At depots with refined oil shortage, arranging a reasonable distribution scheme with limited supply affects operation costs, demand satisfaction rate of gasoline stations (hereafter, ‘station satisfaction’), and overtime penalty. This study considers the refined oil distribution problem with shortages using a multi-objective optimisation approach from the perspective of decision makers of oil marketing companies. The modelling and solving process involves (i) formulation of a crisp multi-depot vehicle routing model with limited supply (MDVRPLS) which considers station priority and soft time windows, (ii) development of a robust optimisation model (ROM) to manage uncertainty in demand, and (iii) the proposal of a multi-objective particle swarm optimisation (MOPSO)algorithm. Results of numerical experiments show that (i) the crisp model can better balance operation costs, station satisfaction, and overtime penalty, which produces 3.33% and 4.60% increase in station satisfaction at an increased unit cost and overtime penalty respectively; (ii) ROM successfully addresses uncertainty in demand compared to the crisp model, which requires an additional 8.81% in cost and 12.85% in penalty; and (iii) the MOPSO manages these MDVRPLS models more effectively than other heuristic algorithms. Therefore, applying ROM of refined oil supply shortage to the management significantly improves the efficiency and resists the disturbance caused by external uncertainties, providing scope for efficient distribution of scarce resources.

In this paper, a concept of fuzzy semientropy is proposed to quantify the downside uncertainty. Several properties of fuzzy semientropy are identified and interpreted. By quantifying the downside risk with the use of semientropy, two mean-semi-entropy portfolio selection models are formulated, and a fuzzy simulation-based genetic algorithm is designed to solve the models to optimality. We carry out comparative analyses among the fuzzy mean-entropy models and the fuzzy mean-semi-entropy models and demonstrate that the mean-semi-entropy models can significantly improve the dispersion of investment. Several illustrative examples using stock dataset from the real-world financial market (China Shanghai Stock Exchange) also show the effectiveness of the models.

By elevating stress levels, accelerated degradation testing (ADT) can obtain sufficient degradation data within limited time to predict the reliability and lifetime for highly reliable and long life products. In general, the degradation data collected in ADT have three kinds of characteristics: the time-stress-dependent structure, the random uncertainties caused by random effects in time dimension, and unit-to-unit variations, and the epistemic uncertainty caused by the small sample problem. However, existing acceleration degradation models based on Brownian motion with drift can successfully consider the time-stress-dependent structure and the random uncertainty, while failing to take the epistemic uncertainty into account. In this paper, based on the random fuzzy theory, a new random fuzzy accelerated degradation model and its corresponding statistical analysis method are proposed. The proposed model can take the above three kinds of characteristics into consideration simultaneously. The application case indicates that the proposed methodology is applicable for modeling the ADT data under small sample size. The simulation results show that the proposed methodology is more stable and slightly more conservative than the ADT model considering unit-to-unit variations. In addition, under small sample size (from 3 to 10), the proposed methodology is more stable and more accurate than the ADT model considering unit-to-unit variations.

The COVID-19 pandemic has severely affected urban transport patterns, including the way residents travel. It is of great significance to predict the demand of urban ride-hailing for residents' healthy travel, rational platform operation, and traffic control during the epidemic period. In this paper, we propose a deep learning model, called MOS-BiAtten, based on multi-head spatial attention mechanism and bidirectional attention mechanism for ride-hailing demand prediction. The model follows the encoder-decoder framework with a multi-output strategy for multi-steps prediction. The pre-predicted result and the historical demand data are extracted as two aspects of bidirectional attention flow, so as to further explore the complicated spatiotemporal correlations between the historical, present and future information. The proposed model is evaluated on the real-world dataset during COVID-19 in Beijing, and the experimental results demonstrate that MOS-BiAtten achieves a better performance compared with the state-of-art methods. Meanwhile, another dataset is used to verify the generalization performance of the model.