An Algorithm for Project Cost-Duration Analysis Problem with Quadratic and Convex Cost Functions

Kuhn-Tucker necessary and sufficient conditions for the nonlinear programming problem are applied to the project cost-duration analysis problem for project networks with convex costs. These conditions give an optimality curve for the problem. A solution is optimal if and only if when the values for activities are plotted on their optimality diagram, the values lie on the optimality curve. An algorithm is given here when the cost is convex and quadratic. The algorithm is also generalized to the case when the cost is convex and piecewise quadratic. The algorithm can be used to solve problems with convex cost functions by approximating them by piecewise quadratic functions.