Information about Goetschalckx Ratliff Order Picking In An Aisle

ORDER PICKING IN AN AISLE

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

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

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

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 M ost 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.

M ost 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.

a T here are 2 basic problems associated with finding a picking tour: Within aisle sequencing problem Between aisle sequencing problem

T here are 2 basic problems associated with finding a picking tour:

Within aisle sequencing problem

Between aisle sequencing problem

P roblem of finding an optimum between aisle sequence Travelling Salesman Problem F or 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

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:

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 Advantage Pattern 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 X X: Integer factor of M TE: 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.

T he 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.

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 i s worthwhile compared to simple traversal policy when # of aisles is very small or order density is low.

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 i s 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

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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