A Branch-and-Price Algorithm for the Online Scheduling of Valet Drivers

Abstract

In the present paper, the online valet driving problem (OVDP) is studied. In this problem, customers request a valet driving service through the platform, then the valets arrive on e-bikes at the designated pickup location and drive the vehicle to the destination. The key task is to assign the valets effectively for driving orders to minimize the overall cost. To serve that purpose, we first propose a new online scheduling strategy that divides the planning horizon into several rounds with fixed length of time, and each round consists of pooling time and scheduling time. By including the features of online scheduling and the power level of e-bikes, this OVDP becomes more practical but nevertheless challenging. To solve the OVDP, we formulate it into a set partitioning model and design a branch-and-price (B&P) algorithm. To improve the computation efficiency, a label setting algorithm is incorporated to address the pricing subproblem, which is accelerated via a heuristic pricing method. As an essential part of the algorithm design, an artificial column technique and a greedy-based constructive heuristic are implemented to obtain the initial solution. Based on the numerical analysis of various scaled instances, it is verified that the proposed B&P algorithm is not only effective in optimum seeking, but also shows a high level of efficiency in comparison with the off-the-shelf commercial solvers. Furthermore, we also explore the impact of pooling and scheduling time on the OVDP and discover a bowl-shaped trend of the objective value with respect to the two time lengths.