The development of online applications for services such as package delivery, crowdsourcing, or taxi dispatching has caught the attention of the research community to the domain of online multi-agent multi-task allocation. In online service applications, tasks (or requests) to be performed arrive over time and need to be dynamically assigned to agents. Such planning problems are challenging because: (i) few or almost no information about future tasks is available for long-term reasoning; (ii) agent number, as well as, task number can be impressively high; and (iii) an efficient solution has to be reached in a limited amount of time. In this paper, we propose SKATE, a successive rank-based task assignment algorithm for online multi-agent planning. SKATE can be seen as a meta-heuristic approach which successively assigns a task to the best-ranked agent until all tasks have been assigned. We assessed the complexity of SKATE and showed it is cubic in the number of agents and tasks. To investigate how multi-agent multi-task assignment algorithms perform under a high number of agents and tasks, we compare three multi-task assignment methods in synthetic and real data benchmark environments: Integer Linear Programming (ILP), Genetic Algorithm (GA), and SKATE. In addition, a proactive approach is nested to all methods to determine near-future available agents (resources) using a receding-horizon. Based on the results obtained, we can argue that the classical ILP offers the better quality solutions when treating a low number of agents and tasks, i.e. low load despite the receding-horizon size, while it struggles to respect the time constraint for high load. SKATE performs better than the other methods in high load conditions, and even better when a variable receding-horizon is used.