Abstract: Systems and methods for controlling automated systems, such as robots and other devices/resources, using integer programming and column generation techniques, are provided. The system retrieves location and movement data corresponding to at least one automated system, and processes the location and movement data using an integer linear programming algorithm. The system also optimizes the integer linear programming algorithm using a column generation algorithm, and solves a pricing problem associated with generating routes for the at least one automated system. Then, the system generates a route based on outputs of the integer linear programming algorithm, the column generation algorithm, and solving of the pricing problem, and transmits the route to the at least one automated system, the at least one automated system executing the route to control a location or a movement of the at least one automated system.

Abstract: Systems and methods for automated vehicle routing using column generation optimization are provided. The system receives capacitated vehicle routing problem (CVRP) input data and generates a minimum weight set cover problem formulation for a CVRP for performing column generation optimization over the input data. The system determines smooth-dual optimal inequalities (S-DOI) and flexible-dual optimal inequalities (F-DOI) for the CVRP for performing the column generation optimization over a valid subset of the input data. Then, the system adapts the S-DOI and the F-DOI to generate smooth and flexible dual optimal inequalities (SF-DOI) for the CVRP for performing the column generation optimization over a relaxed subset of the input data. The system utilizes the SF-DOI to accelerate column generation optimization over the relaxed subset of the input data.

Abstract: A burner and oxygen-injection device (35) for a melting furnace (30) comprising one or more injectors (3, 3?, 3?) consisting of an internal pipe (1) and a head (2), which is fixed to one end of said hollow body and is provided with a nozzle (4) that sets the pipe (1) in communication with the outside. The nozzle has at least the outlet cross section (13) of a substantially oblong shape, in such a way that a subsonic flow of oxygen coming out of said nozzle will open in fanwise fashion, along an inclined plane containing an axis that is substantially horizontal and orthogonal to the axis of the nozzle. The injector (3) comprises holes (6) for injection of gaseous fuel, around said nozzle, arranged along the elongated sides of the outlet cross section of the nozzle. The device (35) also comprises a pipe for injection of carbon in powder form set underneath the nozzle or nozzles (3, 3?, 3?).

Abstract: Device to deliver comburent and combustible gases, such as oxygen, methane or similar, and/or solid combustible materials inside a melting container, the device comprising a first unit (18) functioning as a burner and/or supersonic lance, and a second unit (19) functioning as a burner and/or carbon lance, the units (18, 19) being reciprocally oriented so that the respective streams delivered (21, 22) meet around a point (20) located above or around the upper level of the layer of slag (17), giving rise, during the normal melting cycle, to a substantially stoichiometrically balanced reaction between oxygen and carbon. Melting method using at least one of the devices as above.