A Two-Stage Hybrid Heuristic Algorithm for Simultaneous Order and Rack Assignment Problems

The problem of order and rack assignment to picking stations (ORAPS) is a key joint optimization problem in the order picking process of the robotic mobile fulfillment system (RMFS). Given a set of customer orders and a set of mobile racks, the goal of this problem is to simultaneously assign orders and racks to multiple picking stations so that the racks can provide products to meet the demand of orders by the minimal number of visits to all picking stations. In this article, we build a mathematical model for the ORAPS, which considers all orders assignment with the allocable capacity interval of the picking station and the rack product capacity limitation. To solve the ORAPS problem, we propose a two-stage hybrid heuristic algorithm (TS-HHA) consisting of the reducing stage and the assigning stage. In the reducing stage, a scheme of dynamic programming (DP) is introduced to find a critical rack set, which can focus attention on the most promising racks and increase the speed of problem-solving. In the assigning stage, we propose an optimization strategy that combines a constructive heuristic algorithm and adaptive neighborhood search (CH-ANS). It can generate a high-quality simultaneous assignment scheme and further improve its quality effectively. The computational results show that our proposed algorithm performs better than its competitors on both simulation and practical instances of the ORAPS problem. Note to Practitioners - This article investigates the order and rack assignment to picking stations (ORAPS) problem in the robotic mobile fulfillment system (RMFS) originated from a renowned Chinese logistics platform. We build a more comprehensive and reasonable mathematical programming model for this ORAPS problem and propose a two-stage hybrid heuristic algorithm (TS-HHA) strategy, which can simultaneously assign orders and racks to multiple picking stations so that all customer orders can be processed. The experimental results show that our TS-HHA performs at least 35% better than its competitors on all simulation and practical instances set. We believe that this research work can serve as a kind of generic framework for practical ORAPS problems and be very helpful for operating the RMFS efficiently.