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We discuss the design and software implementation of a nuclear data evaluation pipeline applied for a fully reproducible evaluation of neutron-induced cross sections of $^{56}$Fe above the resolved resonance region using the nuclear model code TALYS combined with relevant experimental data. The emphasis is on the mathematical and technical aspects of the pipeline and not on the evaluation of $^{56}$Fe, which is tentative. The mathematical building blocks combined and employed in the pipeline are discussed in detail. A unified representation of experimental data, systematic and statistical errors, model parameters and defects enables the application of the Generalized Least Squares (GLS) and its natural extension, the Levenberg-Marquardt (LM) algorithm, on a large collection of experimental data. The LM algorithm tailored to nuclear data evaluation accounts for the exact non-linear physics model to determine best estimates of nuclear quantities. Associated uncertainty information is derived from a Taylor expansion at the maximum of the posterior distribution. We also discuss the pipeline in terms of its IT (=information technology) building blocks, such as those to efficiently manage and retrieve experimental data of the EXFOR library and to distribute computations on a scientific cluster. Relying on the mathematical and IT building blocks, we elaborate on the sequence of steps in the pipeline to perform the evaluation, such as the retrieval of experimental data, the correction of experimental uncertainties using marginal likelihood optimization (MLO) and after a screening of thousand TALYS parameters -- including Gaussian process priors on energy dependent parameters -- the fitting of about 150 parameters using the LM algorithm. The code of the pipeline including a manual and a Dockerfile for a simplified installation is available at www.nucleardata.com.