Optimization of Project Schedules in the Critical-Chain Project-Management Max-Plus-Linear Framework

Focusing on projects with uncertain task duration times, we aim to minimize the makespan of a project under the framework of the critical-chain project management approach. In existing frameworks, no attention has been paid to optimality under the “good enough” goal. However, in situations where there are only limited available resources, it is clear that the processing sequence of tasks greatly affects the makespan of the project. Hence, we structure an optimization problem to obtain an exact optimal solution. A discrete algebraic system called max-plus algebra plays is key to calculate the objective-function value. We adhere to seek an exact solution, for which a branch-and-bound technique is relied upon. Through numerical experiments, we find that the computation time highly depends on the structure of precedence constraints and assignment of resources. The developed solver is able to obtain an optimal solution within practical time standards if the number of tasks is not greater than 20.