This work proposes a mathematical programming (MP) representation of discrete event simulation of timed Petri nets (TPN). Currently, mathematical programming techniques are not widely applied to optimize discrete event systems due to the difficulty of formulating models capable to correctly represent the system dynamics. This work connects the two fruitful research fields, i.e., mathematical programming and Timed Petri Nets. In the MP formalism, the decision variables of the model correspond to the transition firing times and the markings of the TPN, whereas the constraints represent the state transition logic and temporal sequences among events. The MP model and a simulation run of the TPN are then totally equivalent, and this equivalence has been validated through an application in the queuing network field. Using a TPN model as input, the MP model can be routinely generated and used as a white box for further tasks such as sensitivity analysis, cut generation in optimization procedures, and proof of formal properties.

这项工作提出了定时 Petri 网 (TPN) 离散事件模拟的数学规划 (MP) 表示。目前，由于难以建立能够正确表示系统动态的模型，数学规划技术尚未广泛应用于优化离散事件系统。这项工作连接了两个富有成效的研究领域，即数学规划和定时 Petri 网。在MP形式中，模型的决策变量对应于TPN的转换触发时间和标记，而约束则代表事件之间的状态转换逻辑和时间序列。MP模型和TPN的仿真运行是完全等价的，并且这种等价性已经通过排队网络领域的应用得到了验证。使用 TPN 模型作为输入，可以例行生成 MP 模型并将其用作白盒，用于进一步的任务，例如敏感性分析、优化过程中的剪切生成以及形式属性证明。