A new approach to the joint order batching and picker routing problem with alternative locations

IF 1.9 3区工程技术 Q3 MANAGEMENT

IMA Journal of Management Mathematics Pub Date : 2023-08-22 DOI:10.1093/imaman/dpad016

Sajjad Hedayati, Mostafa Setak, E. Demir, T. van Woensel

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引用次数: 0

Abstract

The clustered and generalized vehicle routing problem (CGVRP) extends the well-known vehicle routing problem by grouping the demand points into multiple distinct zones, and within each zone, further separation is made by forming clusters. The objective of the CGVRP is to determine the optimal routes for a fleet of vehicles dispatched from a depot, visiting all zones within each cluster. This requires making two simultaneous optimization decisions. Firstly, each zone must be visited by exactly one node, and secondly, all zones within a cluster must be visited by the same vehicle. In this paper, we introduce two mixed-integer linear programming formulations for the CGVRP, aimed at solving a joint order batching and picker routing problem with alternative locations (JOBPR-AL) in a warehouse environment featuring mixed-shelves configuration. Both formulations are tested on three scenarios of randomly generated small- and medium-sized instances. Additionally, we propose a general rule approach for calculating a cost matrix in a rectangular environment. The results demonstrate the effectiveness of the proposed mathematical formulations in efficiently solving problems with up to 180 nodes.

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有备选地点的联合订单批处理和拣选机路由问题的新方法

集群广义车辆路径问题（CGVRP）通过将需求点分组为多个不同的区域来扩展众所周知的车辆路径问题，并且在每个区域内，通过形成集群来进行进一步的分离。CGVRP的目标是为从车辆段派遣的车队确定最佳路线，访问每个集群内的所有区域。这需要同时做出两个优化决策。首先，每个区域必须由一个节点访问，其次，集群内的所有区域必须由同一车辆访问。在本文中，我们介绍了CGVRP的两个混合整数线性规划公式，旨在解决具有混合货架配置的仓库环境中具有替代位置的联合订单批处理和拣选路由问题（JOBPR-AL）。这两个公式都在随机生成的中小型实例的三个场景中进行了测试。此外，我们还提出了一种在矩形环境中计算成本矩阵的通用规则方法。结果证明了所提出的数学公式在有效解决多达180个节点的问题方面的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IMA Journal of Management Mathematics OPERATIONS RESEARCH & MANAGEMENT SCIENCE-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The mission of this quarterly journal is to publish mathematical research of the highest quality, impact and relevance that can be directly utilised or have demonstrable potential to be employed by managers in profit, not-for-profit, third party and governmental/public organisations to improve their practices. Thus the research must be quantitative and of the highest quality if it is to be published in the journal. Furthermore, the outcome of the research must be ultimately useful for managers. The journal also publishes novel meta-analyses of the literature, reviews of the "state-of-the art" in a manner that provides new insight, and genuine applications of mathematics to real-world problems in the form of case studies. The journal welcomes papers dealing with topics in Operational Research and Management Science, Operations Management, Decision Sciences, Transportation Science, Marketing Science, Analytics, and Financial and Risk Modelling.