In this paper we investigate the problem of simultaneously allocating orders and mobile storage racks to static pickers. Here storage racks are allocated to pickers to enable them to pick all of the products for the orders that have been allocated to them. Problems of the type considered here arise in facilities operating as robotic mobile fulfilment systems. We present a formulation of the problem of allocating orders and racks to pickers as an integer program and discuss the complexity of the problem. We present two heuristics (matheuristics) for the problem, one using partial integer optimisation, that are directly based upon our formulation. We also consider the problem of how to sequence the racks for presentation at each individual picker and formulate this problem as an integer program. We prove that, subject to certain conditions being satisfied, a feasible rack sequence for all orders can be produced by focusing on just a subset of the orders to be dealt with by the picker. Computational results are presented, both for order and rack allocation, and for rack sequencing, for randomly generated test problems (that are made publicly available) involving up to 500 products, 150 orders, 150 racks and 10 pickers.

中文翻译：

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移动货架环境中拣货员的订单分配、货架分配和货架排序

在本文中，我们研究了将订单和移动存储架同时分配给静态拣货员的问题。在这里，存储架分配给拣货员，使他们能够拣选已分配给他们的订单的所有产品。在作为机器人移动履行系统运行的设施中会出现这里考虑的类型的问题。我们提出将订单和货架分配给拣货员的问题的公式化为整数程序，并讨论该问题的复杂性。我们针对该问题提出了两种启发式（数学式），一种使用部分整数优化，它们直接基于我们的公式。我们还考虑了如何对每个单独的拣货员展示的货架进行排序的问题，并将这个问题表述为一个整数程序。我们证明，在满足某些条件的情况下，可以通过只关注由拣货员处理的订单子集来为所有订单生成可行的货架序列。计算结果包括订单和货架分配、货架排序、随机生成的测试问题（公开可用），涉及多达 500 个产品、150 个订单、150 个货架和 10 个拣货员。