A Branch and Bound Algorithm for the Weighted Earliness-Tardiness Project Scheduling Problem with Generalized Precedence Relations

In this paper, an exact solution procedure is presented for the Weighted Earliness-Tardiness Project Scheduling Problem (WETPSP) with Generalized Precedence Relations (WETPSP-GPR), taking into account the time value of money (WETPSPDC-GPR) and a fixed deadline for the project. The WETPSP-GPR extends the WETPSP to arbitrary minimal and maximal time-lags between the starting and completion times of activities. We present a new depth-first Branch and Bound (B&B) algorithm for an extended form of the problem, in which the time value of money is taken into account by discounting cash flows, and minimum, as well as maximum, time-lags between different activities may be given. The algorithm is extended with two bounding rules in order to reduce the size of the branch and bound tree. Finally, some test problems are solved and computational results are reported.