Possibilistic compositions and state functions: application to the order promising process for perishables

"This is an Author's Accepted Manuscript of an article published in Grillo, H., M.M.E. Alemany, A. Ortiz, and B. De Baets. 2019. Possibilistic Compositions and State Functions: Application to the Order Promising Process for Perishables. International Journal of Production Research 57 (22). Informa UK Limited: 7006 31. doi:10.1080/00207543.2019.1574039, available online at: https://www.tandfonline.com/doi/full/10.1080/00207543.2019.1574039"[EN] In this paper, we propose the concepts of the composition of possibilistic variables and state functions. While in conventional compositional data analysis, the interdependent components of a deterministic vector must add up to a specific quantity, we consider such components as possibilistic variables. The concept of state function is intended to describe the state of a dynamic variable over time. If a state function is used to model decay in time, it is called the ageing function. We present a practical implementation of our concepts through the development of a model for a supply chain planning problem, specifically the order promising process for perishables. We use the composition of possibilistic variables to model the existence of different non-homogeneous products in a lot (sub-lots with lack of homogeneity in the product), and the ageing function to establish a shelf life-based pricing policy. To maintain a reasonable complexity and computational efficiency, we propose the procedure to obtain an equivalent interval representation based on alpha -cuts, allowing to include both concepts by means of linear mathematical programming. Practical experiments were conducted based on data of a Spanish supply chain dedicated to pack and distribute oranges and tangerines. The results validated the functionality of both, the compositions of possibilistic variables and ageing functions, showing also a very good performance in terms of the interpretation of a real problem with a good computational performance.We would also thank Dr. José De Jesús Arias García for useful discussions during the development of this work. This research has been supported by the Ministry of Science, Technology and Telecommunications, government of Costa Rica (MICITT), through the Program of Innovation and Human Capital for Competitiveness (PINN) (contract number PED-019-2015-1). We acknowledge the partial support of the project 691249, RUCAPS: Enhancing and implementing knowledge based ICT solutions within high risk and uncertain conditions for agriculture production systems , funded by the European Union s research and innovation programme under the H2020 Marie Skłodowska-Curie Actions.Grillo-Espinoza, H.; Alemany Díaz, MDM.; Ortiz Bas, Á.; De Baets, B. (2019). Possibilistic compositions and state functions: application to the order promising process for perishables. International Journal of Production Research. 57(22):7006-7031. https://doi.org/10.1080/00207543.2019.1574039S700670315722Grillo, H., M. Alemany, and A. Ortiz. 2016b. Modelling Pricing Policy Based on Shelf-Life of Non-Homogeneous Available-To-Promise in Fruit Supply Chains, 608–617. doi:10.1007/978-3-319-45390-3_52Steglich, M., and T. Schleiff. 2010. “CMPL: Coliop Mathematical Programming Language.” Technische Hochschule Wildau. doi:10.15771/978-3-00-031701-9

Structure and spacing of cellulose microfibrils in woody cell walls of dicots

The structure of cellulose microfibrils in situ in wood from the dicotyledonous (hardwood) species cherry and birch, and the vascular tissue from sunflower stems, was examined by wide-angle X-ray and neutron scattering (WAXS and WANS) and small-angle neutron scattering (SANS). Deuteration of accessible cellulose chains followed by WANS showed that these chains were packed at similar spacings to crystalline cellulose, consistent with their inclusion in the microfibril dimensions and with a location at the surface of the microfibrils. Using the Scherrer equation and correcting for considerable lateral disorder, the microfibril dimensions of cherry, birch and sunflower microfibrils perpendicular to the [200] crystal plane were estimated as 3.0, 3.4 and 3.3 nm respectively. The lateral dimensions in other directions were more difficult to correct for disorder but appeared to be 3 nm or less. However for cherry and sunflower, the microfibril spacing estimated by SANS was about 4 nm and was insensitive to the presence of moisture. If the microfibril width was 3 nm as estimated by WAXS, the SANS spacing suggests that a non-cellulosic polymer segment might in places separate the aggregated cellulose microfibrils

Spin-to-Orbital Angular Momentum Conversion and Spin-Polarization Filtering in Electron Beams

We propose the design of a space-variant Wien filter for electron beams that induces a spin half-turn and converts the corresponding spin angular momentum variation into orbital angular momentum of the beam itself by exploiting a geometrical phase arising in the spin manipulation. When applied to a spatially coherent input spin-polarized electron beam, such a device can generate an electron vortex beam, carrying orbital angular momentum. When applied to an unpolarized input beam, the proposed device, in combination with a suitable diffraction element, can act as a very effective spin-polarization filter. The same approach can also be applied to neutron or atom beams.Comment: 9 pages, 5 figure

The frozen state in the liquid phase of side-chain liquid-crystal polymers

International audienceQuenched isotropic melts of side-chain liquid-crystal polymers reveal surprisingly an anisotropic polymer conformation. This small-angle neutron-scattering (SANS) result is consistent with the identification of a macroscopic, solidlike response in the isotropic phase. Both experiments (rheology and SANS) indicate that the polymer system appears frozen on millimeter length scales and at the time scales of the observation. This result implies that the flow behavior is not the terminal behavior and that cross-links or entanglements are not a necessary condition to provide elasticity in melts

Mendil et al Reply

International audienceIn the preceding Comment [1], Collin and Martinoty claim that a conventional flow behavior (G' ~ f2 , G'' ~ f) is obtained at 20 $\mu$m gap thickness, for a LC-polymer (LCP105) in the nematic phase, using a filling with a capillary, whereas a solidlike behavior (G' ~ Cst, G" ~ Cst) is observed by approaching two parallel surfaces to the sample (as we apply in our experiment). Our observations of a terminal solidlike behavior are thus interpreted by Collin and Martinoty as an anomaly induced by compression effects. We clearly refute this interpretation. We note that, on Fig. 13 and 14 of a previous paper written by Collin and Martinoty [2], they report no more a conventional flow but an elastic behavior at lower temperature using the capillary filling and the same polymer (LCP105). Their previous observations are thus in contradiction with their present purpose; i.e., a terminal flow behavior

Hemicellulose binding and the spacing of cellulose microfibrils in spruce wood

Cellulose microfibrils in conifers, as in other woody materials, are aggregated into loose bundles called macrofibrils. The centre-to-centre spacing of the microfibrils within these macrofibrils can be estimated from the position of a broad diffraction peak in small-angle neutron scattering (SANS) after deuteration. A known spacing of 3.0 nm, increasing with moisture content, is consistent with direct microfibril to microfibril contact. However recent evidence indicates that conifer microfibrils are partially coated with bound xylan chains, and possibly with lignin and galactoglucomannan, implying a wider centre-to-centre spacing as found in angiosperm wood. Delignification of spruce wood allowed a weak SANS peak to be observed without measurable change in spacing. By deuterating spruce wood in mildly alkaline D2O and then re-equilibrating with ambient H2O, deuterium atoms were trapped in a position that gave a 3.8 nm microfibril spacing under dry conditions as in angiosperm wood, instead of the 3.0 nm spacing normally observed in conifers. After conventional vapour deuteration of spruce wood a minor peak at 3.8 nm could be fitted in addition to the 3.0 nm peak. These observations are consistent with some microfibril segments being separated by bound xylan chains as in angiosperms, in addition to the microfibril segments that are in direct contact

Integrable mixing of A_{n-1} type vertex models

Given a family of monodromy matrices {T_u; u=0,1,...,K-1} corresponding to integrable anisotropic vertex models of A_{(n_u)-1}-type, we build up a related mixed vertex model by means of glueing the lattices on which they are defined, in such a way that integrability property is preserved. Algebraically, the glueing process is implemented through one dimensional representations of rectangular matrix algebras A(R_p,R_q), namely, the `glueing matrices' zeta_u. Here R_n indicates the Yang-Baxter operator associated to the standard Hopf algebra deformation of the simple Lie algebra A_{n-1}. We show there exists a pseudovacuum subspace with respect to which algebraic Bethe ansatz can be applied. For each pseudovacuum vector we have a set of nested Bethe ansatz equations identical to the ones corresponding to an A_{m-1} quasi-periodic model, with m equal to the minimal range of involved glueing matrices.Comment: REVTeX 28 pages. Here we complete the proof of integrability for mixed vertex models as defined in the first versio