A Special Case of the Quadratic Assignment Model with an Application to Storage-and-Retrieval Devices

In a storage-and-retrieval device, items are stored in the slots of the storage bank for subsequent retrieval by a picking mechanism as needed. Many varieties of these robotic devices are in use in manufacturing as well as in logistics and in computer peripherals. The problem of assigning items by type to storage slots in order to minimize the total distance traveled by the picking mechanism is a quadratic assignment model. Although such problems in general are very difficult to solve to optimality, we exhibit a special case that admits an easy solution, namely, the well known “organ pipe” arrangement of items. We illustrate the relevance of the special case to printed circuit board manufacturing.