联合批处理、拣选路径与排序问题的装箱规划模型
A bin packing formulation for the joint batching, routing and sequencing problem
AI总结：
本文针对矩形仓库中带截止日期的联合订单批处理、拣选路径与排序问题，提出装箱规划模型及列生成启发式算法，可最优求解小规模实例并为大规模实例提供高质量界。
摘要：
仓库是涉及不同决策层级的复杂物流问题的场景。本文研究了矩形仓库中带截止日期的联合订单批处理、拣选员路径与排序问题（JOBPRSP-D）。为解决该问题，提出了一种与装箱问题相关的指数线性规划模型。该模型通过一种列生成启发式算法求解，该算法能够提供最优值的下界和上界。我们首先证明JOBPRSP-D与装箱问题相关，而非调度问题。我们利用这一特性推导出若干有效不等式，以增强主问题的求解效率。所提出的算法在公开数据集上进行了评估。它能够在几分钟内最优求解包含多达18个订单的实例。同时，只要拣选员容量足够小，它也能在包含100个订单的较大实例上证明最优性或提供高质量的下界。最后，在所考虑的基准测试中，除两个实例外，所有实例都找到了新的上界。据我们所知，这是第一篇为JOBPRSP-D提供大规模实例最优性保证的文章；因此，这些结果可用于评估针对同一问题所提出的启发式算法的质量。
英文摘要：
Warehouses are the scene of complex logistic problems integrating different decision layers. This paper addresses the Joint Order Batching, Picker Routing and Sequencing Problem with Deadlines (JOBPRSP-D) in rectangular warehouses. To tackle the problem, an exponential linear programming formulation related to bin packing is proposed. It is solved with a column generation heuristic able to provide lower and upper bounds on the optimal value. We start by showing that the JOBPRSP-D is related to a bin packing problem as opposed to a scheduling problem. We take advantage of this aspect to derive a number of valid inequalities that enhance the resolution of the master problem. The proposed algorithm is evaluated on publicly available data-sets. It is able to optimally solve instances with up to 18 orders in a few minutes. It is also able to prove optimality or to provide high-quality lower bounds on larger instances with 100 orders as long as the picker's capacity is small enough. Finally, new upper bounds are found on all the instances except two of the benchmark considered. To the best of our knowledge this is the first article that provides optimality guarantee on large size instances for the JOBPRSP-D; the results can therefore be used to assert the quality of heuristics proposed for the same problem.
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