From theory to practice: maximizing revenues for on-line dial-a-ride

We consider the on-line dial-a-ride problem, where a server fulfills requests that arrive over time. Each request has a source, destination, and release time. We study a variation of this problem where each request also has a revenue that the server earns for fulfilling the request. The goal is to serve requests within a time limit while maximizing the total revenue. We first prove that no deterministic online algorithm can be competitive unless the input graph is complete and edge weights are unit. We therefore focus on these graphs and present a 2-competitive algorithm for this problem. We also consider two variations of this problem: (1) the input graph is complete bipartite and (2) there is a single node that is the source for every request, and present a 1-competitive algorithm for the former and an optimal algorithm for the latter. We also provide experimental results for the complete and complete bipartite graphs. Our simulations support our theoretical findings and demonstrate that our algorithms perform well under settings that reflect realistic dial-a-ride systems.