Applications of integer programming methods to cages

The aim of this paper is to construct new small regular graphs with girth 7 using integer programming techniques. Over the last two decades solvers for integer programs have become more and more powerful and have proven to be a useful aid for many hard combinatorial problems. Despite successes in many related fields, these optimisation tools have so far been absent in the quest for small regular graphs with a given girth. Here we illustrate the power of these solvers as an aid to construct small regular girth 7 graphs from girth 8 cage

Application of semidefinite programming to maximize the spectral gap produced by node removal

The smallest positive eigenvalue of the Laplacian of a network is called the spectral gap and characterizes various dynamics on networks. We propose mathematical programming methods to maximize the spectral gap of a given network by removing a fixed number of nodes. We formulate relaxed versions of the original problem using semidefinite programming and apply them to example networks.Comment: 1 figure. Short paper presented in CompleNet, Berlin, March 13-15 (2013

Product Return Handling

In this article we focus on product return handling and warehousingissues. In some businesses return rates can be well over 20% andreturns can be especially costly when not handled properly. In spiteof this, many managers have handled returns extemporarily. The factthat quantitative methods barely exist to support return handlingdecisions adds to this. In this article we bridge those issues by 1)going over the key decisions related with return handling; 2)identifying quantitative models to support those decisions.Furthermore, we provide insights on directions for future research.reverse logistics;decision-making;quantitative models;retailing and warehousing

From Cages to Trapping Sets and Codewords: A Technique to Derive Tight Upper Bounds on the Minimum Size of Trapping Sets and Minimum Distance of LDPC Codes

Cages, defined as regular graphs with minimum number of nodes for a given girth, are well-studied in graph theory. Trapping sets are graphical structures responsible for error floor of low-density parity-check (LDPC) codes, and are well investigated in coding theory. In this paper, we make connections between cages and trapping sets. In particular, starting from a cage (or a modified cage), we construct a trapping set in multiple steps. Based on the connection between cages and trapping sets, we then use the available results in graph theory on cages and derive tight upper bounds on the size of the smallest trapping sets for variable-regular LDPC codes with a given variable degree and girth. The derived upper bounds in many cases meet the best known lower bounds and thus provide the actual size of the smallest trapping sets. Considering that non-zero codewords are a special case of trapping sets, we also derive tight upper bounds on the minimum weight of such codewords, i.e., the minimum distance, of variable-regular LDPC codes as a function of variable degree and girth

Robotized Warehouse Systems: Developments and Research Opportunities

Robotized handling systems are increasingly applied in distribution centers. They require little space, provide flexibility in managing varying demand requirements, and are able to work 24/7. This makes them particularly fit for e-commerce operations. This paper reviews new categories of robotized handling systems, such as the shuttle-based storage and retrieval systems, shuttle-based compact storage systems, and robotic mobile fulfillment systems. For each system, we categorize the literature in three groups: system analysis, design optimization, and operations planning and control. Our focus is to identify the research issue and OR modeling methodology adopted to analyze the problem. We find that many new robotic systems and applications have hardly been studied in academic literature, despite their increasing use in practice. Due to unique system features (such as autonomous control, networked and dynamic operation), new models and methods are needed to address the design and operational control challenges for such systems, in particular, for the integration of subsystems. Integrated robotized warehouse systems will form the next category of warehouses. All vital warehouse design, planning and control logic such as methods to design layout, storage and order picking system selection, storage slotting, order batching, picker routing, and picker to order assignment will have to be revisited for new robotized warehouses

Optimal Partial Harvesting Schedule for Aquaculture Operations

Abstract When growth is density dependent, partial harvest of the standing stock of cultured species (fish or shrimp) over the course of the growing season (i.e., partial harvesting) would decrease competition and thereby increase individual growth rates and total yield. Existing studies in optimal harvest management of aquaculture operations, however, have not provided a rigorous framework for determining "discrete" partial harvesting (i.e., partially harvest the cultured species at several discrete points until the final harvest). In this paper, we develop a partial harvesting model that is capable of addressing discrete partial harvesting and other partial harvesting using impulsive control theory. We derive necessary conditions of the efficient partial harvesting scheme for a single production cycle. We also present a numerical example to illustrate how partial harvesting can improve the profitability of an aquaculture enterprise compared to single-batch harvesting and gradual thinning. The study results indicate that well-designed partial harvesting schemes can enhance the profitability of aquaculture operations.Partial harvesting, impulsive control theory, aquaculture., Livestock Production/Industries, C61, Q22,

Trends in Mathematical Imaging and Surface Processing

Motivated both by industrial applications and the challenge of new problems, one observes an increasing interest in the field of image and surface processing over the last years. It has become clear that even though the applications areas differ significantly the methodological overlap is enormous. Even if contributions to the field come from almost any discipline in mathematics, a major role is played by partial differential equations and in particular by geometric and variational modeling and by their numerical counterparts. The aim of the workshop was to gather a group of leading experts coming from mathematics, engineering and computer graphics to cover the main developments