Abstract
In this chapter, we model vehicle routing problems containing uncertainty and requiring stepwise planning by a (finite) Markov decision process (MDP). We define the MDP in Sect. 4.2. The MDP contains three (sub-)models: decision states, dynamic decision making, and stochastic transitions. To model routing applications as MDP, we have to determine the three (sub-)models. In Sect. 4.1, we model replanning as dynamism. In Sect. 4.4, we model a decision state for a vehicle routing’s planning situation. We model uncertainty as stochasticity. We give a short overview on how the main drivers of uncertainty generally are modeled in the literature in Sect. 4.5. We finally give an overview on how SDVRPs are modeled as MDPs in Sect. 4.6.
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Notes
- 1.
Notably, in the presented definition, a deterministic problem is always static. Still, the applied solution approach may be dynamic, e.g., applied on a rolling horizon.
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Ulmer, M.W. (2017). Modeling. In: Approximate Dynamic Programming for Dynamic Vehicle Routing. Operations Research/Computer Science Interfaces Series, vol 61. Springer, Cham. https://doi.org/10.1007/978-3-319-55511-9_4
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DOI: https://doi.org/10.1007/978-3-319-55511-9_4
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