Customer prioritisation in business‐to‐business (B2B) manufacturing must be decided from production records. These records rarely contain prices, and they register demand at the level of the work order. The classical Recency–Frequency–Monetary (RFM) construct needs adaptation before it can be applied in this setting. Monetary value is unobserved, temporal resolution is coarse, and the signals that matter to operations lie outside the construct. This study extends RFM with a Quality dimension, defined as the conformity ratio weighted by volume, and a Variety dimension, defined as portfolio breadth. Criterion weights are derived with the Logarithmic Percentage Change‐Driven Objective Weighting (LOPCOW) method in its standard form. Customers are ranked with the Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) method and partitioned into quintile segments. The framework is applied to 5486 work orders from 120 customers of a glass processor over 2022–2024. Four structural signatures characterise the customer base and explain the behaviour of the method. Output is concentrated with a heavy tail (Gini 0.83), and the top quintile supplies 81.6% of conforming output. Setup and scrap intensity scale sublinearly with volume. The Recency boundary produces a threshold in the ranking. The compromise ordering cannot be reduced to any single dimension. An exact identity shows that a LOPCOW weight is a function of the ratio of mean to dispersion of the normalised criterion. The weight therefore measures the shape of a distribution, not managerial importance. Quality (0.58) and Recency (0.33) dominate. Removing either reassigns a third to a half of the customers, whereas removing Frequency or the volume proxy reassigns two. With volume held constant, portfolio breadth is positively associated with setup time per unit (elasticity 0.46), while burden adjusted for volume is uncorrelated with the compromise score. The segmentation is stable under moderate perturbation of the weights (mean adjusted Rand index 0.97 over 2000 draws) and moderately stable under arbitrary weights (0.52). Four objective weighting methods applied to the same matrix give four different weight vectors, so objectivity here means reproducibility rather than uniqueness. The outputs are stated as proposals for operational policy, not as demonstrated effects.
The global challenges we are facing, environmental, economic and health crises, are complex problems that need a methodological approach that honours this complexity. Current approaches, extrapolating the future from past data, will not be able to tackle the profound changes that are to come. Instead, we need complexity methods that uncover mechanisms and processes underlying social phenomena and that let us extrapolate counterfactual future narratives. This paper discusses how the integration of qualitative and computational complexity methods can help with this endeavour.
Forecasting short annual time series is challenging because limited observations increase the risks of unstable optimization, overfitting, and information leakage. This study proposes a standard first-order neural ordinary differential equation trained with finite-memory Grünwald–Letnikov fractional momentum. The fractional operator acts on the parameter update sequence rather than on the latent-state dynamics. The empirical evaluation combines a descriptive comparison on medium-length regional annual energy-consumption series with a 12-year holdout and a reproducible experiment on five extremely short provincial annual series, with the final two observations reserved for strictly recursive testing. The fractional order is selected by particle swarm optimization using only the training data. GLFNODE is compared with a NODE of the same architecture trained using Adam, together with MLP, ARIMA, SARIMA, ETS, and LSTM baselines. Across the five reported series, GLFNODE achieves test MAPE values ranging from 1.848% to 6.300%. Compared with the Adam-trained NODE, GLFNODE reduces the mean MAPE, MAE, and RMSE by 17.56%, 17.14%, and 15.91%, respectively. These results provide reproducible evidence that fractional-memory optimization can improve a compact neural ODE under extremely short-record conditions, particularly relative to the same architecture trained with Adam.
In this work, the exact solutions of nonlinear wave equations are studied in the framework of fractional gas dynamics. Two powerful methods, such as the generalized projective Riccati equation method (GPREM) and modified extended simple equation method (MESM), are applied to solve the fractional gas dynamics equations, which are used to model complex wave phenomena, exactly and analytically. A central role in this approach is played by the Riccati equation, which we can use to obtain the soliton solutions, periodic waves, and other nonlinear wave patterns. We show that both GPREM and MESM give a systematic way to find exact and soliton solutions that are essential to understanding the dynamics of fractional systems and facilitate the introduction of a novel order of the gas dynamics equations, which poses a unique set of challenges. The physical interpretation of these solutions is discussed in terms of wave propagation, stability, and interaction of nonlinear waves. The findings demonstrate the applicability of the Riccati-based techniques to the solution of fractional nonlinear evolution equations and will help in the development of theoretical models in fractional dynamics. This paper sets the groundwork for additional research into the use of fractional calculus in the study of fluid dynamics and wave propagation and could prove useful in other branches of physics and engineering.
The present research provides the solutions of the fractional order (FO) tuberculosis (TB) epidemics model by applying the supervised learning Bayesian regularization neural network (SL-BRNN). The Caputo fractional derivative is executed to solve the TB epidemic model, which is essential to perform the intricate systems with nonlinear relations and delivers a powerful mathematical structure for relating systems with FO dynamics. The model is described into six population groups: susceptible, latent, treatment of Type 1 and 2, infected, and recovered. A construction of network is performed by taking sigmoid activation function and 21 neurons in the hidden layer, 1000 epochs, and optimization through BR. The dataset of the FO-TB epidemics model is calculated using the Adams–Bashforth–Moulton technique in intervals 0 and 1, with a 0.01 step size, which reduces the mean square error by data splitting into training (73%), testing (14%), and validation (13%). Moreover, the data training is performed using the designed construction of the solver based on SL-BRNN. The solutions of three FO-TB epidemics models are presented in three cases by taking the FO derivative values 0.7, 0.8, and 0.9. In addition, the solutions of the proposed SL-RNN are compared with the Levenberg–Marquardt backpropagation algorithm in order to check the accuracy of the scheme. Moreover, the best training values, error histogram, fitness performances, absolute error, and state transition further provide the accuracy and reliability of the designed SL-BRNN.
