Optimum allocation of resources between the random access and rack storage spaces in an automated warehousing system

The throughput capacity of an automated warehousing system is mainly dependent on two factors; the number of available storage spaces and the efficiency of the storage and retrieval system. If it is assumed that only a limited amount of resources are available to build a warehouse, spending most of the resources on providing more spaces or on a more efficient storage and retrieval system becomes a crucial allocation problem. In this paper, a warehouse consisting of two types of storage spaces, random access and rack space, is considered. Random access spaces are assumed to require more resources per unit to provide, but they contribute more to the efficiency of the operation of the system because items can be stored in and retrieved from them without delay. Rack spaces, on the other hand, need the services of a stacking crane for storage and retrieval. As a result, the queueing system formed limits their utilization. Here, a method is presented for the optimum allocation of the resources among these two types of spaces so that the overall throughput capacity of the warehouse is maximized. The problem is formulated and solved as a stochastic optimization problem and a numerical example is provided.