . . . . . . . . . . . . . . . . . . . 145
10.3.1 How to take advantage of optimization . . . . . . . . . . . 147
10.3.2 How much is optimization worth? . . . . . . . . . . . . 152
10.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
10.5 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

11 Flow and balance: Piece-picking by “bucket brigade” 157
11.1 Self-organization . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
11.2 Order-assembly by bucket brigade . . . . . . . . . . . . . . . . . 158
11.2.1 A model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
11.2.2 Improvements that are not . . . . . . . . . . . . . . . . . 162
11.2.3 Some advantages of bucket brigades . . . . . . . . . . . . 164
11.3 Bucket brigades in the warehouse . . . . . . . . . . . . . . . . . 165
11.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
11.5 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

IV Automation 171
12 Carousels, A-frames, and AS/RS 175
12.1 Carousels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
12.1.1 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
12.1.2 Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
12.1.3 Throughput . . . . . . . . . . . . . . . . . . . . . . . . . . 181
12.2 A-frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
12.3 In-aisle cranes, AS/RS, and their relatives . . . . . . . . . . . . . 185
12.3.1 Throughput . . . . . . . . . . . . . . . . . . . . . . . . . . 185
12.4 On the lighter side . . . . . . . . . . . . . . . . . . . . . . . . . . 191
12.5 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

V Special topics 195
13 Cross docking 199
13.1 Why cross dock? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
13.2 Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
13.3 Freight flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
13.3.1 Congestion. . . . . . . . . . . . . . . . . . . . . . . . . . 201
13.4 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
13.4.1 Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
13.4.2 Geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . 204
13.5 Trailer management . . . . . . . . . . . . . . . . . . . . . . . . . 208
13.6 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
13.7 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209









VI Measuring warehouse efficiency 211

14 Activity profiling 215
14.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
14.2 Warehouse activity profiling . . . . . . . . . . . . . . . . . . . . . 216
14.2.1 ABC analysis . . . . . . . . . . . . . . . . . . . . . . . . . 216
14.2.2 Statistical analysis. . . . . . . . . . . . . . . . . . . . . . 219
14.2.3 Doing it . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
14.2.4 Visualization . . . . . . . . . . . . . . . . . . . . . . . . . 234
14.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
14.4 On the lighter side . . . . . . . . . . . . . . . . . . . . . . . . . . 235
14.5 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

15 Benchmarking 239

15.1 Performance measurement . . . . . . . . . . . . . . . . . . . . . . 239
15.2 Benchmarking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
15.2.1 Ratio-based benchmarking . . . . . . . . . . . . . . . . . . 240
15.2.2 Aggregate benchmarking . . . . . . . . . . . . . . . . . . 241
15.3 Are smaller warehouses more efficient? . . . . . . . . . . . . . . . 248
15.4 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

VII Miscellaneous 251

16 Warehousing around the world 255
16.1 North America . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
16.2 East Asia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
16.2.1 India . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
16.2.2 China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
16.2.3 Singapore, Hong Kong, Japan . . . . . . . . . . . . . . . . 258
16.3 South and Central America . . . . . . . . . . . . . . . . . . . . . 261
16.4 Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
17 In preparation 263






































































List of Figures
2.1 If two pipes have the same rates of flow, the narrower pipe holds less fluid. In the same way, faster flow of inventory means less inventory in the pipeline and so reduced inventory costs. . . . . . 10

2.2 A product is generally handled in smaller units as it moves down the supply chain. (Adapted from “Warehouse Modernization and Layout Planning Guide”, Department of the Navy, Naval Supply Systems Command, NAVSUP Publication 529, March 1985, p 8”“17). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 An idealization of how the inventory level at a location changes over time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Use of k locations to hold product under a policy of shared storage 14
2.5 Space utilization increases with additional storage locations under shared storage, but at a diminishing rate. . . . . . . . . . . . 15
3.1 Order-picking is the most labor-intensive activity in most warehouses. Travel can be reduced by careful put away. . . . . . . . . 22
5.1 Simple pallet rack. (Adapted from “Warehouse Modernization and Layout Planning Guide”, Department of the Navy, Naval Supply Systems Command, NAVSUP Publication 529, March 1985, p 8”“17). . . . . . . . . . . . . . . . . . . . . . . . 37
5.2 Shelving, or static rack. (Adapted from “Warehouse Modernization and Layout Planning Guide”, Department of the Navy, Naval Supply Systems Command, NAVSUP Publication 529, March 1985, p 8”“17.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.3 Gravity flow rack. (Adapted from “Warehouse Modernization and Layout Planning Guide”, Department of the Navy, Naval Supply Systems Command, NAVSUP Publication 529, March 1985, p 8-17.) . . . . . . . . . . . . . . . . . . . .. . 41
5.4 Side views of the shelves of three styles of carton flow rack. Each successive style takes more space but makes the cartons more accessible because upper shelves do not overhang lower shelves. . 42
6.1 Flow of unit-loads through a typical warehouse . . . . . . . . . . 50




















6.2 The economic contours of a warehouse floor in which receiving is at the middle bottom and shipping at the middle top. The pallet positions colored most darkly are the most convenient. . . . . . . 53
6.3 The economic contours of a warehouse floor in which receiving and shipping are both located at the middle bottom. The pallet positions colored most darkly are the most convenient. . . . . . . 53
6.4 Flow-through and U-shaped layouts, with double-deep storage. When pallets are stored in lanes, as here, the first pallet position in a lane is more convenient than subsequent pallet positions in that lane. . .. . . . . . . . . . . . . . . . . 55
6.5 An unusual layout that enables more direct travel between stor age locations and a central receiving/shipping location at the bottom of the figure. (Figure courtesy of Kevin Gue and Russ Meller) . . . . . . . . .. . . . . . . . . . . . . . . 56
6.6 Pallets that require extra labor to retrieve . . . . . . . . . . . . . 57
6.7 The floor space charged to a lane includes storage space, any gap between lanes, and one-half the aisle width in front of the lane. . 58
6.8 Waste, measured as pallet position-days that are unoccupied but unavailable, depends on both the lane depth and the aisle width. The four pallets of this sku should be stored either 2-deep or else 4-deep, depending on the width of the aisle. . . . . . . . . . . . . 60
6.9 Layout of a distributor of spare parts. . . . . . . . . . . . . . . . 66
6.10 Pallet location A is more convenient than locations B or C. . . . 68
7.1 Typical flow of cartons through a warehouse . . . . . . . . . . . . 72
7.2 Cartons are picked from the bottom, most convenient, level; when the bottom position has been emptied, a restocked refills it by dropping a pallet from above. Newly arriving pallets are inserted into the (high) overstock. (Adapted from “Warehouse Modernization and Layout Planning Guide”, Department of the Navy, Naval Supply Systems Command, NAVSUP Publication 529, March 1985, p 8”“17). . . . . . . . . . . . . . . . . . . . . . . 73
7.3 Cartons are picked from pallet flow rack onto a conveyor. The flow rack is replenished from behind. (Adapted from “Warehouse Modernization and Layout Planning Guide”, Department of the Navy, Naval Supply Systems Command, NAVSUP Publication 529, March 1985, p 8”“17). . . . . . .. . . . . . . 74
7.4 Net benefit of storing various full-pallet quantities of a sku in the fast-pick area. The dashed line represents a sku that is an immediate candidate for complete inclusion in the fast-pick area. 77
8.1 Typical flow of product through piece-picking . . . . . . . . . . . 88
8.2 In the simplest case, all the skus in the fast-pick area have been already chosen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11














8.3 Optimal Allocations have less variability in volume than Equal Time Allocations and less variability in number of restocks than Equal Space Allocations. . . . . . . . . . . . . . . . . . . . . . . . 98
8.4 Especially large or slow-moving skus are better picked from the reserve area. This allows the space they would otherwise occupy to be devoted to more popular skus. . . . . . . . . . . . . . . . . 100
8.5 The net benefit realized by storing a sku as a function of the quantity stored. The net benefit is zero if sku i is not stored in the forward area; but if too little is stored, restock costs consume any pick savings. . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
8.6 These plastic liners for the beds of pickup trucks nest like a set of spoons and so can be stored in little more space than that required by a single piece. . . . . . . . . . . . . . . . . . . . . . . 110
8.7 Example of slotting that accounts for the geometry of the skus and the storage mode. This pattern of storage minimizes total pick and restock costs for this set of skus and this arrangement of shelves. Numbers on the right report the percentage of picks from this bay on each shelf. (This was produced by software written by the authors.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
8.8 Multiple fast-pick areas, such as flow rack and carousel, each with different economics . . . . . . . . . . . . . . . . . . . . . . . . . . 115
9.1 Storing an item so that it blocks access to another creates useless work and increases the chance of losing product. . . . . . . . . . 126
9.2 Each storage unit may be placed in any of up to six orientations; and each lane might as well be extended to the fullest depth possible and to the fullest height. . . . . . . . . . . . . . . . . . . 127
9.3 Once quantities and orientations of skus have been established there remains the challenge of fitting them all in as few shelves as possible. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
9.4 Pasta and tomato sauce are two skus that have “affinity”: They are stored together in this grocery DC because they are likely to be ordered together. . . . . . . . . . . . . . . . . . . . . . . . . . 131
9.5 For this warehouse, there were very pairs of skus that were picked together frequently during the year. Affinity amongst triplets was negligible. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
10.1 An order picker has only local information, such as a sequence of locations and the view from an aisle (a), from which to determine a pick path that is globally efficient. It is hard for the order picker to know or account for the global layout of the pick area (b). . . 141
10.2 This picking area contains only popular skus and so every order is likely to require walking down the aisle. Thus an efficient route of travel is known in advance. . . . . . . . . . . . . . . . . . . . . 143
10.3 A serpentine pick path can result in unnecessary travel (in this case along aisles 3 and 6). . . . . . . . . . . . . . . . . . . . . . . 143







12 LIST OF FIGURES 10.4 A modified path outline that sorts aisles 4”“6 but not their locations.144
10.5 Example of branch-and-pick . . . . . . . . . . . . . . . . . . . . . 144 10.6 Left: Travel path generated by detouring into and back out of aisles. Right: Travel can be reduced by allowing picker to determine entry and exit from each aisle. . . . . . . . . . . . . . . . . 145
10.7 A much shorter travel path is possible if popular items are stored close to path outline, as on the right. . . . . . . . . . . . . . . . . 146
10.8 To visit the locations on the left, imagine a decision point at the end of each aisle. Because backtracking is forbidden, the order- picker must visit aisle i before visiting aisle i + 1. . . . . . . . . . 147
10.9 Enumeration and summary of paths from Aisle 1 to Aisle 2. Each candidate path is represented by an edge of the same length in the graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
10.10 Enumeration and summary of paths from Aisle 2 to Aisle 3 . . . 149
10.11 Enumeration and summary of paths from Aisle 3 to Aisle 4 . . . 150
10.12 Enumeration and summary of paths from Aisle 4 to completion. 151
10.13 The shortest path on the associated graph gives an efficient pick path in warehouse . . . . . . . . . . . . . . . . . . . . . . . . . . 151
10.14 Only the lengths of the edges along each side of the graph need be updated to reflect new customer orders. . . . . . . . . . . . . 152
10.15 A pick list with travel directions suitable for use on a branch- and-pick pick path outline . . . . . . . . . . . . . . . . . . . . . . 152
10.16 An order-picker must start at the leftmost dot, visit the shaded locations by traveling the aisles of the warehouse, and finish at the right-most dot. . . . . . . . 155
11.1 A simple flow line in which each item requires processing on the same sequence of work stations. . . . . . . . . . . . . . . . . . . . 158
11.2 Positions of the worker 2 immediately after having completed the k-th order and walked back to take over the order of worker 1 (who has walked back to the start of the line to begin a new customer order). . . . . . . . .. . . . . . . . 160
11.3 Because the slope is of absolute value less than 1, the dynamics function converges to a globally attracting fixed point, where f (x) = x. In other words, the assembly line balances itself. . . . 161
11.4 Positions of the workers after having completed k products. . . . 162
11.5 A time-expanded view of a bucket brigade production line with three workers sequenced from slowest to fastest. The solid horizontal line represents the total work content of the product and the solid circles represent the initial positions of the workers. The zigzag vertical lines show how these positions change over time and the rightmost spikes correspond to completed items. The system quickly stabilized so that each worker repeatedly executes the same portion of work content of the product. . . . .










11.6 Average pick rate as a fraction of the work-standard. Zone- picking was replaced by bucket brigade in week 12. (The solid lines represent best fits to weekly average pick rates before and after introduction of the bucket brigade protocol.) . . . . . . . . 167
11.7 Distribution of average pick rate, measured in 2-hour intervals before (clear bars) and after bucket brigades (shaded bars). Under bucket brigades production increased 20% and standard deviation decreased 20%.) . . . . . . . . . . . . . . . . . . . . . 168 11.8 Would bucket brigades be a good way of coordinating order- o pickers in this warehouse? The shaded areas represent locations to be visited to pick an order. . . . . . . . . . . . . . . . . . . . . 170
12.1 A carousel is a rotatable circuit of shelving. (Adapted from “Warehouse Modernization and Layout Planning Guide”, Department of the Navy, Naval Supply Systems Command, NAV- SUP Publication 529, March 1985, p 8”“17.) . . . . . . . . . . . . 176
12.2 Carousels are typically arranged in pods; in this example, there are eight pods, each of three carousels. The carousels are sup- ported by an intricate conveyor and sortation system: The vertical spurs to the right of each pod bring product to be restocked; and the horizontal conveyor at the bottom takes away completed picks to sortation and shipping. . . . . . . . . . . . . . . . . . . . 176
12.3 In our model of a carousel, there are m evenly-spaced storage locations. In what sequence should the locations for a customer order (represented by filled disks) be visited? . . . . . . . . . . . 177
12.4 A shortest sequence to visit the required locations . . . . . . . . 178
12.5 Outline of a dynamic program to compute the shortest route to retrieve a given sequence of orders from a carousel . . . . . . . . 179
12.6 The optimal stocking strategy for a single carousel conveyor is to concentrate the most popular items together in a so-called”organ- pipe” arrangement. . . . . . . . . . . . . . . . . . . . . . . . . . . 181
12.7 An A-frame automated item dispenser, as seen from the top (start) of the conveyor. The flow rack to either side hold product to restock the A-frame, and are in turn restocked from bulk storage.182
12.8 An A-frame is restocked from carton flow rack, which is itself restocked from bulk storage. . . . . . . . . . . . . . . . . . . . . . 183
12.9 An A-frame is an example of a multi-tier forward pick area, with multiple levels of restocking. The flow rack holds an intermediate cache I of product close to the A-frame, which is the forward pick area F . cRI is the average cost per restock of the intermediate cache I from reserve R; and cIF is the average cost per restock of the forward area F from intermediate storage I. . . . . . . . . 183
12.10An equivalent single-tier system in which the cost of restocking the intermediate cache has been amortized over the cost of re- stocking the forward pick area. . . . . . . . . . . . . . . . . . . . 184









14 LIST OF FIGURES

12.11 A automated storage and retrieval system (adapted from “Warehouse Modernization and Layout Planning Guide”, Department of the Navy, Naval Supply Systems Command, NAVSUP Publi- cation 529, March 1985, p 8”“17.) . . . . . . . . . . . . . . . . . . 186

12.12 In a dual command cycle the storage-and-retrieval device puts away an item and then retrieves another before returning to the input-output point. . . . . . . . . . . . . . . . . . . . . . . . . . . 187
13.1 A typical LTL freight terminal. Shaded rectangles represent trail- ers to be unloaded; clear rectangles represent destination trailers to be filled. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
13.2 There is less floor space per door at outside corners and therefore more likely to be congestion that retards movement of freight . . . 202
13.3 A typical crossdock is built in the shape of the letter I (actually, an elongated rectangle), so that freight can flow across from incoming trailers to outgoing trailers. . . . . . . . . . . . . . . . . 204
13.4 Cross docks have been built in a variety of shapes. Clockwise from upper left: An L-shaped terminal of Yellow Transport; a U-shaped terminal of Consolidated Freightways; a T-shaped terminal of American Freightways; an H-shaped terminal of Central Freight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
13.5 Outside corners are vulnerable to congestion; and inside corners forfeit door positions. . . . . . . . . . . . . . . . . . . . . . . . . . 206
13.6 For data representative of The Home Depot an L-shaped dock was never preferable to an I-shaped dock, no matter the size. A T-shaped dock begins to dominate for docks of about 170 doors and a X-shaped dock around 220 doors. . . . . . . . . . . . . . . 207
14.1 How picking is distributed over the skus. The horizontal axis lists the skus by frequency of requests (picks). By showing both actual values and cumulative fractions it is easy to see how concentrated the picking is amongst the most popular skus. . . . . . . . . . . . 224
14.2 A bird”™s eye view of a warehouse, with each section of shelf colored in proportion to the frequency of requests for the skus stored therein. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
14.3 Number of the most popular skus that were requested only during n months (n = 1, . . . , 12) of the year. . . . . . . . . . . . . . . . . 226
14.4 About two-thirds of the orders are for a single line but these account for only about one-third of the picks. . . . . . . . . . . . 227
14.5 Why are there so many skus with exactly a half-year supply? . . 232 15.1 Warehouse C, scaled to the same output as A and plotted as C , reveals inefficiencies of A . . . . . . . . . . . . . . . . . . . . . . . 243
15.2 Any warehouse that, like D , lies within the dotted rectangle, uses less of each input than A to achieve the same output. . . . . 244







LIST OF FIGURES 15
15.3 The synthetic warehouse, indicated by “â—¦”, is a blend of scaled warehouses E and F ; and it reveals warehouse A to be no more than 0.72 efficient. . . . . . . . . . . . . . . . . . . . . . . . . . . 245
15.4 The benchmark warehouse, indicated by “â—¦”, may be considered to have taken all of the best ideas from other warehouses and blended them perfectly. . . . . . . . . . . . . . . . . . . . . . . . 246
15.5 Productivity of 36 warehouses as a function of the square root of the warehouse area. . . . . . . . . . . . . . . . . . . . . . . . . . 248
16.1 This Amazon.com distribution center is typical of the large, high- volume DCs in North America. . . . . . . . . . . . . . . . . . . . 256
16.2 The relatively low cost of labor, high cost of capital, and arti- ficially small market mean that this warehouse in India may be economically efficient. (Photo courtesy of Rohan Reddy) . . . . . 257
16.3 In the US warehouse on the left, cartons of beer have been palletized because labor is expensive compared to capital. The reduction in labor is worth the expense of a forklift plus the additional storage space. In the Chinese warehouse on the right, cartons have been stacked by hand and must be untracked by hand; but labor is cheap and capital is expensive. . . . . . . . . . 258
16.4 Multi-story warehouses are common in Singapore, Hong Kong, and Japan where land is expensive. . . . . . . . . . . . . . . . . . 259
16.5 Multi-story warehouse with no automation but accessibility pro- vided by a spiral truck ramp. . . . . . . . . . . . . . . . . . . . . 259
16.6 A highly automated distribution center in Germany. (Photo courtesy of Kai Wittek) . . . . . . . . . . . . . . . . . . . . . . . . . . 262














































































16 LIST OF FIGURES List of Tables

6.1 Four pallet positions of a sku with constant demand are arranged in various lane depths. The area that is unoccupied but unusable by other skus is waste. Area is measured in pallet positions; and a is the width of the aisle, measured as a fraction of the depth of a pallet position. . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

9.1 Local space efficiencies of each orientation of a 1 × 2 × 3 carton stored in a shelf opening of height 4 and depth 10. (H = Height, D = Depth, W = Width) . . . . . . . . . . . . . . . . . . . . . . . 126
14.1 Top ten items of a chain of retail drug stores, as measured in number of cartons moved during 3 weeks . . . . . . . . . . . . . . 217
14.2 Top ten items of a chain of retail drug stores, as measured by the number of customer requests (picks) during 3 weeks . . . . . . . 217
14.3 Top ten items of a chain of retail drug stores, as measured by the number of pieces sold during 3 weeks . . . . . . . . . . . . . . . . 218
14.4 Top ten office products measured by customer requests during a year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
14.5 Top ten office products by weight shipped during a year . . . . . 219
14.6 Top ten items moving from a grocery warehouse, as measured by number of cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235


















































































Preface

0.1 Why this book

The topic of this book is the science of warehouse layout and operations. We say ”science” because we develop mathematical and computer models. Too much of current warehousing practice is based on rules-of-thumb and simplistic ratios. This is fine as far as it goes; but there is much more that can be done. Most warehouses have elaborate records of exactly what every customer ordered and when. Typically this information is generated by the IT department as part of financial reporting; but this information can be used by operations to “tune”the warehouse layout and operations to the patterns of customer orders. This book shows you how to do this. There are other books on warehousing but they mostly confine themselves to listing types of equipment, types of order-picking, and so on. This is necessary and good; but the emphasis here is not on taxonomy but on developing methodology to optimize warehouse operations. This book is distinctive in another way as well: We try to avoid monolithic optimization models, which are expensive and inflexible. Instead we adopt an approach that emphasizes decentralizing decisions. For example, in allocating space in a warehouse, we will require each stock keeping unit to make a “business plan” that details the economic benefits it will generate in return for space; then we will rank the skus according to which offers the best return. The business plan may well be a mathematical model; but the process of allocations done simply from a sorted list. Such an approach offers great simplicity of use; indeed, one can make decisions dynamically, re-allocating space to the current best bidder of the moment. The trick is in pricing out the bids appropriately. Ultimately, this leads to a view of the pallets, cartons, pieces of product moving through the distribution center as commuters might, with each one aware of its dimensions and requirements for special handling. They might enter into negotiations with their environment to learn, for example, the available space and labor economics of each type of storage, and then make their decisions about how to move through the required processes and on to the customer. This degree of decentralization is imaginable as RFID continues to spread, placing memory and, increasingly, computing power on each item. Another example of decentralization is our treatment of “bucket brigades”





















as a new style of order-picking in which the work is reallocated by the independent movements of the workers. If the bucket brigade is configured properly, the order-pickers will balance the work amongst them and so eliminate bottlenecks. Moreover, this happens spontaneously, without intention or awareness of the workers. This means that the order-picking can be more effective than if planned by a careful engineer or manager.
To some extent the book reflects the challenges of distribution in North America, where there are relatively high labor costs, relatively low capital costs, and high volumes. However, all the tools and models we build can be used in other environments as well, even when their emphasis is on minimizing labor costs. The model will determine the “exchange rate” by which space can be exchanged for time (labor); and so anyone, even in a low labor cost region, can perform the optimization, clarify the exchange of space for time, and then make informed engineering decisions that are appropriate to his or her context.

0.2 Organization

Part I, Issues, equipment, and processes

“We begin with a brief discussion of material flow and provide an simple, aggregate way of viewing it. This “fluid model” provides useful insights in the large.
“Next we give an overview of warehouse operations: Typical kinds of warehouses; how they contribute to the operations of a business; what types of problems a warehouse faces; what resources a warehouse can mobilize to solve those problems; and some simple tools for analysis.
“We survey typical equipment used in a warehouse and discuss the particular advantages and disadvantages of each.

Part II, Warehouse layout

Warehouse layout sets the stage for order-picking, the most important activity in the warehouse. If product is staged for quick retrieval, customers will receive good service at low cost.

Everyone knows how to lay out a warehouse: Conventional wisdom says to put the fastest-moving skus in the most convenient locations. The problem is that all this depends on what is meant by “fast-moving” and what is meant by “convenient”. We elucidate this by building models of space and time (labor) to make this truism mean something precise. Frequently the answer is surprisingly at odds with standard practice and with intuition.

“We start with a particularly simple type of warehouse: A “unit load” warehouse in which the skus arrive on pallets and leave on pallets. In such warehouses, the storage area is the same as the picking area and models of space and time (labor) are simple linear models. Accordingly, we can estimate the work inherent in using storage location and the work inherent in moving each sku through the warehouse. This enables us to say exactly where each pallet should be stored to minimize labor.


“We move to more complicated warehouses in which most skus arrive packaged as pallets and leave as cartons. It is harder to make distinctions amongst all the storage locations, as we could do for unit-load, but we can identify those skus that deserve to be stored as pallets in a forward storage area to minimize labor.

“Next we examine high-volume, labor-intensive warehouses, such as those supporting retail stores: Skus may be stored as cartons and leave as pieces. Orders typically consist of many skus and may be assembled as on an assembly line. We are able to identify those skus that deserve storage as cartons in the forward most locations to minimize labor.

Part III, Order-picking

Order-picking is the most labor-intensive activity in the warehouse. It also determines the service seen by your customers. It must be flawless and fast.

“When there is a common pick-path, order-pickers can operate as a sort of assembly line, “building” each customer order and passing it downstream. We show a new way of coordinating the order-pickers in which each follows a simple, decentralized rule but global coordination emerges spontaneously.

“When there is not a pick-path that is common to all order-pickers, then it must be decided by what path an order-picker should travel through the warehouse to retrieve the items of an order.

Part IV, Automation

When is automation appropriate? How can one estimate the value conferred by automation? With what logic does one imbue automation so that it is effective? We answer these questions for some of the most common types of automation.

Part V, Special topics

Here we discuss some special types of warehouses and the issues that are unusual to them.

“A cross dock is a kind of high-speed warehouse in which product flows with such velocity that there is not point in bothering to put it on a shelf. Occupancy times are measured in hours rather than days or weeks and efficient operation becomes a matter of finely-tuned material handling.

Part VI, Measuring warehouse efficiency








iv PREFACE

“What are the essential statistics by which the operations of a warehouse are to be understood? Where is the information found?

“Which of several warehouses is most efficient? It would be nice to know because then others could copy its best practices. It can be tricky to compare the performance of two different warehouses, especially if they are of different sizes, different configuration, or serve different industries.

Part VII, Miscellaneous

“Local conditions dictate different designs and operations in warehouses around the world. Sometimes what appears to be obvious inefficiency is a rational response to local economics.

In teaching the graduate class in warehousing and distribution at Georgia Tech, we generally follow the book from start to finish, with a single exception. When the class is engaged in a project for a company, we insert a lecture on warehouse activity profiling (Chapter 14) early in the course so the students know how to mine the data typical to a
warehouse.

0.3 Resources

We support this book through our web site www.warehouse-science.com, from which you may retrieve the latest copy and find supporting materials, such as photographs, data sets, programming tools, and links to other resources. We are constantly adding to this collection. The photographs and data sets are from our consulting and from generous companies, whom we thank. At their request, some company identities have been disguised and/or some aspect of the data cloaked.

0.4 But first . . .

A few friends and colleagues have contributed so much to the work on which this book is based that they deserve special mention. We particularly thank Don Eisenstein of the University of Chicago (Chapter 11 and more), Kevin Gue of Auburn University (Chapter 13), and Pete Viehweg for critical reading through-out and comments based on years of experience in industry. Their contributions have been so important that each has some claim to co-authorship. In addition, we have relied on the work of Ury Passy of The Technion (Chapter 8) and Loren”Dr. Dunk” Platzman (Chapter 8). We also thank many friends and colleagues who caught errors or suggested improvements. These include Ileana Castillo of Monterrey Tech, Chen Zhou of Georgia Tech, Russ Meller of the University of Arkansas, and Jacques Renaud of Universit ́ Laval. Thanks also to many students who suffered under earlier versions and found errors: Ayhan Aydin, KarinBoonlertvanich, Asgeir Brenne, Christian Buchmann, Wilson Clemons, Anwesh





0.4. BUT FIRST . . . v

Dayal, Mike Depace, Ozan Gozbasi, Huang Chien-Chung, Li Jiexin, and RonChung Lee. Remaining errors are, we both agree, the fault of my co-author.




































































































vi PREFACE

Part I
Issues, equipment, processes 1

































































































Warehouses are the points in the supply chain where product pauses, however briefly, and is touched. This consumes both space and time (person-hours), both of which are an expense. The goal of this book is to develop mathematical and computer models to allow you to reduce space and time requirements or to exchange one for the other. But first it is necessary to understand the role aware house serves in the supply chain and the means by which it does this. This part starts with the big picture and then looks inside a warehouse































































































Chapter 1

Warehouse rationale

1.1 Why have a warehouse?

Why have a warehouse at all? A warehouse requires labor, capital (land and storage-and-handling equipment) and information systems, all of which are ex-pensive. Is there some way to avoid the expense? For most operations the answer is no. Warehouses, or their various cousins, provide useful services that are unlikely to vanish under the current economic scene. Here are some of their uses:

To better match supply with customer demand: One of the major challenges in managing a supply chain is that demand can change quickly, but supply takes longer to change. Surges in demand, such as seasonalties strain the capacity of a supply chain. Retail stores in particular face seasonal ties that are so severe that it would be impossible to respond without having stockpiled product. For example, Toys R Us does, by far, most of its business in November and December. During this time, their warehouses ship product at a prodigious rate (some conveyors within their warehouses move at up to 35 miles per hour). After the selling season their warehouses spend most of their time building inventory again for the following year. Similarly, warehouses can buffer the supply chain against collapsing demand by providing space in which to slow or hold inventory back from the market.

In both cases, warehouses allow us to respond quickly when demand changes. Response-time may also be a problem when transportation is unreliable. In many parts of the world, the transportation infrastructure is relatively undeveloped or congested. Imagine, for example, shipping sub-assemblies to a factory in Ulan Bator, in the interior of Asia. That product must be unloaded at a busy port, pass through customs, and then travel by rail, and subsequently by truck. At each stage the schedule may be delayed by congestion, bureaucracy, weather, road conditions, and so on. The result is that lead time is long and variable.





















If product could be warehoused in Shanghai or closer to the point of use, it could be shipped more quickly, with less variance in lead time, and so provide better customer service.

Warehouses can also buffer against sudden changes in supply. Vendors may give a price break to bulk purchases and the savings may offset the expense of storing the product. Similarly, the economics of manufacturing may dictate large batch sizes to amortize large setup costs, so that excess product must be stored. Similarly, warehouses provide a place to store a buffer against unreliable demand or price increases.

To consolidate product to reduce transportation costs and to provide customer service.

There is a fixed cost any time product is transported. This is especially high when the carrier is ship or plane or train; and to amortize this fixed cost it is necessary to fill the carrier to capacity. Consequently, a distributor may consolidate shipments from vendors into large shipments for downstream customers. Similarly, when shipments are consolidated, then it is easier to receive downstream. Trucks can be scheduled into a limited number of dock doors and so drivers do not have to wait. The results are savings for everyone.

Consider, for example, Home Depot, where more than a thousand stores are supplied by several thousands of vendors. Because shipments are frequent, no one vendor ships very much volume to any one store. If shipments were sent direct, each vendor would have to send hundreds of trailers, each one mostly empty; or else the freight would have to travel by less-than-truckload carrier, which is relatively expensive. But there is enough volume leaving each vendor to fill trailers to an intermediate cross dock. And each cross dock receives product from many vendors for each store, so that the total freight bound for each store is typically sufficient to fill a trailer. The result is that vendors send fewer shipments and stores receive fewer shipments. Moreover, the freight will have traveled by full-truck-load and so paid significantly less transportation costs.

Another example of the benefits of consolidation is when the differentiation of product is postponed, typically within the warehouse. For example, the finished-goods warehouse of a manufacturer of pet food held 1,500 different products, which represented only 25 different recipes. By holding the product as “bright stack” (unlabeled cans), the product differentiation was postponed until the customer placed an order, when the appropriate cans would be labeled and shipped. This postponement allowed the safety stocks of the 1,500 products to be consolidated into only 25 safety stocks, which were easier to manage and could be reduced due to pooling of risk.

To provide value-added processing: Increasingly, warehouses are being forced to assume value-added processing such as light assembly. This is a result of manufacturing firms adopting a policy of postponement of product differentiation, in which the final product is configured as close to the customeras possible. Manufacturers of personal computers have become especially adept at this. Generic parts, such as keyboards, disk drives, and so on, are shipped to a common destination and assembled on the way, as they pass through a warehouse or the sortation center of a package carrier. This enables the manufacturer to satisfy many types of customer demand from a limited set of generic items, which therefore experience a greater aggregate demand, which can be forecast more accurately. Consequently safety stocks can be lower. In addition, overall inventory levels are lower because each item moves faster.

Another example is pricing and labeling. The state of New York requires that all drug stores label each individual item with a price. It is more economical to do this in a few warehouses, where the product must be handled anyway, than in a thousand retail stores, where this could distract the workers from serving the customer.

1.2 Types of warehouses

Warehouses may be categorized by type, which is primarily defined by the customers they serve. Here are some of the more important distinctions:

A retail distribution center typically supplies product to retail stores, such as Wal-Mart or Target. The immediate customer of the distribution center is a retail store, which is likely to be a regular or even captive customer, receiving shipments on regularly scheduled days. A typical order might comprise hundreds of items; and because the distribution center might serve hundreds of stores, the flow of product is huge. The suite of products changes with customer tastes and marketing plans.

A service parts distribution center is among the most challenging of facilities to manage. They typically hold spare parts for expensive capital equipment, such as automobiles, airplanes, computer systems, or medical equipment. Consequently, a typical facility contains a huge investment in inventory: tens of thousands of parts, some very expensive. (A typical automobile contains almost 10,000 parts.) Because of the large number of parts, total activity in the DC may be statistically predictable, but the demand for any particular part is relatively small and therefore hard to predict. This means that the variance in requests is large and so large quantities of safety stock must be held. Furthermore, when a part is requested, it is generally very urgent, because an important piece of capital equipment might be unusable, such as a truck or a MRI device. To further compound the challenges, there is a typically long lead times to replenish parts to the warehouse.

It is not unusual for customer orders to fall into one of two distinct categories: Some customers, such as vehicle dealers or parts resellers, typically submit large orders, for 10”™s or 100”™s of different skus; while other










customers, such as independent repair shops, might order only what they need to repair a single vehicle. Worse, customers ordering for repair might order before they are absolutely sure which parts need replacement; and so there can be a significant percentage of returns to be handled at the warehouse.

A catalog fulfillment or e-commerce distribution center typically receives small orders from individuals by phone, fax, or the Internet. Orders as typically small, for only 1”“3 items, but there may be many such orders, and they are to be filled and shipped immediately after receipt.

A 3PL warehouse is one to which a company might outsource its warehousing operations. The 3PL provider might service multiple customers from one facility, thereby gaining economies of scale or complementary seasons that the customers would be unable to achieve on their own. 3PL facilities may also be contracted as overflow facilities to handle surges in product flow.

While there are many types of warehouses in the supply chain, one of the main themes of this book is that there is a systematic way to think about a warehouse system regardless of the industry in which it operates. As we shall show, the selection of equipment and the organization of material flow are largely determined by “Inventory characteristics, such as the number of products, their sizes, and turn rates; “Throughput and service requirements, including the number of lines and orders shipped per day; “The footprint of the building and capital cost of equipment.








Chapter 2

Material flow

Here we briefly discuss a few issues that help lay the foundations for warehouse analysis.

2.1 The fluid model of product flow

The “supply chain” is the sequence of processes through which product moves from its origin toward the customer. In our metaphor of fluid flow we may say that warehouses represent storage tanks along the pipeline.

The analogy with fluid flows can also convey more substantial insight. For example, consider a set of pipe segments of different diameters that have been joined in one long run. We know from elementary fluid dynamics that an in-compressible fluid will flow faster in the narrower segments of pipe than in the wider segments. This has meaning for the flow of product: The wider segments of pipe may be imagined to be parts of the supply chain with large amounts of inventory. On average then, an item will move more slowly through the region with large inventory than it will through a region with little inventory. The fluid model immediately suggests other general guidelines to warehouse design and operation, such as:

“Keep the product moving; avoid starts and stops, which mean extra handling and additional space requirements.

“Avoid layouts that impede smooth flow.

“Identify and resolve bottlenecks to flow.

Later we shall rely on the fluid model to reveal more profound insights.
It is worth remarking that the movement to “just-in-time” logistics is roughly equivalent to reducing the diameter of the pipe, which means product flows more quickly and so flow time and in-transit inventory are reduced (Figure 2.1).












CHAPTER 2. MATERIAL FLOW

Figure 2.1: If two pipes have the same rates of flow, the narrower pipe holds less fluid. In the same way, faster flow of inventory means less inventory in the pipeline and so reduced inventory costs.



2.2 Units of handling

Even though it is a frequently useful metaphor, most products do not, of course, flow like incompressible fluids. Instead, they flow more like a slurry of sand and gravel, rocks and boulders. In other words, the product is not infinitely divisible but rather is granular at different scales.

A “stock keeping unit” is the smallest physical unit of a product that is tracked by an organization. For example, this might be a box of 100 Gem Clip brand paper clips. In this case the final customer will use a still smaller unit(individual paper clips), but the supply chain never handles the product at that tiny scale.

Upstream in the supply chain, product generally flows in larger units, such as pallets; and is successively broken down into smaller units as it moves down-stream, as suggested in Figure 2.2. Thus a product might move out of the factory and to regional distribution centers in pallet-loads; and then to local warehouses in cases; and finally to retail stores in inner-packs or even individual pieces, which are the smallest units offered to the consumer. Thus means that our fluid model will be most accurate downstream, where smaller units are moved.

2.3 Storage: “Dedicated” versus “Shared”

Each storage location in a warehouse is assigned a unique address. This includes both fixed storage locations, such as a portion of a shelf and mobile locations such as the forks of a lift truck. Storage locations are expensive because they represent space, with consequent costs of rent, heating and/or air-conditioning, security, and so on. In addition, storage locations are typically within specialized



2.3. STORAGE: “DEDICATED” VERSUS “SHARED”

Figure 2.2: A product is generally handled in smaller units as it moves down the supply chain. (Adapted from “Warehouse Modernization and Layout Planning Guide”, Department of the Navy, Naval Supply Systems Command, NAVSUPPublication 529, March 1985, p 8”“17)

















.12 CHAPTER 2. MATERIAL FLOW



2.3: An idealization of how the inventory level at a location changes overtime equipment, such as shelving or flow rack, which are a capital cost. These costs impel us to use storage space as efficiently as possible.
There are two main strategies used in storing product. The simplest is dedicated storage, in which each location is reserved for an assigned product and only that product may be stored there. Because the locations of products do not change, more popular items can be stored in more convenient locations and workers can learn the layout, all of which makes order-picking more efficient.

The problem with dedicated storage is that it does not use space efficiently. This can be seen by tracking the amount of inventory in a given location. If we plot the inventory level, measured for example by volume, we would see a saw tooth shape such as in Figure 2.3 (which represents an idealization of the inventory process.) In one cycle, the storage location is initially filled but empties as product is withdrawn to send to customers. As a result, on average this storage location is half empty. A warehouse may have thousands or tens-of-thousands of storage locations. If using dedicated storage, each will have an assigned product. Each product may have a different replenishment cycle and so, upon entering such a ware-house, one expects to see many storage locations
Considero que mi candidatura les puede resultar interesante porque reúno los requisitos que ustedes demandan. Como pueden comprobar en mi curriculum vitae, tengo 4 ańos de experiencia en los Departamentos Técnicos de la empresa LARS, donde he sido responsable de la ejecución y desarrollo de proyectos complejos.

Espero consideren mi curriculum vitae y concierten una entrevista próximamente. En espera de su respuesta.

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María García
   
 
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