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Minimizing the Maximum Flow Time in the Online Food Delivery Problem

Authors Xiangyu Guo, Kelin Luo , Shi Li, Yuhao Zhang

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Xiangyu Guo
  • University at Buffalo, NY, USA
Kelin Luo
  • Institute of Computer Science, Universität Bonn, Germany
Shi Li
  • University at Buffalo, NY, USA
Yuhao Zhang
  • Shanghai Jiao Tong University, China

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Xiangyu Guo, Kelin Luo, Shi Li, and Yuhao Zhang. Minimizing the Maximum Flow Time in the Online Food Delivery Problem. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 33:1-33:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


We study a common delivery problem encountered in nowadays online food-ordering platforms: Customers order dishes online, and the restaurant delivers the food after receiving the order. Specifically, we study a problem where k vehicles of capacity c are serving a set of requests ordering food from one restaurant. After a request arrives, it can be served by a vehicle moving from the restaurant to its delivery location. We are interested in serving all requests while minimizing the maximum flow-time, i.e., the maximum time length a customer waits to receive his/her food after submitting the order. We show that the problem is hard in both offline and online settings even when k = 1 and c = ∞: There is a hardness of approximation of Ω(n) for the offline problem, and a lower bound of Ω(n) on the competitive ratio of any online algorithm, where n is number of points in the metric. We circumvent the strong negative results in two directions. Our main result is an O(1)-competitive online algorithm for the uncapacitated (i.e, c = ∞) food delivery problem on tree metrics; we also have negative result showing that the condition c = ∞ is needed. Then we explore the speed-augmentation model where our online algorithm is allowed to use vehicles with faster speed. We show that a moderate speeding factor leads to a constant competitive ratio, and we prove a tight trade-off between the speeding factor and the competitive ratio.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Online algorithm
  • Capacitated Vehicle Routing
  • Flow Time Optimization


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