使用采摘者行进距离的近似值进行排序
Order batching using an approximation for the distance travelled by pickers
摘要：
本文研究了拣货员路径问题中的订单排序问题。我们的方法适用于以标准矩形网格布局排列的仓库（存储区域），因此具有平行过道和两个或多个交叉过道。我们工作的动机是在线杂货店购物，其中订单可能由数十个项目组成。提出的方法直接解决订单排序问题，但使用距离近似来影响订单的排序，而不直接解决路由问题。我们提出了一个基本配方的基础上，决定订单批量在一起，以优化一个目标，近似的采摘路由距离旅行。我们通过改进仓库中有多个块的情况下的近似来扩展我们的公式。我们提出的约束，以消除对称性，以减少所需的计算工作量，以及约束，显着提高我们的制定的线性规划放松的价值。一个启发式算法的基础上部分整数优化我们的数学公式。一旦订单数量已经决定，我们最佳的路线，每个人的采摘使用以前的方法在文献中。公开的测试问题，涉及多达75个订单的广泛的计算结果给出了单和多块仓库配置。
英文摘要：
In this paper we investigate the problem of order batching for picker routing. Our approach is applicable to warehouses (storage areas) arranged in the standard rectangular grid layout, so with parallel aisles and two or more cross-aisles. The motivation underlying our work is online grocery shopping in which orders may be composed of dozens of items. The approach presented directly addresses order batching, but uses a distance approximation to influence the batching of orders without directly addressing the routing problem. We present a basic formulation based on deciding the orders to be batched together so as to optimise an objective that approximates the picker routing distance travelled. We extend our formulation by improving the approximation for cases where we have more than one block in the warehouse. We present constraints to remove symmetry in order to lessen the computational effort required, as well as constraints that significantly improve the value of the linear programming relaxation of our formulation. A heuristic algorithm based on partial integer optimisation of our mathematical formulation is also presented. Once order batching has been decided we optimally route each individual picker using a previous approach presented in the literature. Extensive computational results for publicly available test problems involving up to 75 orders are given for both single and multiple block warehouse configurations.
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