A New Mathematical Approach based on Conic Quadratic Programming for the Stochastic Time-Cost Tradeoff Problem in Project Management

In this paper, we consider a stochastic Time-Cost Tradeoff Problem (TCTP) in PERT networks for project management, in which all activities are subjected to a linear cost function and assumed to be exponentially distributed. The aim of this problem is to maximize the project completion probability with a pre-known deadline to a predefined probability such that the required additional cost is minimized. A single path TCTP is constructed as an optimization problem with decision variables of activity mean durations. We then reformulate the single path TCTP as a cone quadratic program in order to apply polynomial time interior point methods to solve the reformulation. Finally, we develop an iterative algorithm based on Monte Carlo simulation technique and conic optimization to solve general TCTP. The proposed approach has been tested on some randomly generated test problems. The results illustrate the good performance of our new approach.