Minimization of the Makespan a Project in the Critical Chain Project Management Framework Using a Max-Plus Linear Representation

The minimization of the makespan of a project is targeted under the critical chain project management (CCPM) framework. Although the conventional CCPM discipline does not pay attention to the optimality of the solution, the execution sequence of tasks would highly affect the makespan. We hence construct an optimization problem of minimizing the makespan, and develop a solving method for this. In calculating the objective function value, a discrete algebraic system referred to as max-plus algebra plays a key role. The developed algorithm bases on branch-and-cut and branch-and-bound methodologies, by which an exact optimal solution can be obtained.