A Monotone Approximate Dynamic Programming Approach for the Stochastic Scheduling, Allocation, and Inventory Replenishment Problem: Applications to Drone and Electric Vehicle Battery Swap Stations

TL;DR

This paper develops a monotone approximate dynamic programming approach to optimize operations at battery swap stations for EVs and drones, effectively handling demand uncertainty, battery degradation, and inventory management.

Contribution

It introduces a novel monotone ADP method with regression-based initialization for the stochastic scheduling and inventory problem at battery swap stations, improving computational efficiency.

Findings

The new ADP method outperforms exact and other ADP methods in tests.

Theoretical proofs establish monotonicity properties of the value function and policies.

Policy insights are derived for drone swap station operations.

Abstract

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.