Robotic Mobile Fulfillment Systems (RMFSs) are a new type of automated warehouse deployed in e-commerce. In this parts-to-picker system, a fleet of small robots is tasked with retrieving and storing shelves of items in the warehouse. Due to the nature of the e-commerce market, and the high flexibility of RMFSs, there are many opportunities to improve the productivity of the warehouse by optimising operational decisions. Online retailers promise extremely fast deliveries, which requires that new orders be included in the set of requests to fulfil as soon as they are revealed. For this reason, and because of the very dynamic nature of the robots' cycles, decision-making needs to be done in real time, in an uncertain environment. Because such a problem often lacks a formal description, we propose a mathematical framework that models the operational decisions taking place in an RMFS as a stochastic dynamic program. Our objective is to formalise optimisation opportunities, to allow researchers to develop more advanced methods in a well-defined environment. Embedded in a discrete event simulator, this model is illustrated by simulations to compare against standard storage decision rules.

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