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In order to fully exploit the advantages inherent to cooperating heterogeneous multi-robot teams, sophisticated coordination algorithms are essential. Time-extended multi-robot task allocation approaches assign and schedule a set of tasks to a group of robots such that certain objectives are optimized and operational constraints are met. This is particularly challenging if cooperative tasks, i.e. tasks that require two or more robots to work directly together, are considered. In this paper, we present an easy-to-implement criterion to validate the feasibility, i.e. executability, of solutions to time-extended multi-robot task allocation problems with cross schedule dependencies arising from the consideration of cooperative tasks and precedence constraints. Using the introduced feasibility criterion, we propose a local improvement heuristic based on a neighborhood operator for the problem class under consideration. The initial solution is obtained by a greedy constructive heuristic. Both methods use a generalized cost structure and are therefore able to handle various objective function instances. We evaluate the proposed approach using test scenarios of different problem sizes, all comprising the complexity aspects of the regarded problem. The simulation results illustrate the improvement potential arising from the application of the local improvement heuristic.