As a consequence of the liberalisation of the European gas market in the last decades, gas trading and transport have been decoupled. At the core of this decoupling are so-called bookings and nominations. Bookings are special capacity right contracts that guarantee that a specified amount of gas can be supplied or withdrawn at certain entry or exit nodes of the network. These supplies and withdrawals are nominated at the day-ahead. The special property of bookings then is that they need to be feasible, i.e., every nomination that complies with the given bookings can be transported. While checking the feasibility of a nomination can typically be done by solving a mixed-integer nonlinear feasibility problem, the verification of feasibility of a set of bookings is much harder. The reason is the robust nature of feasibility of bookings—namely that for a set of bookings to be feasible, all compliant nominations, i.e., infinitely many, need to be checked for feasibility. In this paper, we consider the question of how to verify the feasibility of given bookings for a number of special cases. For our physics model we impose a steady-state potential-based flow model and disregard controllable network elements. For this case we derive a characterisation of feasible bookings, which is then used to show that the problem is in coNP for the general case but can be solved in polynomial time for linear potential-based flow models. Moreover, we present a dynamic programming approach for deciding the feasibility of a booking in tree-shaped networks even for nonlinear flow models. It turns out that the hardness of the problem mainly depends on the combination of the chosen physics model as well as the specific network structure under consideration. Thus, we give an overview over all settings for which the hardness of the problem is known and finally present a list of open problems.

中文翻译：

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欧洲天然气市场的预订：可行性和计算复杂性结果的表征

在过去的几十年中，由于欧洲天然气市场的开放，天然气的贸易和运输已经脱钩。这种脱钩的核心是所谓的预订和提名。预订是特殊的容量权利合同，可确保在网络的某些入口或出口节点可以供应或提取指定数量的天然气。这些物资和提款将提前一天被提名。预订的特殊之处在于，它们必须可行，即，可以运输符合给定预订的所有提名。虽然检查提名的可行性通常可以通过解决混合整数非线性可行性问题来完成，但验证一组预订的可行性要困难得多。原因是预订的可行性很强，也就是说，要使一组预订可行，就需要检查所有合规的提名，即无数次提名，以确保可行性。在本文中，我们考虑了如何在许多特殊情况下验证给定预订的可行性的问题。对于我们的物理模型，我们强加了基于稳态势的流模型，而忽略了可控的网络元素。对于这种情况，我们得出了可行预订的特征，然后将其用于表明问题出在 对于我们的物理模型，我们强加了基于稳态势的流模型，而忽略了可控的网络元素。对于这种情况，我们得出可行预订的特征，然后将其用于表明问题出在 对于我们的物理模型，我们强加了基于稳态势的流模型，而忽略了可控的网络元素。对于这种情况，我们得出了可行预订的特征，然后将其用于表明问题出在一般情况下的coNP，但对于基于线性势能的流模型，可以在多项式时间内求解。此外，我们提出了一种动态编程方法，即使在非线性流量模型中，也可以确定在树形网络中进行预订的可行性。事实证明，问题的严重性主要取决于所选择的物理模型以及所考虑的特定网络结构的组合。因此，我们对已知问题难度的所有设置进行了概述，并最终给出了未解决问题的列表。