goetschalckx ratliff order picking in an aisle

Order Picking In an AisleArticle by

M.Goetschalckx & H.D. RatliffPresentation by

Zeynep Cançelik

OUTLINE•Policies for picking within an aisle

•Ratliff and Rosental Algorithm

•Optimum Traversal Aisle Tours

•Optimum Aisle Traversal Algorithm

•Cutler Planar TSP

•Optimum “Z” Pick

•Simulations

v

PROBLEM

-Items have to be picked from both sides of an aisle,

-Picker cannot reach items o both sides without changing position

Most warehouses are composed of parallel aisles up to twelve or more feet wide, allowing;

• Products be stored on pallets using fork lifts,•Two way aisle traffic,•Space to pass in the aisles•Space to turn aroun in the aisles.

aThere are 2 basic problems associated with finding a picking tour:

•Within aisle sequencing problem

•Between aisle sequencing problem

Problem of finding an optimum between aisle sequence

Travelling Salesman Problem

For warehouses with single block of parallel aisles with cross aisles only at the ends

Ratliff and Rosental Algorithm

Traversal Aisle Picking Return Aisle Picking

Optimum Traversal Aisle Tours

AW

A : width of 1 slot

M : number of slots on 1 side of the aisle

W :width of the aisle measured in slot widths.

N :number of items in 1 order

n : number of items stored on the left side

m : number of items stored on the right side

Optimum Aisle Traversal Algorithm

No Skip Property:Before an item Rk can be picked in an optimal traversal picking sequence, all of the items R1, R2,...,Rk-1 must already have been picked. (Same holds for the right side.)

B

A

Cutler Planar TSP

•All points lie on 2/3 parallel lines

•O(N^2) Algorithm: # of steps required can be expressed as a quadratic func. of # of points.

• State (Ri, Li, k) •Ri : last item picked on right side•Li: Last item picked on left side•K: picker is currently on the left/ right side

Travel required for those transitions:

The travel for the transition from entry node and to exit node

for right & left

Shortest Path Graph for the Traversal Policy

• Total of (n+1)*m + (m+1)*n+2 = 2*n*m nodes in the graph

•On average n &m are equal to N/2

•Any node has at most 2 outgoing and 2 incoming arcs.

•Computational effort is proportional to number of nodes.

•Sorting items by non decreasing coordinates:

Example of a Traversal Sequence

in an Aisle

Distance required for optimal picking sequence is 19.39

Shortest Path Graph

Optimum “Z” Pick

Each slot is picked in a fixed sequence which remains the same for all orders.

Fixed “Z” Sequence Picking Tour

Case where order contains an item from every slot

Major AdvantagePattern only has to be determined once!

Repetitive Z-pick Pattern

Optimum Length for Z Pattern

(assuming all the slots are visited)

TH(X) : Total travel required by a pattern of length XX: Integer factor of MTE: Travel from entry point to first item+ travel time from last item to exit point

Optimum Traversal Pick Simulation

Influence of the # of items in order & width of the aisle on the picking time are examined.

The variable travel doubles when density of the orders double.

Z-Pick Simulation

•Fixed sequence travel is 12% longer than optimal traversal travel

•Difference is maximal for an aisle with of 4

•Optimization is worthwhile for all cases except for low density and narrow aisles.

OptimumReturn Simulation

O.P.S: Pick all items on one side, cross to the last item on the other side, then pick all items on that side on the return.

Traversal Versus Optimum Block

Simulation

Optimum split traversal and return policies are required!

CONCLUSIONS

•Problem of determining the optimal picking sequence for a single aisle can be solved efficiently on computers.

•Optimum fixed sequence Z-pick is very suitable for manually managed systems; but results in a substantial increase in distance (up to 30%).

•For most practical densities traversal policy is better.

•Rathliff and Rosental is worthwhile compared to simple traversal policy when # of aisles is very small or order density is low.

References

•M.Goetschalckx, M. and H.DRatliff (1988). “Order Picking In An Aisle,” IIE Transactions, 20:1,pp 53-62, viewed 6 March 2008, <http://www.informaworld.com/smpp/title~content=t713772245>

•Assist. Prof. Gürdal Ertek’s “creating good presentations” package

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