Optimization of Project Schedules in the Critical-Chain Project-Management Max-Plus-Linear Framework
Optimization of Project Schedules in the Critical-Chain Project-Management Max-Plus-Linear Framework
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DOI：
10.15866/iremos.v11i4.13485
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发表时间：
2018-08
期刊：
影响因子：
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通讯作者：
H. Goto;Alan T. Murray
中科院分区：
文献类型：
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作者：
H. Goto;Alan T. Murray
针对任务持续时间不确定的项目，在关键链项目管理方法的框架下，我们的目标是最小化项目的完工时间。在现有框架中，没有注意到“足够好”目标下的最优化。然而，在可用资源有限的情况下，任务的处理顺序显然会极大地影响项目的完成时间。因此，我们构造一个优化问题来获得精确的最优解。一种称为极大代数的离散代数系统是计算目标函数值的关键。我们坚持寻求精确的解，这依赖于分支定界技术。通过数值实验，我们发现计算时间高度依赖于优先约束的结构和资源的分配。当任务数不超过20个时，所开发的求解器能够在实际时间标准内获得最优解。
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.