A unified framework for rich routing problems with stochastic demands. (August 2018)

• Record Type: Journal Article
• Authors: Markov, Iliya; Bierlaire, Michel; Cordeau, Jean-François; Maknoon, Yousef; Varone, Sacha
• Is Part Of: Transportation research. Volume 114(2018)
• Page Start: 213
• Page End: 240
• Publication Date: 2018-08
• Subjects: Unified framework -- Rich routing problem -- Stochastic demand -- Forecasting -- Tractability -- Recourse; Transportation -- Research -- Periodicals; Transportation -- Mathematical models -- Periodicals
• DOI: 10.1016/j.trb.2018.05.015
• Languages: English
• ISSNs: 0191-2615

Abstract

Highlights: Proposes a modeling approach capturing dynamic probabilistic information in the objective function that is unaffected by the curse of dimensionality. Models explicitly undesirable events such as stock-outs and route failures, their probabilities, costs, and associated recourse actions. Integrates real-world demand forecasting techniques relaxing typical assumptions from the literature. Maintains computational tractability through the ability to preprocess the probabilistic information for a general inventory policy. Demonstrates the performance of the approach on rich instances derived from real data for two conceptually different routing problems. 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.