Optimal Staged Self-Assembly of General Shapes

We analyze the number of tile types $t$, bins $b$, and stages necessary to assemble $n \times n$ squares and scaled shapes in the staged tile assembly model. For $n \times n$ squares, we prove $\mathcal{O}(\frac{\log{n} - tb - t\log t}{b^2} + \frac{\log \log b}{\log t})$ stages suffice and $\Omega(\frac{\log{n} - tb - t\log t}{b^2})$ are necessary for almost all $n$. For shapes $S$ with Kolmogorov complexity $K(S)$, we prove $\mathcal{O}(\frac{K(S) - tb - t\log t}{b^2} + \frac{\log \log b}{\log t})$ stages suffice and $\Omega(\frac{K(S) - tb - t\log t}{b^2})$ are necessary to assemble a scaled version of $S$, for almost all $S$. We obtain similarly tight bounds when the more powerful flexible glues are permitted.Comment: Abstract version appeared in ESA 201

Computational procedures for stochastic multi-echelon production systems

This paper is concerned with the numerical evaluation of multi-echelon production systems. Each stage requires a fixed predetermined leadtime; furthermore, we assume a stochastic, stationary end-time demand process. In a previous paper, we have developed an analytical framework for determining optimal control policies for such systems under an average cost criterion.\ud \ud The current paper is based on this analytical theory but discusses computational aspects, in particular for serial and assembly systems. A hierarchical (exact) decomposition of these systems can be obtained by considering echelon stocks and by transforming penalty and holding costs accordingly. The one-dimensional problems arising after this decomposition however involve incomplete convolutions of distribution functions, which are only recursively defined. We develop numerical procedures for analysing these incomplete convolutions; these procedures are based on approximations of distribution functions by mixtures of Erlang distributions. Combining the analytically obtained (exact) decomposition results with these numerical procedures enables us to quickly determine optimal order-up-to levels for all stages. Moreover, expressions for the customer service level of such a multi-stage are obtained, yielding the possibility to determine policies which minimize average inventory holding costs, given a service level constraint

Quantifying the efficiency of price-only contracts in push supply chains over demand distributions of known supports

In this paper, we quantify the efficiency of price-only contracts in supply chains with demand distributions by imposing prior knowledge only on the support, namely, those distributions with support [a, b] for 0 < a <_ b < +1. By characterizing the price of anarchy (PoA) under various push supply chain configurations, we enrich the application scope of the PoA concept in supply chain contracts along with complementary managerial insights. One of our major findings is that our quantitative analysis can identify scenarios where the price-only contract actually maintains its efficiency, namely, when the demand uncertainty, measured by the relative range b/a, is relatively low, entailing the price-only contract to be more attractive in this regard

Agent and cyber-physical system based self-organizing and self-adaptive intelligent shopfloor

The increasing demand of customized production results in huge challenges to the traditional manufacturing systems. In order to allocate resources timely according to the production requirements and to reduce disturbances, a framework for the future intelligent shopfloor is proposed in this paper. The framework consists of three primary models, namely the model of smart machine agent, the self-organizing model, and the self-adaptive model. A cyber-physical system for manufacturing shopfloor based on the multiagent technology is developed to realize the above-mentioned function models. Gray relational analysis and the hierarchy conflict resolution methods were applied to achieve the self-organizing and self-adaptive capabilities, thereby improving the reconfigurability and responsiveness of the shopfloor. A prototype system is developed, which has the adequate flexibility and robustness to configure resources and to deal with disturbances effectively. This research provides a feasible method for designing an autonomous factory with exception-handling capabilities

Magnetorheological landing gear: 1. A design methodology

Aircraft landing gears are subjected to a wide range of excitation conditions, which result in conflicting damping requirements. A novel solution to this problem is to implement semi-active damping using magnetorheological (MR) fluids. This paper presents a design methodology that enables an MR landing gear to be optimized, both in terms of its damping and magnetic circuit performance, whilst adhering to stringent packaging constraints. Such constraints are vital in landing gear, if MR technology is to be considered as feasible in commercial applications. The design approach focuses on the impact or landing phase of an aircraft's flight, where large variations in sink speed, angle of attack and aircraft mass makes an MR device potentially very attractive. In this study, an equivalent MR model of an existing aircraft landing gear is developed. This includes a dynamic model of an MR shock strut, which accounts for the effects of fluid compressibility. This is important in impulsive loading applications such as landing gear, as fluid compression will reduce device controllability. Using the model, numerical impact simulations are performed to illustrate the performance of the optimized MR shock strut, and hence the effectiveness of the proposed design methodology. Part 2 of this contribution focuses on experimental validation

An assembly oriented design framework for product structure engineering and assembly sequence planning

The paper describes a novel framework for an assembly-oriented design (AOD) approach as a new functional product lifecycle management (PLM) strategy, by considering product design and assembly sequence planning phases concurrently. Integration issues of product life cycle into the product development process have received much attention over the last two decades, especially at the detailed design stage. The main objective of the research is to define assembly sequence into preliminary design stages by introducing and applying assembly process knowledge in order to provide an assembly context knowledge to support life-oriented product development process, particularly for product structuring. The proposed framework highlights a novel algorithm based on a mathematical model integrating boundary conditions related to DFA rules, engineering decisions for assembly sequence and the product structure definition. This framework has been implemented in a new system called PEGASUS considered as an AOD module for a PLM system. A case study of applying the framework to a catalytic-converter and diesel particulate filter sub-system, belonging to an exhaust system from an industrial automotive supplier, is introduced to illustrate the efficiency of the proposed AOD methodology

Self-Assembly of Arbitrary Shapes Using RNAse Enzymes: Meeting the Kolmogorov Bound with Small Scale Factor (extended abstract)

We consider a model of algorithmic self-assembly of geometric shapes out of square Wang tiles studied in SODA 2010, in which there are two types of tiles (e.g., constructed out of DNA and RNA material) and one operation that destroys all tiles of a particular type (e.g., an RNAse enzyme destroys all RNA tiles). We show that a single use of this destruction operation enables much more efficient construction of arbitrary shapes. In particular, an arbitrary shape can be constructed using an asymptotically optimal number of distinct tile types (related to the shape's Kolmogorov complexity), after scaling the shape by only a logarithmic factor. By contrast, without the destruction operation, the best such result has a scale factor at least linear in the size of the shape, and is connected only by a spanning tree of the scaled tiles. We also characterize a large collection of shapes that can be constructed efficiently without any scaling

Modularity and Delayed Product Differentiation in Assemble-to-order Systems: Analysis and Extensions from a Complexity Perspective

The paper assumes a product design around modular architectures and discusses the suitability of the principle of delayed product differentiation in assemble-to-order environments. We demonstrate that this principle does not enable one to make optimal decisions concerning how variety should proliferate in the assembly process. Therefore, we propose to complement this principle in that we additionally consider the variety induced complexity throughout the assembly process. The weighted Shannon entropy is proposed as a measure for the evaluation of this complexity. Our results show that the delayed product differentiation principle is reliable when the selection probabilities of module variants at each assembly stage are equal and the pace at which value is added in the whole assembly process is constant. Otherwise, the proposed measure provides different results. Furthermore, the entropy measure provides interesting clues concerning eventual reversals of assembly sequences and supports decisions regarding what modules in an assembly stage could be substituted by a common module.modularity; complexity; ATO; delayed product differentiation