Immediate schedule adjustment models and their semi-definite relaxation in project scheduling with temporary resource shortage

Solution methods for unexpected temporary shortage of some resources during the execution period of a project are considered in this paper. Mathematical models for getting immediate adjustment to the existing schedule are established. Semi-definite relaxation technique is also applied to these models for some properly large-scale problems. Relationships between the original models and their semi-definite relaxation problems are analyzed. Finally, some preliminary numerical experiments are performed, and the numerical results show that the proposed models are applicable and feasible to solve the temporary resource shortage problem, and the semi-definite relaxation technique is very helpful to get an immediate schedule adjustment for this kind of problem.