Optimal just-in-time schedules for flexible transfer lines

Flexible transfer lines or mixed-model assembly lines are capable of diversified small-lot production due to negligible switch-over costs. With these lines, it is possible to implement just-in-time (JIT) production, which involves producing only the necessary parts in the necessary quantities at the necessary times. The problem of sequencing flexible transfer lines according to the JIT philosophy can be formulated as a nonlinear integer programming problem. Heuristic algorithms to solve the problem have appeared in the literature. In this paper, we show that the problem can be explicitly reduced to an assignment problem. Thus, we provide an efficient algorithm for an optimal solution to the JIT sequencing problem.     

Level scheduling under limited resequencing flexibility

A mixed-model assembly line requires the solution of a short-term sequencing problem, which decides on the succession of different models launched down the line. A famous solution approach stemming from the Toyota Production System is the so-called Level Scheduling (LS), which aims to distribute the part consumption induced by a model sequence evenly over the planning horizon. LS attracted a multitude of different researchers, who, however, invariably treat initial sequence planning where all degrees of freedom in assigning models to production cycles exist. In the real-world, conflicting objectives and restrictions of preceding production stages, i.e., body and paint shop, simultaneously need to be considered and perturbations of an initial sequence will regularly occur, so that the sequencing problem often becomes a resequencing problem. Here, a given model sequence is to be reshuffled with the help of resequencing buffers (denoted as pull-off tables). This paper shows how to adapt famous solution approaches for alternative LS problems, namely the Product-Rate-Variation (PRV) and the Output-Rate-Variation (ORV) problem, if the (re-)assignment of models to cycles is restricted by the given number of pull-off tables. Furthermore, the effect of increasing re-sequencing flexibility is investigated, so that the practitioner receives decision support for buffer dimensioning, and the ability of the PRV in reasonably approximating the more detailed ORV in a resequencing environment is tested.     

Level Scheduling for batched JIT supply

A mixed-model assembly line requires the solution of a short-term sequencing problem which decides on the succession of different models launched down the line. A famous solution approach stemming from the Toyota Production System is the so-called Level Scheduling, which aims at distributing the part consumption induced by the model sequence evenly over time. Traditional Level Scheduling seeks to closely approximate target demand rates at every production cycle, however, such a strict leveling is only required if parts are directly pulled from a connected feeder line. In real-world assembly lines, parts are predominately delivered in (small) batches at certain points in time. In such a situation, a Just-in-Time supply is already facilitated whenever the cumulative consumption is leveled in accordance with each part’s delivery schedule, while the exact consumption pattern between two delivery points seems irrelevant. The paper on hand provides new Level Scheduling models, proves complexity, presents exact and heuristic solution procedures and shows inferiority of traditional Level Scheduling for such a batched JIT-supply of parts.     

Component Partitioning Under Demand and Capacity Uncertainty in Printed Circuit Board Assembly

This paper considers the problem of configuring a printed circuit board (PCB) assembly line experiencing uncertainty in demand and capacity. The PCB assembly process involves a single line of automatic placement machines, a variety of board types, and a number of component types. The line is set up only once, at the beginning of a production cycle, to eliminate setups between board types. Using this strategy, the line therefore can assemble all different types of PCBs without feeder changes. The problem then becomes to partition component types to the different machines in the hope of processing all boards quickly with a good workload balance. In this paper, the board demands and machine breakdowns are random but follow some probability distribution, which can be predicted from past observations of the system. We formulate this problem as a stochastic mixed-integer programming formulation with the objective of minimizing the expected makespan for assembling all PCBs during a production cycle. The results obtained indicate significant improvement over the existing methods. We hope that this research will provide more PCB assembly facilities with models and techniques to hedge against variable forecasts and capacity plans     

Equipment selection and task assignment for multiproduct assembly system design

A multiproduct assembly system produces a family of similar products, where the assembly of each product entails an ordered set of tasks. An assembly system consists of a sequence of workstations. For each workstation, we assign a subset of the assembly tasks to be performed at the workstation and select the type of assembly equipment or resource to be used by the workstation. The assembly of each product requires a visit to each workstation in the fixed sequence. The problem of system design is to find the system that is capable of producing all the products in the desired volumes at minimum cost. The system cost includes the fixed capital costs for the assembly equipment and tools and the variable operating costs for the various workstations. We present and illustrate an optimization procedure that assigns tasks to workstations and selects assembly equipment for each workstation.     

The sandpile scheduler

This paper studies a self-organized criticality model called sandpile for dynamically load-balancing tasks arriving in the form of Bag-of-Tasks in large-scale decentralized system. The sandpile is designed as a decentralized agent system characterizing a cellular automaton, which works in a critical state at the edge of chaos. Depending on the state of the cellular automaton, different responses may occur when a new task is assigned to a resource: it may change nothing or generate avalanches that reconfigure the state of the system. The abundance of such avalanches is in power-law relation with their sizes, a scale-invariant behavior that emerges without requiring tuning or control parameters. That means that large—catastrophic—avalanches are very rare but small ones occur very often. Such emergent pattern can be efficiently adapted for non-clairvoyant scheduling, where tasks are load balanced in computing resources trying to maximize the performance but without assuming any knowledge on the tasks features. The algorithm design is experimentally validated showing that the sandpile is able to find near-optimal schedules by reacting differently to different conditions of workloads and architectures.     

THE MIXED-MODEL ANALYSIS OF VARIANCE APPLIED TO QUANTITATIVE GENETICS: BIOLOGICAL MEANING OF THE PARAMETERS

The mixed-model factorial analysis of variance has been used in many recent studies in evolutionary quantitative genetics. Two competing formulations of the mixed-model ANOVA are commonly used, the “Scheffe” model and the “SAS” model; these models differ in both their assumptions and in the way in which variance components due to the main effect of random factors are defined. The biological meanings of the two variance component definitions have often been unappreciated, however. A full understanding of these meanings leads to the conclusion that the mixed-model ANOVA could have been used to much greater effect by many recent authors. The variance component due to the random main effect under the two-way SAS model is the covariance in true means associated with a level of the random factor (e.g., families) across levels of the fixed factor (e.g., environments). Therefore the SAS model has a natural application for estimating the genetic correlation between a character expressed in different environments and testing whether it differs from zero. The variance component due to the random main effect under the two-way Scheffe model is the variance in marginal means (i.e., means over levels of the fixed factor) among levels of the random factor. Therefore the Scheffe model has a natural application for estimating genetic variances and heritabilities in populations using a defined mixture of environments. Procedures and assumptions necessary for these applications of the models are discussed. While exact significance tests under the SAS model require balanced data and the assumptions that family effects are normally distributed with equal variances in the different environments, the model can be useful even when these conditions are not met (e.g., for providing an unbiased estimate of the across-environment genetic covariance). Contrary to statements in a recent paper, exact significance tests regarding the variance in marginal means as well as unbiased estimates can be readily obtained from unbalanced designs with no restrictive assumptions about the distributions or variance-covariance structure of family effects.     

Efficient control of population structure in model organism association mapping

Genomewide association mapping in model organisms such as inbred mouse strains is a promising approach for the identification of risk factors related to human diseases. However, genetic association studies in inbred model organisms are confronted by the problem of complex population structure among strains. This induces inflated false positive rates, which cannot be corrected using standard approaches applied in human association studies such as genomic control or structured association. Recent studies demonstrated that mixed models successfully correct for the genetic relatedness in association mapping in maize and Arabidopsis panel data sets. However, the currently available mixed-model methods suffer from computational inefficiency. In this article, we propose a new method, efficient mixed-model association (EMMA), which corrects for population structure and genetic relatedness in model organism association mapping. Our method takes advantage of the specific nature of the optimization problem in applying mixed models for association mapping, which allows us to substantially increase the computational speed and reliability of the results. We applied EMMA to in silico whole-genome association mapping of inbred mouse strains involving hundreds of thousands of SNPs, in addition to Arabidopsis and maize data sets. We also performed extensive simulation studies to estimate the statistical power of EMMA under various SNP effects, varying degrees of population structure, and differing numbers of multiple measurements per strain. Despite the limited power of inbred mouse association mapping due to the limited number of available inbred strains, we are able to identify significantly associated SNPs, which fall into known QTL or genes identified through previous studies while avoiding an inflation of false positives. An R package implementation and webserver of our EMMA method are publicly available.     

Design of Supervisors to Avoid Deadlock in Flexible Assembly Systems

Modern production systems exhibit a high degree of resource sharing that can lead to deadlock conditions. Deadlock arises when some parts remain indefinitely blocked because each of them requests access to a resource held by some other parts. One of the tasks of the control system lies in preventing such situations from occurring by proper resource management. This article addresses the deadlock problem for an important class of production facilities, that is, flexible assembly systems, that can perform both manufacturing or assembly operations. In particular, we develop an approach to deadlock avoidance based on a supervisory control that works by inhibiting or enabling the events involving resource allocation. The article proposes two supervisors characterized by easy implementation, efficiency, and flexibility in resource management. The analysis of some case studies, performed by discrete event simulation, confirms the effectiveness of the approach.     

A unified modeling of Kanban systems using petri nets

The success of some Just In Time (JIT) systems has led to a growing interest in Kanban systems, which provide a way to implement a JIT control policy. Much work has recently been devoted to this problem, and especially many models have been developed to evaluate the performance of such systems. In this article, we focus our attention of these existing models. Each author uses his/her own representation, which is not formal in most cases, and so it is often difficult to understand the proposed model and to compare it with others. In this article, we show that Petri nets are well suited to provide a unified modeling of Kanban systems. We first propose a basic model, then show that most models encountered in the literature can easily be represented by a Petri net model. Once such a formal model is obtained, it can then be used to analyze the behavior of the system, both qualitatively and quantitatively. Some preliminary results pertaining to the quantitative analysis are presented at the end of the article.     

Design of single assembly line for the delayed differentiation of product variants

Delayed Product Differentiation (DPD) can reduce the manufacturing complexities arising due to the proliferation of products variety. A new optimization model constructs the optimum layout of delayed differentiation assembly lines for a mix of products to be manufactured by the same system and optimizes the position of the differentiation points. This model employs a classification tool (Cladistics) used in biological analysis and modifies it for use in planning DPD assembly lines configurations in order to incorporate the assembly precedence constraints, required production rates of different product variants and existing production capacity of work stations. The optimum layout configuration ensures that the quantities required of different products are produced on the same line; while achieving balance, minimizing duplication of stations and maximizing the overall system utilization. The developed model has been applied to a group of automobile engine accessories normally assembled on different lines. The use of Cladistics to analyze product variants that are candidates for delayed assembly is an original approach for designing the assembly line layout and identifying the best differentiation points. It also helps rationalize the design of product variants and their features to further delay their assembly differentiation and achieve economy of scale without affecting their functionality.     

A Column-Generation Approach for the Assembly System Design Problem with Tool Changes

This assembly system design problem (ASDP) is to prescribe the minimum-cost assignment of machines, tooling, and tasks to stations, observing task precedence relationships and cycle time requirements. The ASDP with tool changes (ASDPTCs) also prescribes the optimal sequence of operations at each station, including tool changes, which are important, for example, in robotic assembly. A unique solution approach decomposes the model into a master problem, which is a minimum-cost network-flow problem that can be solved as a linear program, and subproblems, which are constrained, shortest-path problems that generate station configurations. Subproblems are solved on state-operation networks, which extend earlier formulations to incorporate tooling considerations. This paper presents a specialized algorithm to solve the subproblems. Computational tests benchmark the approach on several classes of problems, and the results are promising. In particular, tests demonstrate the importance of using engineering judgment to manage problem complexity by controlling the size of state-operation networks     

One Giant Leap for Categorizers: One Small Step for Categorization Theory

We explore humans’ rule-based category learning using analytic approaches that highlight their psychological transitions during learning. These approaches confirm that humans show qualitatively sudden psychological transitions during rule learning. These transitions contribute to the theoretical literature contrasting single vs. multiple category-learning systems, because they seem to reveal a distinctive learning process of explicit rule discovery. A complete psychology of categorization must describe this learning process, too. Yet extensive formal-modeling analyses confirm that a wide range of current (gradient-descent) models cannot reproduce these transitions, including influential rule-based models (e.g., COVIS) and exemplar models (e.g., ALCOVE). It is an important theoretical conclusion that existing models cannot explain humans’ rule-based category learning. The problem these models have is the incremental algorithm by which learning is simulated. Humans descend no gradient in rule-based tasks. Very different formal-modeling systems will be required to explain humans’ psychology in these tasks. An important next step will be to build a new generation of models that can do so.     

Structural characterization of components of protein assemblies by comparative modeling and electron cryo-microscopy

We explore structural characterization of protein assemblies by a combination of electron cryo-microscopy (cryoEM) and comparative protein structure modeling. Specifically, our method finds an optimal atomic model of a given assembly subunit and its position within an assembly by fitting alternative comparative models into a cryoEM map. The alternative models are calculated by MODELLER [J. Mol. Biol. 234 (1993) 313] from different sequence alignments between the modeled protein and its template structures. The fitting of these models into a cryoEM density map is performed either by FOLDHUNTER [J. Mol. Biol. 308 (2001) 1033] or by a new density fitting module of MODELLER (Mod-EM). Identification of the most accurate model is based on the correlation between the model accuracy and the quality of fit into the cryoEM density map. To quantify this correlation, we created a benchmark consisting of eight proteins of different structural folds with corresponding density maps simulated at five resolutions from 5 to 15 angstroms, with three noise levels each. Each of the proteins in the set was modeled based on 300 different alignments to their remotely related templates (12-32% sequence identity), spanning the range from entirely inaccurate to essentially accurate alignments. The benchmark revealed that one of the most accurate models can usually be identified by the quality of its fit into the cryoEM density map, even for noisy maps at 15 angstroms resolution. Therefore, a cryoEM density map can be helpful in improving the accuracy of a comparative model. Moreover, a pseudo-atomic model of a component in an assembly may be built better with comparative models of the native subunit sequences than with experimentally determined structures of their homologs.     

UsnRNP biogenesis: mechanisms and regulation

Macromolecular complexes composed of proteins or proteins and nucleic acids rather than individual macromolecules mediate many cellular activities. Maintenance of these activities is essential for cell viability and requires the coordinated production of the individual complex components as well as their faithful incorporation into functional entities. Failure of complex assembly may have fatal consequences and can cause severe diseases. While many macromolecular complexes can form spontaneously in vitro, they often require aid from assembly factors including assembly chaperones in the crowded cellular environment. The assembly of RNA protein complexes implicated in the maturation of pre-mRNAs (termed UsnRNPs) has proven to be a paradigm to understand the action of assembly factors and chaperones. UsnRNPs are assembled by factors united in protein arginine methyltransferase 5 (PRMT5)- and survival motor neuron (SMN)-complexes, which act sequentially in the UsnRNP production line. While the PRMT5-complex pre-arranges specific sets of proteins into stable intermediates, the SMN complex displaces assembly factors from these intermediates and unites them with UsnRNA to form the assembled RNP. Despite advanced mechanistic understanding of UsnRNP assembly, our knowledge of regulatory features of this essential and ubiquitous cellular function remains remarkably incomplete. One may argue that the process operates as a default biosynthesis pathway and does not require sophisticated regulatory cues. Simple theoretical considerations and a number of experimental data, however, indicate that regulation of UsnRNP assembly most likely happens at multiple levels. This review will not only summarize how individual components of this assembly line act mechanistically but also why, how, and when the UsnRNP workflow might be regulated by means of posttranslational modification in response to cellular signaling cues.     

Dynamically heterogenous partitions and phylogenetic inference: an evaluation of analytical strategies with cytochrome b and ND6 gene sequences in cranes

ki ctes over whether molecular sequence data should be partitioned for phylogenetic analysis often confound two types of heterogeneity among partitions. We distinguish historical heterogeneity (i.e., different partitions have different evolutionary relationships) from dynamic heterogeneity (i.e., different partitions show different patterns of sequence evolution) and explore the impact of the latter on phylogenetic accuracy and precision with a two-gene, mitochondrial data set for cranes. The well-established phylogeny of cranes allows us to contrast tree-based estimates of relevant parameter values with estimates based on pairwise comparisons and to ascertain the effects of incorporating different amounts of process information into phylogenetic estimates. We show that codon positions in the cytochrome b and NADH dehydrogenase subunit 6 genes are dynamically heterogenous under both Poisson and invariable-sites + gamma-rates versions of the F84 model and that heterogeneity includes variation in base composition and transition bias as well as substitution rate. Estimates of transition-bias and relative-rate parameters from pairwise sequence comparisons were comparable to those obtained as tree-based maximum likelihood estimates. Neither rate-category nor mixed-model partitioning strategies resulted in a loss of phylogenetic precision relative to unpartitioned analyses. We suggest that weighted-average distances provide a computationally feasible alternative to direct maximum likelihood estimates of phylogeny for mixed-model analyses of large, dynamically heterogenous data sets.     

SEXUAL SELECTION BY THE HANDICAP MECHANISM

The handicap mechanism of sexual selection by female choice has been strongly criticized because it does not cause sexual selection to reinforce viability selection and it cannot account for the origin of mating preferences. However, several models indicate that the handicap mechanism can have important effects when operating in conjunction with Fisher's mechanism in polygynous populations. These models have been criticized because they require that fitness remains heritable indefinitely. I develop a simple haploid model of the handicap mechanism based on nonheritable variation in paternal investment, thus eliminating the problem of heritable fitness. This model produces the same evolutonary dynamics as both simple and quantitative genetic models of the handicap mechanism based on heritable fitness. If the parameters are such that Fisherian runaway selection does not occur in the null model (i.e., the polymorphic equilibria, which lie along the “Fisher line,” are stable), then the handicap mechanism turns the Fisher line into an evolutionary trajectory upon which all other trajectories converge. This occurs because Fisher's mechanism generates no net selection on female preference when the population is on the Fisher line, so that any additional source of selection (direct or indirect) on female choice causes the population to evolve deterministically along the Fisher line. This change in the evolutionary dynamics has the important consequence of eliminating the potential for rapid population divergence for mating systems via genetic drift along the Fisher line.     

Structure Learning in a Sensorimotor Association Task

Learning is often understood as an organism''s gradual acquisition of the association between a given sensory stimulus and the correct motor response. Mathematically, this corresponds to regressing a mapping between the set of observations and the set of actions. Recently, however, it has been shown both in cognitive and motor neuroscience that humans are not only able to learn particular stimulus-response mappings, but are also able to extract abstract structural invariants that facilitate generalization to novel tasks. Here we show how such structure learning can enhance facilitation in a sensorimotor association task performed by human subjects. Using regression and reinforcement learning models we show that the observed facilitation cannot be explained by these basic models of learning stimulus-response associations. We show, however, that the observed data can be explained by a hierarchical Bayesian model that performs structure learning. In line with previous results from cognitive tasks, this suggests that hierarchical Bayesian inference might provide a common framework to explain both the learning of specific stimulus-response associations and the learning of abstract structures that are shared by different task environments.     

Functional interactions between the proline-rich and repeat regions of tau enhance microtubule binding and assembly.

Tau is a neuronal microtubule-associated protein that promotes microtubule assembly, stability, and bundling in axons. Two distinct regions of tau are important for the tau-microtubule interaction, a relatively well-characterized "repeat region" in the carboxyl terminus (containing either three or four imperfect 18-amino acid repeats separated by 13- or 14-amino acid long inter-repeats) and a more centrally located, relatively poorly characterized proline-rich region. By using amino-terminal truncation analyses of tau, we have localized the microtubule binding activity of the proline-rich region to Lys215-Asn246 and identified a small sequence within this region, 215KKVAVVR221, that exerts a strong influence on microtubule binding and assembly in both three- and four-repeat tau isoforms. Site-directed mutagenesis experiments indicate that these capabilities are derived largely from Lys215/Lys216 and Arg221. In marked contrast to synthetic peptides corresponding to the repeat region, peptides corresponding to Lys215-Asn246 and Lys215-Thr222 alone possess little or no ability to promote microtubule assembly, and the peptide Lys215-Thr222 does not effectively suppress in vitro microtubule dynamics. However, combining the proline-rich region sequences (Lys215-Asn246) with their adjacent repeat region sequences within a single peptide (Lys215-Lys272) enhances microtubule assembly by 10-fold, suggesting intramolecular interactions between the proline-rich and repeat regions. Structural complexity in this region of tau also is suggested by sequential amino-terminal deletions through the proline-rich and repeat regions, which reveal an unusual pattern of loss and gain of function. Thus, these data lead to a model in which efficient microtubule binding and assembly activities by tau require intramolecular interactions between its repeat and proline-rich regions. This model, invoking structural complexity for the microtubule-bound conformation of tau, is fundamentally different from previous models of tau structure and function, which viewed tau as a simple linear array of independently acting tubulin-binding sites.     

Steady-state kinetic behaviour of functioning-dependent structures

A fundamental problem in biochemistry is that of the nature of the coordination between and within metabolic and signalling pathways. It is conceivable that this coordination might be assured by what we term functioning-dependent structures (FDSs), namely those assemblies of proteins that associate with one another when performing tasks and that disassociate when no longer performing them. To investigate a role in coordination for FDSs, we have studied numerically the steady-state kinetics of a model system of two sequential monomeric enzymes, E(1) and E(2). Our calculations show that such FDSs can display kinetic properties that the individual enzymes cannot. These include the full range of basic input/output characteristics found in electronic circuits such as linearity, invariance, pulsing and switching. Hence, FDSs can generate kinetics that might regulate and coordinate metabolism and signalling. Finally, we suggest that the occurrence of terms representative of the assembly and disassembly of FDSs in the classical expression of the density of entropy production are characteristic of living systems.