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Cost optimization for workflow scheduling while meeting deadline is one of the fundamental problems in utility computing. In this paper, a two-phase cost-efficient scheduling algorithm called critical chain is presented. The proposed algorithm uses the concept of slack time in both phases. The first phase is deadline distribution over all tasks existing in the workflow which is done considering critical path properties of workflow graphs. Critical chain uses slack time to iteratively select most critical sequence of tasks and then assigns sub-deadlines to those tasks. In the second phase named mapping step, it tries to allocate a server to each task considering task's sub-deadline. In the mapping step, slack time priority in selecting ready task is used to reduce deadline violation. Furthermore, the algorithm tries to locally optimize the computation and communication costs of sequential tasks exploiting dynamic programming. After proposing the scheduling algorithm, three measures for the superiority of a scheduling algorithm are introduced, and the proposed algorithm is compared with other existing algorithms considering the measures. Results obtained from simulating various systems show that the proposed algorithm outperforms four well-known existing workflow scheduling algorithms. [ABSTRACT FROM AUTHOR]