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The drift towards new challenges in grid computing, including the utility grid paradigm and service level agreements based on quality-of-service guarantees, implies the need for new, robust, multi-criteria scheduling algorithms that can be applied by the user in an intuitive way. Multiple scheduling criteria addressed by the related grid research include execution time, the cost of running a task on a machine, reliability, and different data quality metrics. The existing bi-criteria scheduling approaches are usually dedicated for certain criterion pairs only that require the user to define one's preferences either as weights assigned to the criteria or as fixed constraints defined for one of the criteria. These requirements are often not feasible for the user and not suited to the specificity of the multi- criteria scheduling problem. We propose a novel requirement specification method based on a sliding constraint, and we model the problem as an extension of the multiple-choice knapsack problem. We propose a general bi-criteria scheduling heuristic called dynamic constraint algorithm (DCA) based on dynamic programming, dedicated to the problem model defined by us. In the experimental study, we show that in most of the problem variants, DCA outperforms two existing algorithms designed for the same problem. It also shows relatively low scheduling times for workflows of medium size.