# On Project Cost-Duration Analysis Problem with Quadratic and Convex Cost Functions

## Abstract

Optimality conditions for convex programming problem are applied to the project cost-duration analysis problem for project network with convex cost. The optimality conditions give an optimality curve or an out-of-kilter type diagram for this 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 developed for the case when the cost is quadratic and convex. The different steps of the algorithm generate the solutions in such a way that it always lies on the optimality curve. Thus, problems with convex cost functions can be approximated by quadratic functions. This is better than linear approximation as is generally discussed in literature.

## Keywords

Activity Network Critical Path Terminal Node Project Duration Convex Programming Problem## Preview

Unable to display preview. Download preview PDF.

## References

- 1).Berge, C., and Ghouila-Houri, A., Programming, Games and Transportation Networks, John Wiley & Sons, Inc., 1962.Google Scholar
- 2).Dessouky, M. I., and Dunne, E. J., “Cost-Duration Analysis with the Cut Network,” AIIE Transactions, Vol. III, No. 2, pp. 150–163, 1971.Google Scholar
- 3).Elmagraby, S. E., The Design of Production Systems, Reinhold Publishing Corp., 1966.Google Scholar
- 4).Fulkerson, D. R., “A Network Flow Computation for Project Cost Curves,” Management Science, 7, No. 3, pp. 167–178, Jan. 1961.CrossRefGoogle Scholar
- 5).Florian, M. and Robillard P., “An Implicit Enumeration Algorithm for the Concave Cost Network Flow Problem,” Management Science, Vol. 18, No. 3, pp. 184–193, Nov. 1971.CrossRefGoogle Scholar
- 6).Masad, Iri, Network Flow, Transportation and Scheduling Theory and Algorithms, Academic Press, 1969.Google Scholar
- 7).Minty, G.J., “Monotone Networks,“Proceedings of the Royal Society of London, Ser. A, pp 194–212, 1960.Google Scholar
- 8).Zangwill, W.I., “Minimum Concave Cost flows in Certain Networks,” Management Science, Vol. 14, No. 7, pp 429–450, 1968.CrossRefGoogle Scholar
- 9).Zangwill, W.I., Non-Linear Programming: A Unified Approach, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1969.Google Scholar