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The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators.
While previously network operator and gas vendor where united, they were forced to split up into independent companies.
The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way.
We show that these new paradigms lead to new and challenging mathematical optimization problems.
In order to solve them and to provide meaningful results for practice, all aspects of the underlying problems, such as combinatorics, stochasticity, uncertainty, and nonlinearity, have to be addressed.
With such special-tailored solvers, free network capacities and topological network extensions can, for instance, be determined.
The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor were united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We discuss how these changing paradigms lead to new and challenging mathematical optimization problems. This includes the validation of nominations, that asks for the decision if the network’s capacity is sufficient to transport a specific amount of flow, the verification of booked capacities and the detection of available freely allocable capacities, and the topological extension of the network with new pipelines or compressors in order to increase its capacity. In order to solve each of these problems and to provide meaningful results for the practice, a mixture of different mathematical aspects have to be addressed, such as combinatorics, stochasticity, uncertainty, and nonlinearity. Currently, no numerical solver is available that can deal with such blended problems out-of-the-box. The main goal of our research is to develop such a solver, that moreover is able to solve instances of realistic size. In this article, we describe the main ingredients of our prototypical software implementations.
Perspectives
(2015)
Die mittel- und längerfristige Planung für den Gastransport hat sich durch
Änderungen in den regulatorischen Rahmenbedingungen stark verkompliziert.
Kernpunkt ist die Trennung von Gashandel und -transport. Dieser Artikel
diskutiert die hieraus resultierenden mathematischen Planungsprobleme,
welche als Validierung von Nominierungen und Buchungen, Bestimmung der
technischen Kapazität und Topologieplanung bezeichnet werden. Diese
mathematischen Optimierungsprobleme werden vorgestellt und Lösungsansätze
skizziert.
The industrial treatment of waste paper in order to regain valuable
fibers from which recovered paper can be produced, involves several
steps of preparation. One important step is the separation of stickies
that are normally attached to the paper. If not properly separated,
remaining stickies reduce the quality of the recovered paper or even
disrupt the production process. For the mechanical separation process
of fibers from stickies a separator screen is used. This machine has
one input feed and two output streams, called the accept and the
reject. In the accept the fibers are concentrated, whereas the reject
has a higher concentration of stickies. The machine can be controlled
by setting its reject rate. But even when the reject rate is set
properly, after just a single screening step, the accept still has too
many stickies, or the reject too many fibers. To get a proper
separation, several separators have to be assembled into a
network. From a mathematical point of view this problem can be seen as
a multi-commodity network flow design problem with a nonlinear,
controllable distribution function at each node. We present a
nonlinear mixed-integer programming model for the simultaneous
selection of a subset of separators, the network's topology, and the
optimal setting of each separator.
Numerical results are obtained via
different types of linearization of the nonlinearities and the use of
mixed-integer linear solvers, and compared with state-of-the-art
global optimization software.