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We consider a stochastic time-cost tradeoff problem that determines how much to crash activities with the purpose of minimizing the expected summation of crashing and tardiness costs. We propose a threshold policy that makes a crashing decision contingent on a project׳s current status; crashing an activity to compensate delayed starting time from a predetermined threshold. First, we present a dynamic programming (DP) formulation to find the threshold values, and prove that the resulting threshold policy is optimal for a serial-graph project. Since the above optimality does not hold generally, we develop a DP-based procedure to construct a threshold policy for arbitrary-graph projects.

We show through the computational experiments that our threshold policy is rapidly constructed by this procedure, and its cost is not very far from the theoretical lower bound.