We develop a family of rollout policies based on fixed routes to obtain dynamic solutions to the vehicle routing problem with stochastic demand and duration limits (VRPSDL). In addition to a traditional one-step rollout policy, we leverage the notions of the pre-and post-decision state to distinguish two additional rollout variants. We tailor our rollout policies by developing a dynamic decomposition scheme that achieves high quality solutions to large problem instances with reasonable computational effort. Computational experiments demonstrate that our rollout policies improve upon the performance of a rolling horizon procedure and commonly employed fixed-route policies, with improvement over the latter being more substantial.

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Although increasing amounts of transaction data make it possible to characterize uncertainties surrounding customer service requests, few methods integrate predictive tools with prescriptive optimization procedures to meet growing demand for small-volume urban transport services. We incorporate temporal and spatial anticipation of service requests into approximate dynamic programming (ADP) procedures to yield dynamic routing policies for the single-vehicle routing problem with stochastic service requests, an important problem in city-based logistics. We contribute to the routing literature as well as to the field of ADP. We combine offline value function approximation (VFA) with online rollout algorithms resulting in a high-quality, computationally tractable policy. Our offline-online policy enhances the anticipation of the VFA policy, yielding spatial and temporal anticipation of requests and routing developments. Our combination of VFA with rollout algorithms demonstrates the potential benefit of using offline and online methods in tandem as a hybrid ADP procedure, making possible higher-quality policies with reduced computational requirements for real-time decision-making. Finally, we identify a policy improvement guarantee applicable to VFA-based rollout algorithms, showing that base policies composed of deterministic decision rules lead to rollout policies with performance at least as strong as that of their base policy.

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We develop restocking-based rollout policies to make real-time, dynamic routing decisions for the vehicle routing problem with stochastic demand and duration limits. Leveraging dominance results, we develop a computationally tractable method to estimate the value of an optimal restocking policy along a fixed route. Embedding our procedure in rollout algorithms, we show restocking-based rollout out performs a priori-based rollout, demonstrating the value of explicitly considering preemptive capacity replenishment in a rollout approach for dynamic routing. We also demonstrate the effectiveness of basic local search versus more sophisticated mechanisms for the heuristic component of the rollout procedure.

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Electric vehicles offer a pathway to more sustainable transportation, but their adoption entails new challenges not faced by their petroleum-based counterparts. A difficult task in vehicle routing problems addressing these challenges is determining how to make good charging decisions for an electric vehicle traveling a given route. This is known as the fixed route vehicle charging problem. An exact and efficient algorithm for this task exists, but its implementation is sufficiently complex to deter researchers from adopting it. In this work we introduce frvcpy, an open-source Python package implementing this algorithm. Our aim with the package is to make it easier for researchers to solve electric vehicle routing problems, facilitating the development of optimization tools that may ultimately enable the mass adoption of electric vehicles. Summary of Contribution: This work describes a novel software tool for the vehicle routing community. The tool, frvcpy, addresses one of the primary challenges faced by the vehicle routing community when considering problems involving the adoption of electric vehicles (EVs): how to make optimal charging decisions. The state-of-the-art algorithm for solving these problems is sufficiently complex to deter researchers from using it, leading them to adopt less robust methods. frvcpy offers an easy-to-use, lightweight implementation of this algorithm, providing optimal solutions in low (∼5 ms) runtime. It is designed to be easily embedded in larger solution schemes for general EV routing problems, requiring minimal input, offering compatibility with the community standard file types, and offering access both through the command line and a Python API. The tool has thus far proven adaptable, having been used by researchers studying EV routing problems with novel constraints. Our aim with frvcpy is to make it easier for researchers to solve EV routing problems, facilitating the development of optimization tools that may contribute toward the mass adoption of electric vehicles.

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