A goal programming model for project crashing with piecewise linear time-cost trade-off

Abstract This paper presents a goal-programming model for the project-crashing problem. A convex type non-linear time-cost relationship is approximated by piecewise linear function, each segment representing a surrogate activity. The four goals considered in the model are: meeting a compressed project completion schedule; ensuring that certain activities are not compressed due to overriding quality considerations; confining the expenses to a specified budget; and minimizing the total direct cost of crashing. A case pertaining to two piecewise linear segments is reported and the goal programming model is solved using a Sequential Linear Goal Programming algorithm implemented via an MPSX (Mathematical Programming System Extended) package. An optimal crashing policy for the project is evolved, and an extensive sensitivity analysis is reported to examine the effect of changing the priority structure of goals and unit crashing costs on the optimality of the solution.