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.

New Quantization Approach for the Anomaly: The Increase in Time Float following Consumption

Anomalous scenarios in projects with generalized precedence relations (GPRs) have been arousing widely interest. A recent relevant discovery of anomaly under GPRs is that an activity’s time float increases following its consumption. The scenario is contrary to a common idea for plan management, and it also changes relationships between time floats and maximum prolongations of activity durations. Classic computations may be invalid to time parameters under GPRs. This study tests the fact that the current analysis on the anomaly has limitations so that it may provide improper guidelines for project scheduling and lead to undesirable effects. A new quantization algorithm is presented for the anomaly that overcomes the limitations of the current works. In particular, the algorithm confirms accurate time parameters and maximum duration prolongations of activities under constraints that retain project duration. The accuracy of quantization for the anomaly is particularly important for project scheduling with GPRs. Moreover, an application of the anomaly is developed in the resource-constrained project scheduling with activity splitting and GPRs, and an illustration is provided to test the fact that the new quantization result of the anomaly is an essential guarantee to achieve optimal solutions.