In this paper, we define a time-extended multirobot task allocation problem, design and analyze some heuristics to tackle the problem complexity in computational resource constrained settings. The robots (or agents) can perform a limited amount of work per unit of time, while the tasks have durations and deadlines by which they must be completed. These constraints, in addition to a relatively small number of agents, may not allow the allocation of all tasks. The heuristics we present are easy-to-implement, tuning free and fast. We analyze these heuristics theoretically with respect to computational complexity. Then, we empirically compare them with respect to performance criteria on a synthetic testset. In so doing, we offer solutions for devices with computation power limitations. The same algorithms can also be embedded into metaheuristics or hyper-heuristics to efficiently and effectively solve the problem.