Sizing of a homogeneous fleet of robots in a logistics warehouse

Abstract

Abstract We are interested in the problem of determining the size of a fleet of robots able to perform transport operations in a logistics warehouse. The operations are divided into several phases: loading, loaded travel, unloading and empty travel. We first determine the minimum number of robots needed to transport a set of homogeneous loads from point A to point B over a determined time interval. For the same number of robots, many assignments exist. We determine the assignment that minimizes the makespan, which is also the one which balances the loads between robots. If we consider an infinity of pickup stations, we obtain a simple analytical expression to find the optimal number of robots. With a single pickup station, we present a simple algorithm that computes the optimal fleet size. Finally, we show that the extension with heterogeneous loads can be formulated as a bin packing problem.