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In this paper, by considering benefits of customers and logistics planning departments, a bi-level programming model is presented to seek the optimal location for logistics distribution centers. The upper-level model is to determine the optimal location by minimizing the planners' cost, and the lower gives an equilibrium demand distribution by minimizing the customers' cost. Based on the special form of constraints, a simple heuristic algorithm is proposed. Finally, a numerical example is used to illustrate the application of the method, which shows that the algorithm is feasible and advantageous.

Background Jiangsu was one of the first four pilot provinces to engage in comprehensive health care reform in China, which has been on-going for the past 5 years. This study aims to evaluate the equity, efficiency and productivity of health care resource allocation in Jiangsu Province using the most recent data, analyse the causes of deficiencies, and discuss measures to solve these problems. Methods Data were extracted from the Jiangsu Health/Family Planning Statistical Yearbook (2015–2019) and Jiangsu Statistical Yearbook (2015–2019). The Gini coefficient (G), Theil index (T) and health resource density index (HRDI) were chosen to study the fairness of health resource allocation in Jiangsu Province. Data envelopment analysis (DEA) and the Malmquist productivity index (MPI) were used to analyse the efficiency and productivity of this allocation. Results From 2014 to 2018, the total amount of health resources in Jiangsu Province increased. The G of primary resource allocation by population remained below 0.15, and that by geographical area was between 0.14 and 0.28; additionally, the G of health financial resources was below 0.26, and that by geographical area was above 0.39. T was consistent with the results for G and Lorenz curves. The HRDI shows that the allocated amounts of health care resources were the highest in southern Jiangsu, except for the number of health institutions. The average value of TE was above 0.93, and the DEA results were invalid for only two cities. From 2014 to 2018, the mean TFPC in Jiangsu was less than 1, and the values exceeded 1 for only five cities. Conclusion The equity of basic medical resources was better than that of financial resources, and the equity of geographical allocation was better than that of population allocation. The overall efficiency of health care resource allocation was high; however, the total factor productivity of the whole province has declined due to technological regression. Jiangsu Province needs to further optimize the allocation and increase the utilization efficiency of health care resources.

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The cascade failures in scale-free networks with community structure are studied and cascade propagation of such networks with different modularity parameters is simulated. It is found that the network with small modularity is much easier to trigger cascade failures than that of the larger one. Furthermore, different removal strategies have some what large effects on the cascade failures aftereffect. The simulations also show that larger modularity and reserve capacity coefficient will delay the breakdown caused by a cascade of network. This is particularly important for such real networks with community as traffic networks, distribution networks, and electrical power grids.