Optimal Probabilistic Compression of PERT Networks

An approach is developed to determine an optimal activity compression policy when a project is required to be completed at a certain time with a prespecified probability. The approach is based on a probabilistic version of linear programming, called chance constrained linear programming (CCLP). In the CCLP formulation of the optimal network compression, each activity duration is not replaced by the mean duration. Instead each constraint is required to be satisfied by a prespecified probability. These chance constraints can be replaced by equivalent deterministic constraints when the mean and variance of each activity duration is known. The resulting CCLP formulation is solved for a numerical example. The solution has several managerial implications. Most significantly, the solution provides a quantitative means to assess the trade‐off between the cost and risk associated with the project duration. Moreover, computational efforts necessary to solve CCLP are no greater than those necessary to solve deterministic linear programming formulation of optimal network compression.