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This paper studies a complex parallel scheduling problem with non-crossing constraint, sequence dependent setup times, eligibility restrictions, and precedence relationships motivated by reclaimer scheduling in dry bulk terminals. In a stockyard of any dry bulk terminal, stockpiles are handled by reclaimers. Therefore, improving the operational efficiency of reclaimers is critical for the overall performance of these terminals which are struggling with increasing workload. We study the variants of this problem with and without stacking operations. For each variant, we present a lower and an upper bound. A strong lower bound is obtained by relaxing the non-crossing constraint and solving the resulting problem to the optimality. While this relaxation still addresses a challenging scheduling problem, proposed arc-time-indexed formulation copes with the instances of practical size. We develop a novel constraint programming formulation to provide an upper bound for the problem. Computational experiments show this robust approach is able to generate near-optimal schedules for different stockyard configurations within a minute.