Project compression with nonlinear cost functions

This paper presents three mixed-integer linear programming models to assist project managers in making decisions to compress project completion time under realistic activity time-cost relationship assumptions. The models assume nonlinear activity time-cost functions that are rational functions that can be convex or concave. A user of the models needs to estimate an activity time between normal and crash times where the rate of increase in the cost of performing an activity changes significantly. An efficient piecewise linearization method is presented through which nonlinear cost functions can be approximated in a mixed-integer linear programming model. Each of the models focuses on a different objective a project manager may pursue, such as minimizing project completion subject to a crash budget constraint, or minimizing total project cost, or minimizing total cost under late completion penalties or minimizing total cost with early completion bonuses of a project contract. The paper also uses a simple example which has activities that have all the different types of cost functions discussed in the paper to demonstrate how each model can be used for a project manager's different objectives.