Preprocessing the Discrete Time-Cost Tradeoff Problem with Generalized Precedence Relations

This study investigates the deadline of the discrete time-cost tradeoff problem (DTCTP-D) with generalized precedence relations (GPRs). This problem requires modes to be assigned to the activities of a project such that the total cost is minimized and the total completion time and the precedence constraints are satisfied. Anomalies under GPRs are irreconcilable with many current theories and methods. We propose a preprocessing technology, an equivalent simplification approach, which is an effective method for solving large-scale complex problems. We first study a way to deal with the anomalies under GPRs, such as the reduce (increase) in project completion as a consequence of prolonging (shortening) an activity, and discover relationships between time floats and path lengths. Then, based on the theories, we transform the simplification into a time float problem and design a polynomial algorithm. We perform the simplification and improve the efficiency of the solution by deleting redundant calculation objects.