The Stochastic Container Relocation Problem

The Container Relocation Problem (CRP) is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers, while respecting a given order of retrieval. However, the assumption of knowing the full retrieval order of containers is particularly unrealistic in real operations. This paper studies the stochastic CRP (SCRP), which relaxes this assumption. A new multi-stage stochastic model, called the batch model, is introduced, motivated, and compared with an existing model (the online model). The two main contributions are an optimal algorithm called Pruning-Best-First-Search (PBFS) and a randomized approximate algorithm called PBFS-Approximate with a bounded average error. Both algorithms, applicable in the batch and online models, are based on a new family of lower bounds for which we show some theoretical properties. Moreover, we introduce two new heuristics outperforming the best existing heuristics. Algorithms, bounds and heuristics are tested in an extensive computational section. Finally, based on strong computational evidence, we conjecture the optimality of the “Leveling” heuristic in a special “no information” case, where at any retrieval stage, any of the remaining containers is equally likely to be retrieved next

Comparison of pure and combined search strategies for single and multiple targets

We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with L\'evy search based on long-tailed jump length distributions. We then compare these results with a search process combined of two different long-tailed jump length distributions. Moreover, we study the case of multiple targets located by a L\'evy searcher.Comment: 16 pages, 12 figure

Chinese Trade Expansion and Development and Growth in Today's World

The current Chinese trade expansion brings benefit to many parties, both outside and inside the Chinese Mainland. It also poses huge challenges to others, in foreign countries, also in China. The event is important for its own sake, but also what it implies when rapid growth happens to countries large in population and size (including India, Russia, Brazil). It has to be understood in context. Conventional wisdom in economics and popular explanations cannot explain Chinese growth, let alone its implications. Only with suitable adaptations of what the economic discipline has to offer, can one assess the nature of what we observe and the policy measures needed for today. Like other episodes after Industrial Revolution, the late industrialization in China also relies on outside technology, often gained through trade and foreign investment. Because of the de-colonization after 1945, such growth can succeed even with scanty domestic resource. Like other East Asian economies, participation in cross border supply chains along its neighbors offers China an effective entrée. What makes China different from the other East Asian economies is size. The presence of a huge labor reserve keeps wage down, profit up, attracts foreign investment coming with technology, but may also lead to deteriorated terms of trade and income inequality at home, de-industrialization and the loss of development opportunities abroad, also resource shortage and environment damage, some of these are irreversible in nature. Over all, the development is the result of efficiency gain, which is basically desirable. It takes international cooperation to steer such development toward mutually beneficial paths. It is also desirable for China to accelerate job creation at home and avoid irreversible environment harm. These are well recognized by Chinese decision makers. More can be done.

A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing

This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive manufacturing requires highly-accurate multiscale and multiphysics analyses. Only high performance computing tools are able to handle such complexity in time frames compatible with time-to-market. However, efficiency, without loss of accuracy, has rarely held the centre stage in the numerical community. Here, in contrast, the framework is designed to adequately exploit the resources of high-end distributed-memory machines. It is grounded on three building blocks: (1) Hierarchical adaptive mesh refinement with octree-based meshes; (2) a parallel strategy to model the growth of the geometry; (3) state-of-the-art parallel iterative linear solvers. Computational experiments consider the heat transfer analysis at the part scale of the printing process by powder-bed technologies. After verification against a 3D benchmark, a strong-scaling analysis assesses performance and identifies major sources of parallel overhead. A third numerical example examines the efficiency and robustness of (2) in a curved 3D shape. Unprecedented parallelism and scalability were achieved in this work. Hence, this framework contributes to take on higher complexity and/or accuracy, not only of part-scale simulations of metal or polymer additive manufacturing, but also in welding, sedimentation, atherosclerosis, or any other physical problem where the physical domain of interest grows in time