Robotic Mobile Fulfillment Systems (RMFSs) are a recent 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.

机器人移动履行系统 (RMFS) 是最近在电子商务中部署的一种自动化仓库。在这个零件到拣选系统中，一队小型机器人的任务是在仓库中检索和存储货架上的物品。由于电子商务市场的性质以及 RMFS 的高度灵活性，有很多机会可以通过优化运营决策来提高仓库的生产力。在线零售商承诺极快的交付，这要求新订单一经披露就包含在一组请求中以执行。出于这个原因，并且由于机器人周期的动态特性，决策需要在不确定的环境中实时完成。因为这样的问题往往缺乏正式的描述，我们提出了一个数学框架，将 RMFS 中发生的操作决策建模为随机动态程序。我们的目标是形式化优化机会，使研究人员能够在明确定义的环境中开发更先进的方法。该模型嵌入在离散事件模拟器中，通过模拟来说明，以与标准存储决策规则进行比较。