Roshan Mahes | Searcharxiv

arXiv2023

Dynamic Appointment Scheduling

This paper considers appointment scheduling in a setting in which at every client arrival the schedule of all future clients can be adapted. Starting our analysis with an explicit treatment of the case of exponentially distributed service times, we then develop a phase-type-based approach to also cover cases in which the service times' squared coefficient of variation differs from 1. The approach relies on dynamic programming, with the state information being the number of clients waiting, the elapsed service time of the client in service, and the number of clients still to be scheduled. The use of dynamic schedules is illustrated through a set of numerical experiments, showing (i) the effect of wrongly assuming exponentially distributed service times, and (ii) the gains (over static schedules, that is) achieved by rescheduling.

math.PR↗

arXiv2022

Learn Global and Optimize Local: A Data-Driven Methodology for Last-Mile Routing

In last-mile routing, the task of finding a route is often framed as a Traveling Salesman Problem to minimize travel time and associated cost. However, solutions stemming from this approach do not match the realized paths as drivers deviate due to navigational considerations and preferences. To prescribe routes that incorporate this tacit knowledge, a data-driven model is proposed that aligns well with the hierarchical structure of delivery data wherein each stop belongs to a zone - a geographical area. First, on the global level, a zone sequence is established as a result of a minimization over a cost matrix which is a weighted combination of historical information and distances (travel times) between zones. Subsequently, within zones, sequences of stops are determined, such that, integrated with the predetermined zone sequence, a full solution is obtained. The methodology is particularly promising as it propels itself within the top-tier of submissions to the Last-Mile Routing Research Challenge, while it maintains an elegant decomposition that ensures a feasible implementation into practice. The concurrence between prescribed and realized routes underpins the adequateness of a hierarchical breakdown of the problem and the fact that drivers make a series of locally optimal decisions when navigating. Furthermore, experimenting with the balance between historical information and distance exposes that historic information is pivotal in deciding a starting zone of a route. The experiments also reveal that at the end of a route, historical information can best be discarded, making the time it takes to return to the station the primary concern.

math.OC↗