In this paper, a proactive and reactive multi-project scheduling problem is addressed. This problem is related to the influences of uncertain factors, which leads to a deviation between actual scheduling and baseline scheduling, and a recovery strategy is established in order to generate a baseline scheduling scheme. This paper introduces a proactive multi-project scheduling sub-model. When the activity is interrupted, the proactive scheduling scheme is used as the baseline scheduling scheme, which is embedded in the reactive scheduling, and then, the reactive scheduling sub-model is established. The proposed model can be used to generate alternative schedules, and to meet this need, a genetic simulated annealing algorithm is proposed. A buffer change operator (SC) and a crossover operator are designed in a genetic simulated annealing algorithm so that in the early stages of the algorithm, an optimum individual is produced and protected. The performance comparison shows that the genetic simulated annealing algorithm significantly outperforms the previous algorithms.INDEX TERMS Multi-project scheduling, proactive and reactive scheduling, genetic simulated annealing algorithm, optimization model.

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Carbon emission constraints and trading policies in e-commerce environments have brought huge challenges to the operation of supply chain enterprises. In order to ensure the good operation of the e-commerce supply chain in a low-carbon environment, a supply chain scheduling optimization method based on integration of production and transportation with carbon emission constraints is proposed; we use it to analyze the impact of centralized decision-making mode and decentralized decision-making mode on supply chain scheduling and establish a scheduling optimization model that aims at optimal carbon emissions and costs. A multilevel genetic algorithm was designed according to the characteristics of the model, and numerical examples are used to verify the effectiveness of the model and algorithm. The results show that the centralized decision-making mode plays the role of the carbon emission constraints to the greatest extent; the carbon emissions and the cost are smallest in the centralized decision-making mode. The decentralized decision-making mode leads to the overall cost preference of the supply chain due to separate decisions made by enterprises, and the carbon emissions in the supply chain are greater. Transportation experts, business managers and government departments are interesting for integrated production and transportation scheduling in e-commerce supply chain with carbon emission constraints. Further research should address integrated production and transportation scheduling in dual-channel low supply chains.

General Stochastic Hybrid Systems (GSHS) have been formulated to represent various types of uncertainties in hybrid dynamical systems. In this paper, we propose computational techniques for Bayesian estimation of GSHS. In particular, the Fokker-Planck equation that describes the evolution of uncertainty distributions along GSHS is solved by spectral techniques, where an arbitrary form of probability density of the hybrid state is represented by a mixture of Fourier series. The method is based on splitting the Fokker-Planck equation represented by an integro-partial differential equation into the partial differentiation part for continuous diffusion and the integral part for discrete transition, and integrating the solution of each part. The propagated density function is used with a likelihood function in the Bayes' formula to estimate the hybrid state for given sensor measurements. The unique feature of the proposed technique is that the probability density describing complete stochastic properties of the hybrid state is constructed without relying on the common Gaussian assumption, in contrast to other methods that compute certain expected values such as mean or variance. We apply the proposed method to the estimation of two examples: the bouncing ball model and the Dubins vehicle model. We show that the proposed technique yields propagated densities consistent with Monte Carlo simulations, more accurate estimates over the Gaussian based approach and some computational benefits over a particle filter.

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