The problem of integrated scheduling of supply chain has a huge impact on operational efficiency and cost effectiveness. The increasing number of nodes, different time window constraints for customers, and a variety of uncertain scenarios make supply chain scheduling complicated. This research develops a multi-objective multi-period mixed-integer programming optimization model. We consider comprehensively the effect of demand uncertainty, time window constraints, the constraints of node capability, multi-period and sub-period factors. As the conflicting benefit factors, the cost and service level are two optimization objectives. The first objective function aims to minimize the total cost in all periods. The second objective function considers service level through minimizing the material flow of out-of-stock items in all periods to maximize the service level. And the suppliers' capacity, the selection of suppliers, manufacturers' productivity, the transaction relationship, the sub-period time, the inventory capacity and lead time for delivery are also considered. Then total costs and service levels are normalized, whose sum is the objective function. And the problem is transformed into a multi-period non-linear optimization problem. An improved Mixed Genetic Algorithm is designed to solve the model. Finally, the practicability of the proposed model and algorithm is demonstrated through its application in an electronics supply chain case study. The results indicate that the proposed model and algorithm can provide a promising approach to fulfill a multi-objective multi-period integrated scheduling plan under uncertain demand scenarios.INDEX TERMS Integrated scheduling, mixed-integer programming optimization, supply chain, improved mixed genetic algorithm, demand uncertainty.

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The triggering of supply chain brittleness has a significant impact on enterprise benefits under attack from the COVID-19 pandemic. The complexity of the supply chain system, the uncertainty of the COVID-19 pandemic, and demand uncertainty have made the triggering and propagation of supply chain brittleness complicated. In this study, a brittleness evolution model based on adaptive agent graph theory has been constructed. The parameters of brittleness evolution, including brittleness entropy and the vertex state value, have been quantitatively designed, and the brittleness evolution model in which the adaptability of nodes is considered and is not considered is constructed. A simulation algorithm based on the integrated scheduling model of the supply chain has been established. Finally, the practicability of the proposed model and algorithm is demonstrated via a case study of an electronic supply chain network. The results indicate that the proposed model and algorithm can effectively analyze the brittleness evolution law of the supply chain under the impact of the COVID-19 pandemic, including the evolution law of the vertex state, the brittleness entropy of the vertex, the global entropy of brittleness, the seasonal evolution law of the supply chain brittleness, and the evolution law of the brittleness behavior.

In the present paper, a preliminary exploration which includes the theoretical analysis and experimental study on the wave propagation through a micro gap was carried out. Harmonic waves, normal incidence, smooth and flat interface were taken into account. The theoretical and experimental results both show that the initial gap width has significant influences on the harmonics. Their relations may be effective on nondestructive evaluation of a pre-existing gap.