Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

The complexity of the neutron transport phenomenon throws its shadows on every physical system wherever neutron is produced or used. In the current study, an ab initio derivation of the neutron self-shielding factor to solve the problem of the decrease of the neutron flux as it penetrates into a material placed in an isotropic neutron field. We have employed the theory of steady-state neutron transport, starting from Stuart's formula. Simple formulae were derived based on the integral cross-section parameters that could be adopted by the user according to various variables, such as the neutron flux distribution and geometry of the simulation at hand. The concluded formulae of the self-shielding factors comprise an inverted sigmoid function normalized with a weight representing the ratio between the macroscopic total and scattering cross-sections of the medium. The general convex volume geometries are reduced to a set of chord lengths, while the neutron interactions probabilities within the volume are parameterized to the epithermal and thermal neutron energies. The arguments of the inverted-sigmoid function were derived from a simplified version of neutron transport formulation. Accordingly, the obtained general formulae were successful in giving the values of the experimental neutron self-shielding factor for different elements and different geometries.Comment: 14 pages, 5 figures, 1 graphical abstract, 73 references, and 2 tables, include improvement of illustration and story-telling writing styl

Stimulated perturbation on the neutron flux distribution in the mutually-dependent source-to-absorber geometry

The complexity of the neutron transport phenomenon throws its shadows on every physical system wherever neutron is produced or absorbed. The Monte Carlo N-Particle Transport Code (MCNP) was used to investigate the flux perturbations in the neutron field caused by an absorber. The geometry of the present experiment was designed to reach a simulation of an isotopic neutron field. The neutron source was a ${}^{241}$AmBe with the production physics of neutrons is dependent only on alpha-beryllium interaction and is independent of what happened to the neutron after it was generated. The geometries have been designed to get a volume of uniform neutron densities within a spherical volume of radius 15 cm in every neutron energy group up to 10 MeV. Absorbers of different dimensions were placed within the volume to investigate the field perturbation. Different neutron absorbers were used to correlate the phenomenon to the integral cross-section of the absorber. Flux density inside and outside the absorber samples was determined, while the spatial neutron flux distribution produced by the AmBe source without an absorber was taken as a reference. This study displayed that absorbers of various dimensions perturb the neutron field in a way that is dependent on the absorption and scattering cross-sections, particularly in the neutron resonance region. Unlike the simple picture of reducing the number density of neutrons, the perturbation was found to influence the moderation of neutrons in the medium, significantly above 1 MeV.Comment: 10 pages, 13 figures, 26 reference

The Top-Dog Index: A New Measurement for the Demand Consistency of the Size Distribution in Pre-Pack Orders for a Fashion Discounter with Many Small Branches

We propose the new Top-Dog-Index, a measure for the branch-dependent historic deviation of the supply data of apparel sizes from the sales data of a fashion discounter. A common approach is to estimate demand for sizes directly from the sales data. This approach may yield information for the demand for sizes if aggregated over all branches and products. However, as we will show in a real-world business case, this direct approach is in general not capable to provide information about each branch's individual demand for sizes: the supply per branch is so small that either the number of sales is statistically too small for a good estimate (early measurement) or there will be too much unsatisfied demand neglected in the sales data (late measurement). Moreover, in our real-world data we could not verify any of the demand distribution assumptions suggested in the literature. Our approach cannot estimate the demand for sizes directly. It can, however, individually measure for each branch the scarcest and the amplest sizes, aggregated over all products. This measurement can iteratively be used to adapt the size distributions in the pre-pack orders for the future. A real-world blind study shows the potential of this distribution free heuristic optimization approach: The gross yield measured in percent of gross value was almost one percentage point higher in the test-group branches than in the control-group branches.Comment: 22 pages, 15 figure

Integrating production scheduling and transportation procurement through combinatorial auctions

This study uses the winner determination problem (WDP) to integrate auction transportation procurement with decisions related to production scheduling. The basic problem arises when a manufacturer has to clear a combinatorial auction to decide whether to cover transportation needs by using the in-house fleet or to procure transportation through auction. Thus, the manufacturer should include an additional decision level by integrating the WDP with production scheduling to gain efficiency and achieve savings in the logistics system. To the best of our knowledge, this is the first time production and transportation procurement problems are being solved simultaneously in an integrated manner. The study proposes a mathematical formulation and develops two heuristic approaches for solving the integrated problem. Extensive computational experiments and sensitivity analyses are reported to validate the model, assess the performance of the heuristics, and show the effect of integration on total cost. © 2020 The Authors. Networks published by Wiley Periodicals LLC

Criticality Analysis of Activity Networks under Interval Uncertainty

Dedicated to the memory of Professor Stefan Chanas - The extended abstract version of this paper has appeared in Proceedings of 11th International Conference on Principles and Practice of Constraint Programming (CP2005) ("Interval Analysis in Scheduling", Fortin et al. 2005)International audienceThis paper reconsiders the Project Evaluation and Review Technique (PERT) scheduling problem when information about task duration is incomplete. We model uncertainty on task durations by intervals. With this problem formulation, our goal is to assert possible and necessary criticality of the different tasks and to compute their possible earliest starting dates, latest starting dates, and floats. This paper combines various results and provides a complete solution to the problem. We present the complexity results of all considered subproblems and efficient algorithms to solve them