Evaluating time-cost trade-off in a resource constraint GERT-type project scheduling problem considering rework

Abstract

In practice, rework is a major threat to projects’ performance and increases the risk of not delivering the outcomes on time and budget. The classical project scheduling methods are incapable of considering the rework and stochastic structure for projects in the planning phase. The current study models the stochastic projects through a GERT network in which the occurrence of rework is allowed. The aim is to find the optimal execution mode for each activity so that the project is completed within the desired time and the resource constraint is satisfied. We develop a multi-mode time–cost trade-off resource constraint project scheduling problem under uncertainty to find a here-and-now solution to minimise project completion time. The problem is solved using a combination of flow-graph theory and a branch and bound method for the developed integer programming model. As the project structure is stochastic, a distinct set of all possible realised paths is considered. To the best of our knowledge, there is no similar test instance in the literature, hence, the solution methodology is implemented on a randomly generated numerical example. The reported computational results exhibit the sensitivity of objective function to the changes in available resource amount.