Optimal Block Stacking

I am pleased to announce that Shahab Derhami, Jeff Smith and I have just had a manuscript accepted in International Journal of Production Research entitled, “Optimizing Space Utilization in Block Stacking Warehouses.” Congratulations especially to Shahab—this is the first paper from his dissertation research!

The origin of this paper was a consulting engagement Jeff and I had with a beverage manufacturer, in which pallets roll off a production line and then are stored for a time before shipping. The finished goods warehouse uses deep lane block stacking, as is common in many large lot, unit load handling environments. The company wanted to know how deep lanes should be to make the best use of space.

Space lost due to honeycombing

Block stacking warehouses waste space in two ways: aisles to allow lift truck travel and partially filled lanes, which another sku cannot occupy because it would block access to the sku already stored there. As explained in Bartholdi and Hackman’s textbook, each lane makes a contribution to both types of waste. If lanes are too shallow, then too much storage space is devoted to aisles; if too deep, then too much storage lane space is wasted. An optimal design balances this tradeoff.

The academic literature has well-known results for optimal lane depth in the case of instantaneous resupply, which is appropriate for warehouses storing product received from suppliers. Pallets for a particular sku arrive at the same time, so the production rate is “infinite.” A second assumption behind existing results is continuous demand, rather than discrete demand. Our paper relaxes both of these assumptions: production rate can be finite—even less than the rate of demand, and demand is discrete. (The production rate can be less than the rate of demand if demand is only intermittent. Imagine all demand for a particular sku happening only on Friday, for example.) The paper develops approximations for the optimal lane depths for block stacking areas with one or multiple skus.

The main insight we develop in the paper is that using the infinite production rate model in a finite production rate environment produces lane depths about twice as deep as they should be, but that the resulting loss of space is modest (less than about 2 percent). Said another way, the space utilization curve, as a function of lane depth, is quite flat.

However, shorter, optimal lanes means more aisles and therefore more flexibility with respect to travel for lift truck drivers or autonomous vehicles. The effects of lane depth on travel costs have not been considered in our work or in the literature.

We welcome your comments.



  1. Kev,
    Found your paper by Googling “lane depth selection in block stacking warehouse” (you’ll want to know why, and I’ll tell you in Karlsruhe, assuming you’ll be there). Isn’t it amazing that in the 35 years since Jessica’s dissertation, you are the first guys to say, “Wait a minute, the pallets don’t all show up at the same time!” Just goes to show that there are still plenty of interesting problems waiting out there for somebody to identify. Well done!

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