A Monotone Approximate Dynamic Programming Approach for the Stochastic Scheduling, Allocation, and Inventory Replenishment Problem: Applications to Drone and Electric Vehicle Battery Swap Stations. (arXiv:2105.07026v1 [math.OC])

There is a growing interest in using electric vehicles (EVs) and drones for
many applications. However, battery-oriented issues, including range anxiety
and battery degradation, impede adoption. Battery swap stations are one
alternative to reduce these concerns that allow the swap of depleted for full
batteries in minutes. We consider the problem of deriving actions at a battery
swap station when explicitly considering the uncertain arrival of swap demand,
battery degradation, and replacement. We model the operations at a battery swap
station using a finite horizon Markov Decision Process model for the stochastic
scheduling, allocation, and inventory replenishment problem (SAIRP), which
determines when and how many batteries are charged, discharged, and replaced
over time. We present theoretical proofs for the monotonicity of the value
function and monotone structure of an optimal policy for special SAIRP cases.
Due to the curses of dimensionality, we develop a new monotone approximate
dynamic programming (ADP) method, which intelligently initializes a value
function approximation using regression. In computational tests, we demonstrate
the superior performance of the new regression-based monotone ADP method as
compared to exact methods and other monotone ADP methods. Further, with the
tests, we deduce policy insights for drone swap stations.

Source: https://arxiv.org/abs/2105.07026

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