## Detailed Design of Fishbone Warehouse Layout

Warehouses around the world have the same layout, called the traditional layout, which is characterized by the arrangement of parallel aisles, orthogonal to the walls. In 2009, Gue and Meller introduced the fishbone layout, a layout with two diagonal cross aisles and the aisles in the lower zones are perpendicular to the aisles in the upper zones. The improvement in the performance of the layout is accomplished by making travel distances closer to be Euclidean. rather than the rectilinear paths that have to be traveled in traditional layouts. Gue and Meller found that the expected travel distance of the fishbone layout is up to 20% lower compared with traditional layouts for unit load warehouses with single command operations.

The fishbone layout has also caught the attention of warehouse practitioners, who have implemented it in some warehouses and distribution centers, mostly in the United States. These implementations are mostly supported by human decision making and expert guidance, given that there is not a scientific method to design the storage area. In a fishbone layout these become important, because obtaining a regular pattern for the arrangement of the racks while satisfying a desired storage capacity is a highly complex combinatorial problem.

In a paper entitled “Detailed design of fishbone warehouse layouts with vertical travel”, we present a mathematical model to design fishbone warehouses.

The paper shows how to answer questions such as

- How many openings should each aisle contain? and
- What is the best angle for the diagonal aisles?
- How high should racks be?

The goal is to make an optimal tradeoff between material handling cost and cost of space. Our method is useful for practitioners when all openings of the warehouse are equal, a random storage policy is adopted and the material handling system is constituted only by forklifts (all forklifts are equal).

source: Kevin Gue

We start by establishing a standard geometry for fishbone layouts.

- The layout is constituted by four triangular areas, which we will call Zones and we denote them as Zone
_{1}, Zone_{2}, Zone_{3}, and Zone_{4}. - The four triangular zones are equal.
- The line segment between p
_{1}and p_{2}is perpendicular to the line segment between p_{1}and p_{3}. - There is a central aisle between Zone
_{2}and Zone_{3}. - All aisles have the same width.

Based on this standard geometry, we developed an algorithm that designs a fishbone layout given four characteristics:

- The number of openings of the top row of Zone
_{1}(s) . - The number of rows in Zone 1 (n).
- The number increment in number of openings between rows in the Zone
_{1 }(I_{2}) . - The number of tiers of openings (T)

Then, we present an optimization model that finds the values for the four primary characteristics that minimize the total operational cost of the warehouse. Finally, we solve the optimization model using a genetic algorithm.

Contrary to several approaches where usually only one aspect is taken into account for defining the warehouse layout (generally the expected travel distance), our model is more complete as it delivers

the detailed design of the layout, optimizing the total operational cost of the warehouse, considering both area cost and material handling cost. Additionally, our method provides its output in a practical way

for a warehouse practitioner as it delivers the coordinate (x, y, z) for each opening of the layout.

We demonstrated the use of our method through a hypothetical numerical example based on a typical operation of a distribution center in Kentucky, USA, which helps us to illustrate implementation insights. Since the introduction of the fishbone design, the expected improvement on the expected travel distance is 20% leading to lower material handling cost compared with parallel aisles design. But it is also expected that the area of a fishbone design will be greater than that of a parallel aisles design for the same desired storage capacity, in consequence, higher area cost is expected. Therefore when comparing the fishbone layout with the parallel aisles design, there is a trade off between area cost and material handling cost.

This method aims to diminish dependence upon experts and human decision making in the process of implementing a fishbone layout on greenfield projects, and fulfills an identified need of warehouse practitioners by integrating the most recent advances on non-traditional layouts and detailed warehouse design.