The proposed methodology will derive the allocation of stores
to floor locations, minimizing the total distance travelled within
the warehouse. The distance will be the sum of the picking and
shipping distance. In the shipping distance, it is considered that
each store orders’ are moved from the floor location to the shipping
dock independently from other stores – each store will have multiple
pallets and their movement is done in one or more pallet
truck routes.
On the other hand, the picking distance is more elaborated.
Consider one pallet of boxes of bananas. This pallet will be distributed,
usually, by more than one store. In this way, the picking
distance is obtained by the distance travelled in a route that visits
more than one floor location. In order to overcome the routing
problem, integrated with the allocation problem, our model is built
over the concept of clusters of floor locations.
A cluster of floor locations is a group of N floor locations, that
are neighbours (i.e., they are immediately located side-by-side)
and that will be visited by one worker in one picking route. In this
way, if the picking starts in floor location a1, it will continue until
floor location ax, where x is the number of floor locations in that
cluster. Thus, the distance travelled in this route is the distance
from the reception point to location a1, the linear distance (we only
assume linear clusters, i.e., all floor locations located in the same
aisle) of the cluster and the distance from location ax to the reception
point, so the worker can start a new picking operation. In the
example of Fig. 2, a cluster with 6 floor locations is exemplified.
In order to define the number of floor locations per each cluster,
we require specific data from the problem at hand. This data will
enable to calculate, for the period of data gathered, the average
number of stores whose demand is fulfilled from one pallet. With
this data, a fixed size of clusters is defined. The required data
encompasses the following items: (i) the list of stores to whom
the demand has to be fulfilled and adequately numbered, (ii) the
list of floor locations adequately numbered, (iii) the distance from
each floor location to the reception point, considering that each
floor space is divided in carton and plastic boxes and that this division
may require different distances to the reception point, (iv) the