L9 Detailed slotting - Lunds tekniska högskola · L9 – Detailed slotting MTTN25 – Warehousing and Materials Handling Joakim Kembro Engineering Logistics ... problems, in discrete

MTTN25 2011‐09‐16

Warehousing and Materials Handling 1

LUNDS UNIVERSITETLUNDS UNIVERSITET

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L9 – Detailed slottingMTTN25 – Warehousing and Materials Handling

Joakim KembroEngineering Logistics

Lund University2010-09-14


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Learning objectives

• Understand underlying logic behind slotting SKUs a in warehouse

• Understand how the placement and orientation of SKUs affect efficiency

• Learn how to package SKUs into a warehouse


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Content

• General slotting

• Case orientation

• Packing shelves


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Slotting refers to the careful placement of individual cases within the warehouse

• The most immediate goals in slotting a warehouse are the following:

– Squeeze more product into available space– Achieve ergonomic efficiency by putting popular and/or heavy

items at waist level• At the same time, one wants to avoid creating congestion by

concentrating popular items too much• Store similar-looking products apart to reduce the chance of a

picking error• Storing products in the warehouse by product family

– Store products by order affinity– Cost in space, but save in labor

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Turning the product flow of a warehouse into a spaghetti dish, reveals areas with congestion

STENA Technoworld GmbH

- for internal use only -

Congestion between forklift trucks

Compression of TV-boards is time consuming

Limited space available for safety stock Low productivity. Long

average throughput time compared to observed

Production disruptions due to tools and material handling

Dismantling line is occasionally starved due to lack of material

Scaling cages and pallets increase non-value added time

Improve downstream solutions for TV-boards and Plastics

Folding of cages is time consuming

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Placement and slotting in the warehouse

• Store according to ergonomic efficiency (waist and chest levels: golden-zoning


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Placement and slotting in the warehouse

• Store by some group identification (picked and packed together)

• Store by order affinity– Travel reduction: Storing two SKUs near each other may reduce

the travel of the order pickers– Order completion: If two items that are frequently requested

together also frequently comprise the entire order, then one can, in effect, convert the 2-line order to a single line order by storing those two SKUs together

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Content



• Packing shelves

• Modeling in AMPL


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Case orientation and stack level

• Most significant for SKUs stored in less-than-pallet quantities

• Storage unit of many such SKUs is a carton

• Placed on a shelf in any of up to six orientations

• Once an orientation has been selected, shelf space above and behind is unusable by other items


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Case orientation and stack level can determine shelf efficiency

• Assume that we have – A carton with dimension {1 × 2 × 3}– Shelf opening of height 4 and depth 10

• Then, we get a shelf efficiency accordingly:

H,D,W {1,2,3} {1,3,2} {2,1,3} {2,3,1} {3,1,2} {3,2,1}Efficiency 1 0.9 1 0.9 0.75 0.75


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Content



• Packing shelves

• Modeling in AMPL

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Packing the right way increase space utilization

• Assume that n SKUs to be slotted are known together with the quantity of each

• SKUs are to be slotted into shelf openings, all of identical and fixed dimensions

• Use the fewest shelf openings possible to hold all SKUs• General logic:

– Sort SKUs in a list– Take the next SKU from the list and pack it onto the shelf most

suitable for it– Once placed, never reconsider


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Formulating the bin-packing problem

• I = {1,…,n}, set of n items• J = {1,…,m}, set of m bins• vi = weight of item i

• c = capacity of the bin• xij = pack item i in bin j

(yes/no)• yi = open bin j (yes/no)


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Next-fit: Place item in open bin if it fits, otherwise open new bin

• Initialization:– Given a list of item weights, L = {w1,w2,…,wn}– Place item 1 in bin 1 and remove from L.

• Iterations:1. If item i fit in bin j, place i in j. If not, open a new bin j + 1 and

place i in bin j + 1. Let m = m + 12. Remove item i from L. Let i = i + 13. While items remain in L, repeat from Step 1


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First-fit: Keeps unfull bins open and places next item in lowest-numbered bin in which it fits


• Iterations:1. Find the lowest numbered bin j in which item i fits, and place i

in j. If i does not fit in any bin, open a new bin and number it m+ 1 and let m = m + 1

2. Remove item i from L. Let i = i + 13. While items remain in L, repeat from Step 1

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Best-fit: Keeps unfull bins open and places next item in fullest bin in which it fits


• Iterations:1. Find the bin j whose contents are maximum but not greater

than 1 – wi (empty space in bin i), and place i in j. If i does not fit in any bin, open a new bin and number it m + 1 and let m = m + 1

2. Remove item i from L. Let i = i + 13. While items remain in L, repeat from Step 1


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Assignment

• Implement bin-packing algorithm of choice• Pack SKUs into shelves (Each shelf has width 10)• How many shelves are needed?• What is the level of utilization?• Compare to optimal solution!

Item 1 2 3 4 5 6 7Width 5 6 7 4 8 2 1Next-fitBest-fit


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Additional packing algorithms

– Worst-fit– First-fit decreasing– Best-fit decreasing

– If you want to use as few shelves as possible: Pack from a list in which the skus have been sorted from greatest width of allocation to least.

– If you wish to concentrate picking: Pack from a list in which skushave been sorted from most picks per width of allocation to least.

– If there are shelves of different heights: Put each sku on the least-high shelf on which it will fit.


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Mid-class review

• What has been good so far?

• What needs to be improved?

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Content



• Packing shelves

• Modeling in AMPL (optional)


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What is AMPL?

• AMPL - A Modeling Language for Mathematical Programming

• Linear and nonlinear optimization problems, in discrete or continuous variables

• Use common notation and familiar concepts to formulate optimization models and examine solutions

• See http://www.ampl.com


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Concept of AMPL

Run

Model

Data

Run

Model

DataAMPL Solver Output


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Formalization of the problem of allocating Nforward pallet positions

• subject to

• ui pallets of SKU i are stored in the forward pick area, zi

• li pallets of SKU i are stored in the forward pick area, xi

• ui − li pallets of SKU i are stored in the forward pick area, yi

max spi crdi xi sDi crdi yi i s p j D j

j z j

li xi ui li yi i u jz j

j N

xi, yi ,zi 0,1 yi xi

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Model-file

• Sets:– SKU list

• Parameters:– SKU data– Process times– Pallet positions

• Variables:– Include minimum or not, xi

– Include the rest or not, yi

– Include all or not, zi

• Objective: Maximize benefit in FPA• Constraints: Keeping FPA SKUs within capacity limit

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Run

Model

Data

Run

Model

Data


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Data-file (contains the actual data)

• Sets: – SKU list

• Parameters:– Number of less-than-pallet picks, pi

– Number of pallets moved by such picks, di

– Number of pallets moved by full-pallet picks, Di

– Minimum number of pallets to be stored in the FPA, li– Maximum on-hand inventory, ui

– Average savings in minutes from the FPA s– Minutes per restock of the forward area, cr

– Number of pallets positions, N

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Run

Model

Data

Run

Model

Data


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Run-file

• option solver ‘<<solver name>>’• model <<name>>.mod• data <<name>>.dat• solve (invokes solver)• display objective• display <<name of variable>>

Also possible to write results to a file!• (display variable >> filename.out;)

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Run

Model

Data

Run

Model

Data


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Learning objectives

• Understand underlying behind slotting SKUs in warehouse• Understand how the placement and orientation of SKUs affect

efficiency• Learn how to package SKUs into a warehouse• Learn to model an optimization problem using AMPL

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Thank you for today!

Joakim KembroPhD Candidate

Department of Industrial Management and Logistics

Box 118, SE-221 00 LUND, SwedenVisiting address Ole Römers väg 1, Lund

Phone +46 46 222 33 27Fax +4 46 222 46 15

E-mail [email protected]

Documents

L9 Detailed slotting - Lunds tekniska högskola · L9 – Detailed slotting MTTN25 – Warehousing and Materials Handling Joakim Kembro Engineering Logistics ... problems, in discrete