An integer programming formulation for the project scheduling problem with irregular time-cost tradeoffs

Four integer programming formulations are studied for the irregular costs project scheduling problem with time/cost trade-offs (PSIC). Three formulations using standard assignment type variables are tested against a more novel integer programming formulation. Empirical tests show that in many instances the new formulation performs best and can solve problems with up to 90 activities in a reasonable amount of time. This is explained by a reduced number of binary variables, a tighter linear programming (LP) relaxation, and the sparsity and embedded network structure of the constraint matrix of the new formulation.