A unified framework for rich routing problems with stochastic demands

Iliya Markov, Michel Bierlaire, Jean François Cordeau, Yousef Maknoon, Sacha Varone

Research output: Contribution to journalArticleScientificpeer-review

9 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)213-240
Number of pages28
JournalTransportation Research Part B: Methodological
Volume114
DOIs
Publication statusPublished - 2018

Keywords

  • Forecasting
  • Recourse
  • Rich routing problem
  • Stochastic demand
  • Tractability
  • Unified framework

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