A unified framework for rich routing problems with stochastic demands

Journal Article (2018)
Author(s)

Iliya Markov (École Polytechnique Fédérale de Lausanne)

M. Bierlaire (École Polytechnique Fédérale de Lausanne)

Jean François Cordeau (HEC Montreal)

Yousef Maknoon (TU Delft - Transport and Logistics)

Sacha Varone (University of Applied Sciences Western Switzerland)

Research Group
Transport and Logistics
DOI related publication
https://doi.org/10.1016/j.trb.2018.05.015
More Info
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Publication Year
2018
Language
English
Research Group
Transport and Logistics
Volume number
114
Pages (from-to)
213-240

Abstract

We introduce a unified framework for rich vehicle and inventory routing problems with complex physical and temporal constraints. Demands are stochastic, can be non-stationary, and are forecast using any model that provides the expected demands and their error term distribution, which can be any theoretical or empirical distribution. We offer a detailed discussion on the modeling of demand stochasticity, focusing on the probabilities and cost effects of undesirable events, such as stock-outs, breakdowns and route failures, and their associated recourse actions. Tractability is achieved through the ability to pre-compute or at least partially pre-process the stochastic information, which is possible under mild assumptions for a general inventory policy. We integrate the stochastic aspect into a mixed integer non-linear program, illustrate applications to various problem classes, and show how to model specific problems through the lens of inventory routing. The case study is based on two sets of realistic instances, representing a waste collection inventory routing problem and a facility maintenance problem, respectively. We analyze the effects of our assumptions on modeling realism and tractability, and demonstrate that our framework significantly outperforms deterministic policies in its ability to limit the number of undesirable events for the same routing cost.

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