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A poor quality affects project makespan and its total costs negatively, but it can be recovered by repair works during construction. We construct a new non-linear programming model based on the classic multi-mode resource constrained project scheduling problem considering repair works. In order to obtain satisfactory quality without a high increase of project cost, the objective is to minimize total quality cost which consists of the prevention cost and failure cost according to Quality-Cost Analysis. A binary dependent normal distribution function is adopted to describe the activity quality; Cumulative quality is defined to determine whether to initiate repair works, according to the different relationships among activity qualities, namely, the coordinative and precedence relationship. Furthermore, a shuffled frog-leaping algorithm is developed to solve this discrete trade-off problem based on an adaptive serial schedule generation scheme and adjusted activity list. In the program of the algorithm, the frog-leaping progress combines the crossover operator of genetic algorithm and a permutation-based local search. Finally, an example of a construction project for a framed railway overpass is provided to examine the algorithm performance, and it assist in decision making to search for the appropriate makespan and quality threshold with minimal cost.