New Paper: Chevrons, Leaves, and Butterflies

I am pleased to announce that a new paper co-authored with Ömer Öztürkoğlu and Russ Meller entitled, “Optimal unit-load warehouse designs for single-command operations,” will appear in IIE Transactions. The paper introduces three new designs—the Chevron, Leaf, and Butterfly, each of which is optimal for a range of warehouse sizes. You can download a pre-press version of the paper here.

The Chevron design has a single, vertical cross aisle and picking aisles at angles 45 and 135 degrees. As with the Fishbone design, the idea is to allow workers to take “straight line paths” to locations as closely as possible.

The Leaf design is similar to the Fishbone in that it has two cross aisle segments, but we have relaxed the requirement that picking aisles be vertical or horizontal. Cross aisles in the Leaf design are steeper than in a Fishbone design, and picking aisles on the right and left sides are at an angle that reduces expected travel.

Notice that the Leaf requires more space around the pickup & deposit (P&D) point at the bottom,  which is a disadvantage of the design because the otherwise best locations are displaced.  This phenomenon is even more notable in the Butterfly:

So, there is a tradeoff: increasing the number of cross aisles makes travel nearer and nearer to direct “travel-by-flight,” but at the cost of displacing the locations nearest the P&D point. When is it no longer beneficial to add additional cross aisles?

Below is a plot that partially answers that question. The Chevron design has the lowest expected travel distance (highest percent improvement over a traditional design) when the number of aisles in an equivalent traditional design is 27 or fewer. For warehouses between 29 and 63 aisles, the Leaf design is slightly better than Chevron. For warehouses greater than 65 aisles, the Butterfly is ever-so slightly better than Leaf.

Above I said that expected travel distance only partially answers the question of which design to choose. That’s because the sacrifice in space for these designs is very different. Below is a plot of percent increase in area (over an equivalent traditional design, which is very dense) for each of the designs at a variety of sizes. It should be clear from the plot that the Butterfly is simply not competitive on space terms alone. For very large warehouses, the Leaf provides only slightly better travel distance, but a significantly higher requirement for space.

These observations lead us to conclude that for operations conforming to our main assumptions the Chevron is the best design for warehouses of realistic size. For all the details, please read the paper!

Warning: The results of this paper are relevant only for single-command operations, in which workers visit a single location to make a pick or a stow. These designs are not intended for order picking operations, in which workers visit many locations during a picking tour.

If you are considering implementing one of these designs, please contact me with the form below:

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