Optimal resource allocation and routing in robotic mobile fulfillment systems

Abstract

This paper addresses a combinatorial optimization problem in the context of a robotic mobile fulfillment system deployed in a warehouse that consists of movable racks, a picker, and a fleet of mobile robots. The objective is to efficiently prepare a set of orders with specified due dates by bringing the racks to a picking station in a sequential manner, where the picker selects the required products for the open orders, namely the orders that are being processed simultaneously. The picking station has a limited capacity for processing of open orders. Our goal is to minimize the total travel times of the robots and the delays in fulfilling orders. To achieve this, several decision variables need to be determined, including order sequencing, rack allocation, rack scheduling, and mobile robot routing. We formulate the problem as a mixed integer programming model and devise a heuristic algorithm grounded in decomposition principles to address the problem across two distinct phases. Additionally, we introduce two variable neighborhood search (VNS) algorithms tailored to resolve each respective phase within the aforementioned heuristic framework. The performance of the proposed solution approaches is evaluated and compared using two sets of randomly generated test instances, encompassing small-size and large-size instances. Furthermore, we conduct an analysis to examine the influence of key parameters on the objective function value.