A time - Cost trade-off algorithm for nonserial linear projects

In the last decade, a number of methods based on the theories of linear and dynamic programming were developed for the scheduling of linear projects. However, these methods are only capable of handling sequential or serial activities. In this paper, a dynamic programming formulation for the scheduling of nonsequential or nonserial activities is presented. The objective of the current formulation is to determine the project time-cost profile, which determines possible project durations and their minimum project total costs. The formulation considers the effects of crew formations, interruptions, and lags for production activities in determining the minimum project total cost, minimum project direct cost, and minimum project duration. In addition, the approach presented is capable of handling activity durations and interruptions described by continuous and discrete functions. The formulation is also capable of handling both serial and nonserial linear projects. An example project is provided to illustrate the computational steps, validate the calculation algorithm, and show the capabilities of the proposed method.