Longest path time–cost analysis of construction projects with generalised activity constraints

Time–cost analysis is an important element of project scheduling, especially for lengthy and costly construction projects, as it evaluates alternative schedules and establishes an optimum one considering any project completion deadline. Existing methods for time–cost analysis have not adequately considered typical activity and project characteristics, such as generalised precedence relationships between activities and external time constraints, that would provide a more realistic representation of actual construction projects. The present work aims to incorporate such characteristics in the analysis and proposes a method for developing optimal project time–cost curves based on critical path analysis. In this method, the project is described through a matrix where all paths are tabulated with respect to activities. The project matrix includes values of 1, 0, or -1 depending on the type of precedence relation between an activity and its adjacent ones within a path. Integer programming is employed to choose among all activity crashing alternatives those which reduce path durations to a desired project length value with the lowest possible crashing cost. The method has been successfully tested on a number of cases and results are presented to illustrate its application and demonstrate its merits.