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Approximation Algorithms for Cumulative Vehicle Routing with Stochastic Demands

Authors Jingyang Zhao , Mingyu Xiao

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Author Details

Jingyang Zhao
  • University of Electronic Science and Technology of China, Chengdu, China
Mingyu Xiao
  • University of Electronic Science and Technology of China, Chengdu, China

Funding

The work is supported by the National Natural Science Foundation of China, under the grants 62372095, 62172077, and 62350710215.

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Jingyang Zhao and Mingyu Xiao. Approximation Algorithms for Cumulative Vehicle Routing with Stochastic Demands. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 59:1-59:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ISAAC.2024.59

Abstract

In the Cumulative Vehicle Routing Problem (Cu-VRP), we need to find a feasible itinerary for a capacitated vehicle located at the depot to satisfy customers' demand, as in the well-known Vehicle Routing Problem (VRP), but the goal is to minimize the cumulative cost of the vehicle, which is based on the vehicle’s load throughout the itinerary. If the demand of each customer is unknown until the vehicle visits it, the problem is called Cu-VRP with Stochastic Demands (Cu-VRPSD). In this paper, we propose a randomized 3.456-approximation algorithm for Cu-VRPSD, improving the best-known approximation ratio of 6 (Discret. Appl. Math. 2020). Since VRP with Stochastic Demands (VRPSD) is a special case of Cu-VRPSD, as a corollary, we also obtain a randomized 3.25-approximation algorithm for VRPSD, improving the best-known approximation ratio of 3.5 (Oper. Res. 2012). At last, we give a randomized 3.194-approximation algorithm for Cu-VRP, improving the best-known approximation ratio of 4 (Oper. Res. Lett. 2013).

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Cumulative Vehicle Routing
  • Stochastic Demands
  • Approximation Algorithms

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