Application Cutting Plane Method for Stochastic Time Cost Trade off Problem in Project PERT Type Networks

We develop a Confidence Level (C.L) based approach for Stochastic Time-Cost Trade off Problem (STCTP) in a PERT type networks, where activities are subjected to linear cost functions and assumed that exponentially distributed. The objective of proposed method is improving the probability of project completion time in a prespecified due date to a predefined probability (C.L). For this purpose, we construct a non-linear convex program with decision variables of activity mean times. The objective of the described model is minimization of direct costs of project compression/ crashing. The proposed model has effective managerial advantages for prevention of project tardiness. Project planners can decrease potential risk of real environment by increasing Confidence Level of project completion to a reasonable value (predefined). For solving formulation of constructed model, we present a well-established hybrid approach which uses mixed simulation, mathematics (Cutting Plane Method) and heuristic. This hybrid approach solves an approximated linear programming that obtained by using cutting planes, for path with maximum Path Criticality Index (Calculated by using simulation results), in each iteration. In the last step, the approach uses a heuristic algorithm for optimal elimination of Cutting Plane approximation. Finally for demonstration of model ability, two illustrative examples are discussed

Keywords:

Stochastic networks , Time Cost Trade off , Project crashing , Confidence Level , Path Criticality Index