A tight formulation for the dial-a-ride problem

IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE European Journal of Operational Research Pub Date : 2024-09-20 DOI:10.1016/j.ejor.2024.09.028
Daniela Gaul, Kathrin Klamroth, Christian Pfeiffer, Michael Stiglmayr, Arne Schulz
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Abstract

Ridepooling services play an increasingly important role in modern transportation systems. With soaring demand and growing fleet sizes, the underlying route planning problems become increasingly challenging. In this context, we consider the dial-a-ride problem (DARP): Given a set of transportation requests with pick-up and delivery locations, passenger numbers, time windows, and maximum ride times, an optimal routing for a fleet of vehicles, including an optimized passenger assignment, needs to be determined. We present tight mixed-integer linear programming (MILP) formulations for the DARP by combining two state-of-the-art models into novel location-augmented-event-based formulations. Strong valid inequalities and lower and upper bounding techniques are derived to further improve the formulations. We then demonstrate the theoretical and computational superiority of the new models: First, the linear programming relaxations of the new formulations are stronger than existing location-based approaches. Second, extensive numerical experiments on benchmark instances show that computational times are on average reduced by 53.9% compared to state-of-the-art event-based approaches.
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拨号乘车问题的严密表述
拼车服务在现代运输系统中发挥着越来越重要的作用。随着需求的激增和车队规模的扩大,潜在的路线规划问题变得越来越具有挑战性。在这种情况下,我们考虑了 "拨号乘车 "问题(DARP):给定一组包含接送地点、乘客人数、时间窗口和最长乘车时间的运输请求,需要确定车队的最优路线,包括优化的乘客分配。我们通过将两个最先进的模型结合到基于位置-事件增强的新公式中,为 DARP 提出了严密的混合整数线性规划(MILP)公式。我们还推导出了强有效不等式和上下限技术,以进一步改进这些公式。然后,我们证明了新模型在理论和计算上的优越性:首先,新公式的线性规划松弛比现有的基于位置的方法更强。其次,在基准实例上进行的大量数值实验表明,与最先进的基于事件的方法相比,计算时间平均缩短了 53.9%。
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来源期刊
European Journal of Operational Research
European Journal of Operational Research 管理科学-运筹学与管理科学
CiteScore
11.90
自引率
9.40%
发文量
786
审稿时长
8.2 months
期刊介绍: The European Journal of Operational Research (EJOR) publishes high quality, original papers that contribute to the methodology of operational research (OR) and to the practice of decision making.
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