A tri-level optimization model for inventory control with uncertain demand and lead time

We propose an inventory control model for an uncapacitated warehouse in a manufacturing facility under demand and lead time uncertainty. The objective is to make ordering decisions to minimize the total system cost. We introduce a two-stage tri-level optimization model with a rolling horizon to address the uncertain demand and lead time regardless of their underlying distributions. In addition, an exact algorithm is designed to solve the model. We compare this model in a case study with three decision-making strategies: optimistic, moderate, and pessimistic. Our computational results suggest that the performances of these models are either consistently inferior or highly sensitive to cost parameters (such as holding cost and shortage cost), whereas the new tri-level optimization model almost always results in the lowest total cost in all parameter settings

Magnetic Evolution and Temperature Variation in a Coronal Hole

We have explored the magnetic flux evolution and temperature variation in a coronal-hole region, using Big Bear Solar Observatory (BBSO) deep magnetograms and {\it SOHO}/EIT images observed from 2005 October 10 to 14. For comparison, we also investigated a neighboring quiet region of the Sun. The coronal hole evolved from its mature stage to its disappearance during the observing period. We have obtained the following results: (1) When the coronal hole was well developed on October 10, about 60 % of the magnetic flux was positive. The EUV brightness was 420 counts pixel$^{-1}$, and the coronal temperature, estimated from the line ratio of the EIT 195 {\AA} and 171 {\AA} images, was 1.07 MK. (2) On October 14, when the coronal hole had almost disappeared, 51 % of the magnetic flux was positive, the EUV radiance was 530 counts pixel$^{-1}$, and the temperature was 1.10 MK. (3) In the neighboring quiet region, the fraction of positive flux varied between 0.49 and 0.47. The EUV brightness displayed an irregular variation, with a mean value of 870 counts pixel$^{-1}$. The temperature was almost constant at 1.11 MK during the five-day observation. Our results demonstrate that in a coronal hole less imbalance of the magnetic flux in opposite polarities leads to stronger EUV brightness and higher coronal temperatures

Metacommunity Structure of Stream Insects across Three Hierarchical Spatial scales

A major challenge in community ecology is to understand the underlying factors driving metacommunity (i.e., a set of local communities connected through species dispersal) dynamics. However, little is known about the effects of varying spatial scale on the relative importance of environmental and spatial (i.e., dispersal related) factors in shaping metacommunities and on the relevance of different dispersal pathways. Using a hierarchy of insect metacommunities at three spatial scales (a small, within-stream scale, intermediate, among-stream scale, and large, among-sub-basin scale), we assessed whether the relative importance of environmental and spatial factors shaping metacommunity structure varies predictably across spatial scales, and tested how the importance of different dispersal routes vary across spatial scales. We also studied if different dispersal ability groups differ in the balance between environmental and spatial control. Variation partitioning showed that environmental factors relative to spatial factors were more important for community composition at the within-stream scale. In contrast, spatial factors (i.e., eigenvectors from Moran's eigenvector maps) relative to environmental factors were more important at the among-sub-basin scale. These results indicate that environmental filtering is likely to be more important at the smallest scale with highest connectivity, while dispersal limitation seems to be more important at the largest scale with lowest connectivity. Community variation at the among-stream and among-sub-basin scales were strongly explained by geographical and topographical distances, indicating that overland pathways might be the main dispersal route at the larger scales among more isolated sites. The relative effect of environmental and spatial factors on insect communities varied between low and high dispersal ability groups; this variation was inconsistent among three hierarchical scales. In sum, our study indicates that spatial scale, connectivity, and dispersal ability jointly shape stream metacommunities.Peer reviewe