Elementary Theory of Optimal Silo Storage Design

Abstract

This study indicates a method for calculating an economic division of warehouses into compartments when different varieties have to be stored simultaneously and separately. The study deals with cases where the total storage capacity demand and the number of varieties are known and fixed, but where the storage capacity demand of each variety is unknown. Problems of this nature exist in the preliminary designing of grain silos, fleets of transport vehicles, utensils in public kitchens, etc. If the warehouse capacity can cope with the total storage capacity demand, but the number of compartments is insufficient, it is possible that part of the material to be stored cannot be accommodated, although certain compartments may only be partly filled; this will be due to the impossibility of storing different varieties together. The materials will have to be stored in other warehouses, at a higher charge per capacity unit than that of the warehouse in question.

The division of the warehouse into a large number of compartments will assure storage of most, if not all, the material. On the other hand, increase in the number of compartments (and installations) makes for increased investment in transport installation, partitions and additional storage capacity to compensate for space taken up by these partitions and installations.

The object of this study is to introduce a method for calculating the optimal division of a warehouse into compartments, so that the annual costs of storage and capital investment are minimized.

It is possible-by introducing not very restrictive statistical assumptions-to calculate the annual costs of storing excluded material elsewhere for different modes of partitioning a warehouse into compartments. The annual building cost of the warehouse is calculated in the ordinary way.

In this study a solution is offered for the partitioning of a warehouse into equal compartments. It is to be expected that the extension of this solution to cases of the partition into compartments, differing from each other as to storage capacity, will tend to lower costs.