This paper introduces the problem of scheduling a dual-spreader crane when lifts are subject to a weight limit. A mathematical model is formulated and a fast method for computing a lower bound on the optimal value is proposed. An efficient heuristic approach is designed and subsequently built into a simulated annealing framework to solve the problem. The optimization and heuristic approaches are tested on problem instances of various sizes. The results indicate that the optimization approach produces proven optimal solutions to small-sized instances but fails to solve instances of practical meaning. The heuristic approach can easily match the performance of the optimization approach for small instances and outperforms the optimization approach when tackling larger instances. On average, the heuristic approach produces solutions whose objective values are within 6% of the lower bound.