Abstract: The example embodiments are directed to methods and systems for generating a model of an optimum flow of materials within a supply network based on a relax mixed integer programming model. For example, the method may include generating, via a software application, a model of the supply network based on the data stored in the storage device, executing a MIP optimizer on the model to generate a configuration of a flow of materials within the supply network, wherein the MIP optimizer is instructed to relax discrete constraints within the supply network when generating the configuration, generating a graphical user interface that includes a plurality of graphical objects corresponding to a plurality of locations included in the configuration and directional edges between the plurality of graphical objects corresponding to the flow of the materials between the plurality of locations, and displaying the graphical user interface.

Abstract: The invention is directed to carbon fibers prepared from polyacrylonitrile (PAN) dopes aged at low temperatures. The PAN dopes are aged at low temperatures to facilitate the formation of certain structures in the PAN polymer. When the PAN comprising these structures is formed into carbon fibers, these fibers have improved tensile properties. Alternative methods of introducing the certain structures into PAN fibers are also provided for by the invention.

Abstract: The example embodiments are directed to methods and systems for generating a model of an optimum flow of materials within a supply network based on a relax mixed integer programming model. For example, the method may include generating, via a software application, a model of the supply network based on the data stored in the storage device, executing a MIP optimizer on the model to generate a configuration of a flow of materials within the supply network, wherein the MIP optimizer is instructed to relax discrete constraints within the supply network when generating the configuration, generating a graphical user interface that includes a plurality of graphical objects corresponding to a plurality of locations included in the configuration and directional edges between the plurality of graphical objects corresponding to the flow of the materials between the plurality of locations, and displaying the graphical user interface.