Allocating Capacity with Demand Competition: Fixed Factor Allocation*

We consider a supply chain consisting of a supplier and two retailers. The supplier sells a single product to the retailers, who, in turn, retail the product to customers. The supplier has limited production capacity, and the retailers compete for the supplier’s capacity and are duopolists engaged in Cournot competition for their customers. When the sum of the retailers’ orders exceeds the supplier’s capacity, the supplier allocates his capacity according to a preannounced allocation rule. We propose a new capacity allocation rule, fixed factor allocation, which incorporates the ideas of proportional and lexicographic allocations: it prioritizes retailers as in lexicographic allocation, but guarantees only a fixed proportion of the total available capacity to the prioritized retailer. We show that (1) the fixed factor allocation rule incorporates lexicographic and proportional allocations from the perspectives of the supplier and the supply chain; (2) under fixed factor allocation, the supply chain profit is not affected by the allocation factor when it is greater than a threshold; (3) the retailers share the supply chain profit with the supplier depending on the value of the allocation factor; and (4) the fixed factor allocation coordinates the supply chain when the market size is sufficiently large. We also compare fixed factor with proportional and lexicographic allocations, respectively. Furthermore, we demonstrate how the supplier can optimize his capacity level and wholesale price under fixed factor allocation.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137548/1/deci12234.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137548/2/deci12234_am.pd

3D weak-dispersion reverse time migration using a stereo-modeling operator

Reliable 3D imaging is a required tool for developing models of complex geologic structures. Reverse time migration (RTM), as the most powerful depth imaging method, has become the preferred imaging tool because of its ability to handle complex velocity models including steeply dipping interfaces and large velocity contrasts. Finite-difference methods are among the most popular numerical approaches used for RTM. However, these methods often encounter a serious issue of numerical dispersion, which is typically suppressed by reducing the grid interval of the propagation model, resulting in large computation and memory requirements. In addition, even with small grid spacing, numerical anisotropy may degrade images or, worse, provide images that appear to be focused but position events incorrectly. Recently, stereo-operators have been developed to approximate the partial differential operator in space. These operators have been used to develop several weak-dispersion and efficient stereo-modeling methods that have been found to be superior to conventional algorithms in suppressing numerical dispersion and numerical anisotropy. We generalized one stereo-modeling method, fourth-order nearly analytic central difference (NACD), from 2D to 3D and applied it to 3D RTM. The RTM results for the 3D SEG/EAGE phase A classic data set 1 and the SEG Advanced Modeling project model demonstrated that, even when using a large grid size, the NACD method can handle very complex velocity models and produced better images than can be obtained using the fourth-order and eighth-order Lax-Wendroff correction (LWC) schemes. We also applied 3D NACD and fourth-order LWC to a field data set and illustrated significant improvements in terms of structure imaging, horizon/layer continuity and positioning. We also investigated numerical dispersion and found that not only does the NACD method have superior dispersion characteristics but also that the angular variation of dispersion is significantly less than for LWC. Read More: http://library.seg.org/doi/abs/10.1190/geo2013-0472.1National Natural Science Foundation (China) (Grant 41230210)Massachusetts Institute of Technology. Earth Resources Laboratory (Founding Members Consortium

3D Weak-Dispersion Reverse-Time Migration with a StereoModeling Method

The finite difference method has been widely used in seismic modeling and reverse time migration. However, it generally has two issues: large computational cost and numerical dispersion. Recently, a nearly-analytic discrete operator was developed to approximate the partial differential operators. Based on this spatial discretization, many weak-dispersion and efficient StereoModeling methods have been developed, which are found to be superior to conventional algorithms in suppressing numerical dispersion. In this paper, we generalize one StereoModeling method, the nearly-analytic central difference method (NACD), from 2D to 3D and apply it to 3D reverse-time migration. Numerical results show that the NACD can be used effectively as a new tool for seismic modeling and migration. The reverse time migration (RTM) results for the 3D SEG/EAGE Phase A classic dataset 1 show that the NACD can get a much better image than the Lax-Wendroff correction (LWC) method particularly when using a coarse grid size.Massachusetts Institute of Technology. Earth Resources Laboratory (Founding Members Consortium

Characterization of subglacial landscapes by a two-parameter roughness index

Peer reviewedPublisher PD

SEGA: Structural Entropy Guided Anchor View for Graph Contrastive Learning

In contrastive learning, the choice of ``view'' controls the information that the representation captures and influences the performance of the model. However, leading graph contrastive learning methods generally produce views via random corruption or learning, which could lead to the loss of essential information and alteration of semantic information. An anchor view that maintains the essential information of input graphs for contrastive learning has been hardly investigated. In this paper, based on the theory of graph information bottleneck, we deduce the definition of this anchor view; put differently, \textit{the anchor view with essential information of input graph is supposed to have the minimal structural uncertainty}. Furthermore, guided by structural entropy, we implement the anchor view, termed \textbf{SEGA}, for graph contrastive learning. We extensively validate the proposed anchor view on various benchmarks regarding graph classification under unsupervised, semi-supervised, and transfer learning and achieve significant performance boosts compared to the state-of-the-art methods.Comment: ICML'2