The performance of priority rules for the dynamic stochastic resource-constrained multi-project scheduling problem: an experimental investigation
研究了矩阵组织中项目经理如何选择优先规则来调度动态到达的项目，以最小化加权项目延迟。实验发现W(CR+SPT)规则在多数情况下表现最佳。
Abstract We consider the problem of a project manager of a matrix organization responsible for the timely completion of projects arriving over time and requiring the usage of a set of resources under his/her purview. A project is defined by a set of activities, precedence relations between activities, resource requirements, a customer due date, and a priority (a weight). Arriving projects are released to a flow control system that monitors the progress of activities and schedules the set of available activities, i.e., activities that are ready to be processed, as appropriate. A critical feature of such control systems is the decision process for choosing the next activity to seize a given resource. This is the focus of this paper. In the past several decades, various heuristic priority rules have been proposed in the literature to support this type of decision in differing settings such as the job shop problem and the deterministic resource-constrained project scheduling problem. A gap exists with respect to testing the various rules all together in the more realistic dynamic-stochastic multi-project environment when the objective is to minimize weighted project tardiness. The purpose of this paper is to fill this gap. Results show that the priority rule “Weighted Critical Ratio and Shortest Processing Time” $$(\hbox {W}(\hbox {CR}+\hbox {SPT}))$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mtext>W</mml:mtext> <mml:mo>(</mml:mo> <mml:mtext>CR</mml:mtext> <mml:mo>+</mml:mo> <mml:mtext>SPT</mml:mtext> <mml:mo>)</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> is the best performing rule with respect to minimizing weighted project tardiness. $$\hbox {W}(\hbox {CR}+\hbox {SPT})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>W</mml:mtext> <mml:mo>(</mml:mo> <mml:mtext>CR</mml:mtext> <mml:mo>+</mml:mo> <mml:mtext>SPT</mml:mtext> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> is shown to be a variant of the family of “Modified Due Date” rules first introduced by Baker and Bertrand (J Oper Manage 1(3):37–42, 1982). Repeated application of Duncan’s Multiple Range test demonstrates the robustness of our findings. For the environmental parameters (due date tightness, variation of expected activity durations, and utilization of resource), the $$\hbox {W}(\hbox {CR}+\hbox {SPT})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>W</mml:mtext> <mml:mo>(</mml:mo> <mml:mtext>CR</mml:mtext> <mml:mo>+</mml:mo> <mml:mtext>SPT</mml:mtext> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> rule is dominant with respect to weighted project tardiness among the eleven priority rules tested. Only when the number of resources is very modest (either 1 or 3 resources) or under a purely parallel resource network is $$\hbox {W}(\hbox {CR}+\hbox {SPT})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>W</mml:mtext> <mml:mo>(</mml:mo> <mml:mtext>CR</mml:mtext> <mml:mo>+</mml:mo> <mml:mtext>SPT</mml:mtext> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> not the dominant rule. In those cases, its variant $$\hbox {W}(\hbox {CR}+\hbox {GSPT})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>W</mml:mtext> <mml:mo>(</mml:mo> <mml:mtext>CR</mml:mtext> <mml:mo>+</mml:mo> <mml:mtext>GSPT</mml:mtext> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> is the best performing rule with respect to weighted project tardiness.