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The Grid has enabled the scientific community to make faster progress. Scientific experiments and data analyses once spanning several years can now be completed in a matter of hours. With the advancement of technology, the execution of scientific experiments, often represented as workflows, has become more demanding. Thus, there is a vital need for improvements in the scheduling of scientific workflows. Efficient execution of scientific workflows can be achieved by the timely allocation of the resources. Advance reservation can ensure the future availability of heterogeneous resources and help a scheduler to produce better schedules. We propose a novel resource mapping technique for jobs of a Grid workflow in an advance reservation environment. Using a dynamic critical path based job selection method, our proposed technique considers the conditional mapping of parent and child jobs to the same resource, trying to minimise the communication duration between jobs and thus optimising the workflow completion time. The proposed method is analysed in both static and dynamic environments, and the simulation results show encouraging performance especially for workflows where the communication costs are higher than the computation costs. We also propose a hybrid of multiple scheduling heuristics for the aforementioned problem, which chooses the best among multiple schedules computed by different algorithms. Simulation results show a significant improvement over well known scheduling heuristics in terms of workflow completion time. Considering the advance reservation environment, a better schedule for the earliest completion of a workflow can be achieved if better paths can be found for the transfer of data files between jobs executed on different resources. We propose a K-shortest path based routing algorithm for finding good paths in the advance reservation environment. The results show that our proposed algorithm performs very well in terms of the earliest arrival time of the data. Finally, we also study a modified partner based scheduling heuristic for non-advance reservation environments. The results demonstrate that our proposed algorithm is a promising candidate for adoption in such Grid environments.