A Multi-Stage Approach to Time-Cost Trade-Off Analysis using Mathematical Programming

Time-cost trade-offs are a critical construction planning issue, which have received significant amount of research. Many existing solutions are based on evolutionary algorithms, which are search-based and ignore the structure of time-cost trade-off problems. Mathematical programming methods were applied previously but their computational limitations have been widely recognized. This study proposed a multi-stage approach based on linear programming and integer programming to improve the efficiency of time-cost trade-off analysis using mathematical programming. Three models are used in this approach- a normal duration model, a reduction time model, and an adjustment model. The normal duration model finds the normal project duration. The reduction time model seeks optimum solutions to minimize the total cost subject to a project deadline by assuming all crash-able activities are linear-continuous (LC). The adjustment model finds feasible solution for non-linear-continuous (NLC) activities whose reduction time given by the reduction model is not reasonable. It is a pure binary programming model. Using this approach, the reduction time model narrows down the number of NLC activities that need reduction time adjustment. This step improves the adjustment model computational efficiency. A case study issued to demonstrate the application and the potential of this approach.