Multiperiod Dispatching and Routing for On-Time Delivery in a Dynamic and Stochastic Environment

On-demand delivery has become increasingly popular around the world. Brick-and-mortar grocery stores, restaurants, and pharmacies are providing fast delivery services to satisfy the growing home delivery demand. Motivated by a large meal and grocery delivery company, we model and solve a multiperiod driver dispatching and routing problem for last-mile delivery systems where on-time performance is the main target. The operator of this system needs to dispatch a set of drivers and specify their delivery routes in a stochastic environment, in which random demand arrives over a fixed number of periods. The resulting dynamic program is challenging to solve due to the curse of dimensionality. We propose a novel approximation framework to approximate the value function via a simplified dispatching program. We then develop efficient exact algorithms for this problem based on Benders decomposition and column generation. We validate the superior performance of our framework and algorithms via extensive numerical experiments. Tested on a real-world data set, we quantify the value of adaptive dispatching and routing in on-time delivery and highlight the need of coordinating these two decisions in a dynamic setting. We show that dispatching multiple vehicles with short trips is preferable for on-time delivery, as opposed to sending a few vehicles with long travel times

Double-Carrier Phase-Disposition Pulse Width Modulation Method for Modular Multilevel Converters

Modular multilevel converters (MMCs) have become one of the most attractive topologies for high-voltage and high-power applications. A double-carrier phase disposition pulse width modulation (DCPDPWM) method for MMCs is proposed in this paper. Only double triangular carriers with displacement angle are needed for DCPDPWM, one carrier for the upper arm and the other for the lower arm. Then, the theoretical analysis of DCPDPWM for MMCs is presented by using a double Fourier integral analysis method, and the Fourier series expression of phase voltage, line-to-line voltage and circulating current are deduced. Moreover, the impact of carrier displacement angle between the upper and lower arm on harmonic characteristics is revealed, and further the optimum displacement angles are specified for the circulating current harmonics cancellation scheme and output voltage harmonics minimization scheme. Finally, the proposed method and theoretical analysis are verified by simulation and experimental results