In this paper, we study a m-parallel machine scheduling problem with a non-crossing constraint motivated by crane scheduling in ports. We decompose the problem to allow time allocations to be determined once crane assignments are known and construct a backtracking search scheme that manipulates domain reduction and pruning strategies. Simple approximation heuristics are developed, one of which guarantees solutions to be at most two times the optimum. For large-scale problems, a simulated annealing heuristic that uses random neighborhood generation is provided. Computational experiments are conducted to test the algorithms.
