Discrete Mathematics and Applications
The Vehicle Routing Problem

13. Routing under Uncertainty: An Application in the Scheduling of Field Service Engineers

Abstract

13.1 Introduction
In the classical definition of VRP, it is assumed that the associated parameters, concerning factors such as cost, customer demands, and vehicle travel times, are deterministic. This conjecture often is too simplistic in today's dynamic environment, where there exist increasing requirements on levels of productivity and service and a corresponding commitment to enlarged and more elaborate transportation systems. In parallel with the need to manage such a growing number of systems there exists an increased amount of data augmentation and volatility. Hence, when an organization does not possess enough flexibility in its labor assignments, does not possess any real-time parameter information, or cannot analyze data in an online manner, deterministic models cannot always be implemented and stochastic models need to be considered.
The Stochastic VRP (SVRP) differs from the VRP by the introduction of some element of variability within the system in question. Unlike its deterministic equivalent, the SVRP is ambiguously defined since it belongs to a class of a priori optimization problems (see Bertsimas, Jaillet, and Odoni [3]) for which it is impractical to consider an a posteriori approach that computes an optimal solution whenever the random variables are realized. Instead, an a priori solution attempts to obtain the best solution, over all possible problem scenarios, before the realization of any single scenario. Roberts and Hadjiconstantinou [24] evaluated the computational performance of such a solution method. The authors showed that an a priori solution for a VRP where demand is uncertain lies, on average, within 8% of the solution obtained by a reoptimization-based, a posteriori strategy.
The specific type of SVRP to be considered in this case study is the VRP with Stochastic Service Times (VRPSST).

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Information

Published In

cover image Discrete Mathematics and Applications
The Vehicle Routing Problem
Pages: 331 - 352
Editors: Paolo Toth and Daniele Vigo
ISBN (Print): 0898714982
ISBN (Print): 978-0-89871-498-2
ISBN (Online): 978-0-89871-851-5

History

Published online: 23 March 2012

Keywords

  1. transportation problems
  2. programming

Keywords

  1. 05

Keywords

  1. 388.3'1'0285--dc21

Keywords

    QA402.6 . V44 2001Transportation problems (Programming)

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Eleni Hadjiconstantinou

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