Designing a single-vendor and multiple-buyers' integrated production inventory model for interval type-2 fuzzy demand and fuzzy rule based deterioration

In this paper, a single-vendor and multiple-buyers' integrated production inventory model is investigated where deterioration rate of the item is assumed to change in accordance with the weather conditions of a particular region. It relies upon the values of certain attributes that have a direct influence on the extent of deterioration. These parameter values are easily forecasted and thereby can be utilized to determine the item depletion rate, which is executed here using Mamdani fuzzy inference scheme. Besides, a nearest interval approximation formula for the defuzzification of interval type-2 fuzzy number (IT2FN) is developed. Its application in the proposed model is brought off by considering imprecise demand patterns at the buyers' locations which are in the form of IT2FNs. The model optimizes the total number of shipments to be made to the buyers within a complete cycle so as to minimize the overall integrated cost incurred. An optimization problem with interval objective function is formulated. A detailed illustration of the theoretical results is further demonstrated with the help of numerical example, followed by sensitivity analysis which provides insights into better decision making.

Production/Inventory Policies for a Two-Echelon System with Credit Period Incentives

Trade credit is a crucial source of capital particularly for small businesses with limited financing opportunities. Inventory models considering trade credit financing have been widely studied. However, while there is extensive research on the single-vendor single-buyer inventory model allowing delays in payments, the systems where the vendor supplies to more than one buyer have received less attention. In this paper, we analyze a two-echelon inventory system where a single vendor supplies an item to two buyers who face a constant deterministic demand. The vendor produces the items at a finite rate and offers the buyers a delay payment period. That is, the buyers can delay the payment for the purchased items until the end of the credit period. Therefore, during such a period, the buyers sell the items and use the sales revenue to earn interest. At the end of the credit period, the buyers should pay the purchasing cost to the vendor for which external funding may be necessary. It is widely accepted that, in general, centralized policies reduce the total cost of the supply chain. Therefore, we first deal with an integrated model assuming that the vendor and the buyers make decisions jointly. However, in some cases, the buyers are not willing to collaborate, and the management of the supply chain has to be carried out in a decentralized manner. Hence, we also address the problem under a non-cooperative setting. Numerical examples are presented to illustrate both models. Additionally, we perform a computational experiment to compare both strategies, and a sensitivity analysis of the parameters is also carried out. From the results, we derived that, in general, it was more profitable to follow the integrated policy excepting when the replenishment costs for the buyers were high. Finally, in order to validate the computational results, a statistical analysis is performed.

“Real-world” radiomics from multi-vendor MRI: an original retrospective study on the prediction of nodal status and disease survival in breast cancer, as an exemplar to promote discussion of the wider issues

Background Most MRI radiomics studies to date, even multi-centre ones, have used “pure” datasets deliberately accrued from single-vendor, single-field-strength scanners. This does not reflect aspirations for the ultimate generalisability of AI models. We therefore investigated the development of a radiomics signature from heterogeneous data originating on six different imaging platforms, for a breast cancer exemplar, in order to provide input into future discussions of the viability of radiomics in “real-world” scenarios where image data are not controlled by specific trial protocols but reflective of routine clinical practice. Methods One hundred fifty-six patients with pathologically proven breast cancer underwent multi-contrast MRI prior to neoadjuvant chemotherapy and/or surgery. From these, 92 patients were identified for whom T2-weighted, diffusion-weighted and contrast-enhanced T1-weighted sequences were available, as well as key clinicopathological variables. Regions-of-interest were drawn on the above image types and, from these, semantic and calculated radiomics features were derived. Classification models using a variety of methods, both with and without recursive feature elimination, were developed to predict pathological nodal status. Separately, we applied the same methods to analyse the information carried by the radiomic features regarding the originating scanner type and field strength. Repeated, ten-fold cross-validation was employed to verify the results. In parallel work, survival modelling was performed using random survival forests. Results Prediction of nodal status yielded mean cross-validated AUC values of 0.735 ± 0.15 (SD) for clinical variables alone, 0.673 ± 0.16 (SD) for radiomic features only, and 0.764 ± 0.16 (SD) for radiomics and clinical features together. Prediction of scanner platform from the radiomics features yielded extremely high values of AUC between 0.91 and 1 for the different classes examined indicating the presence of confounding features for the nodal status classification task. Survival analysis, gave out-of-bag prediction errors of 19.3% (clinical features only), 36.9–51.8% (radiomic features from different combinations of image contrasts), and 26.7–35.6% (clinical plus radiomics features). Conclusions Radiomic classification models whose predictive ability was consistent with previous single-vendor, single-field strength studies have been obtained from multi-vendor, multi-field-strength data, despite clear confounding information being present. However, our sample size was too small to obtain useful survival modelling results.