# Given a set of sets and a storage area, find an order that minimizes the sum of the differences between each set and the storage area

This problem is based on an order picking problem with a forward area.

The problem description is as follows. We have a warehouse with a set of items $I$ and a forward area $F$ of size $k$. Each day, there is a set $D$ of deliveries. Each delivery $d_i$ is a set of items such that $d_i \subset I$ and $|d_i| < k$. The items for each delivery have to be picked from $F$ and each delivery must be completed before the items for the next delivery can be picked. The items in $F$ are not consumed ($F$ contains pallets of each item, and we assume that a pallet does not run out). If a delivery requires an item that is not in $F$, the required item can be swapped with an existing item.

We now need to find an order $d_1,...,d_n$, such that we minimize the amount of swaps needed.

My question is: is there any available literature on this kind of problem? Specifically regarding genetic algorithms, since that is the goal of my research.

Thus far, the closest thing I have found is the Traveling Salesman Problem, using the minimum number of swaps between deliveries as distance measure. However, since the items in $F$ are not only influenced by the predecessor of a delivery, the distance between two consecutive deliveries also depends on (all) previous deliveries.

• Are you after the problem's complexity or algorithms for solving it? – Raphael Oct 3 '14 at 10:09