Abstract: The problem of order batching in parts-to-picker intelligent warehouse based on automatic guided vehicle(AGV)is studied. The costs of workers picking items from shelves and the costs of AGV transporting shelves are considered simultaneously. An integer programming model of order batching problem is established to minimize the total costs. Based on the items contained in each order and the shelves where the items of an order are stored, the weighted similarity is formulated to describe the relationship between orders. The positive correlation between weighted similarity and total picking cost is analyzed. Based on the weighted similarity between orders, a greedy algorithm for solving the model is designed. The simulation is done on a specific example. The sensitivity analysis of weighted coefficient is done. The influence of weighting coefficient change on batching results, and the relationship among the value of and the cost of λ worker picking one item c₁ and the cost of AGV moving one shelf c₂ are analyzed. The results show that the approximate optimal solution of the order batching problem can be obtained in a short time by using the greedy algorithm with appropriate weighting coefficient. For small scale examples, the approximate ratio is less than 1.35 in the worst case. Using the model and algorithm in this paper for order batching, two types of costs are considered at the same time, which can effectively improve the efficiency and reduce the total costs of order picking.

Key words: intelligent warehouse, AGV, order batching, integer programming model, weighted similarity, greedy algorithm

摘要： 研究了基于自动引导小车(AGV)的“货到人”智能仓库订单分批拣选问题, 在同时考虑工作人员拣选商品成本和AGV搬运货架成本的前提下, 建立了以总成本极小化为目标函数的订单分批问题整数规划模型。根据订单中包含的商品信息和商品所在的货架信息构建了描述订单之间关系的加权相似度指标, 分析了加权相似度与总拣选成本之间的正相关关系。基于订单之间的加权相似度设计了求解模型的贪婪算法。利用具体算例进行模拟计算, 分析了加权系数的变化对订单分批结果的影响, 以及加权系数λ的取值与工作人员拣取一件商品的成本c₁和AGV搬运一次货架的成本c₂之间的关系, 得到了贪婪算法中加权系数λ的确定方法。进一步分析了贪婪算法的计算时间和计算效果, 结果显示, 通过适当选取加权系数, 利用贪婪算法可以在短时间内得到订单分批问题的近似最优解;对于小规模算例, 贪婪算法在最坏情况下近似比不超过1.35。利用本文的模型和算法进行订单分批, 兼顾了工作人员拣取商品的成本和AGV搬运货架的成本, 可以有效提高订单拣选效率, 降低订单拣选总成本。

关键词: 智能仓库, AGV, 订单分批, 整数规划模型, 加权相似度, 贪婪算法