Determining optimal zone boundaries for three-class-based puzzle-based compact storage systems

Thanks to their advantages, such as high storage density and short response time to customers´ requests, puzzle-based compact storage systems have been increasingly installed in warehouses and distribution centers recently. This study addresses zone boundary optimization for puzzle-based compact storage systems when a three-class-based storage policy is implemented, in attempting to facilitate system design. We first identify 3 cases, where a puzzle-based compact storage system can be divided into 3 zones for items classified as A, B, and C classes. Subsequently, we derive the system expected response time and further develop a mix-integer nonlinear model to optimize zone boundaries by minimizing the derived response time. At last, in view of the problem complexity, we reformulate the zone boundary optimization model as a dynamic programming model, and solve it accordingly. As shown by the numerical example, although the solution procedure is relatively complex, the results can be applied in practice in a straightforward way. In addition, in comparison with randomized and two-class-based storage policies, three-class-based policy can significantly reduce response time of puzzle-based compact storage systems.