Scheduling tasks on a flexible manufacturing machine to minimize tool change delays

This paper considers the problem of scheduling a given set of precedence constraint tasks on a flexible machine equipped with a tool magazine where each task requires exactly one of the tools during its execution. Changing from one tool to another requires a certain amount of time that depends on the pair of tools being exchanged. We present a new algorithmic approach for general task precedence relations when it is desired to sequence the tasks in such a way that the total time required for tool changes is minimized. The proposed algorithm is of polynomial time complexity in case of task precedences of limited width w, i.e. for precedence relations where each subset of independent tasks has not more than w elements. Since the task precedences width w could be arbitrary, we describe two heuristic algorithms and empirically evaluate their effectiveness in finding schedules with minimum total time required for tool changes.     

CHANGES IN SCHOOL STUDENTS’ OBSERVATIONS AND REASONING DURING A 4-PHASE TEACHING SEQUENCE

We examine the written responses of fifteen students (aged about 14½ years) to a homework task and their responses to the same task in a subsequent lesson. Students were asked to make observations about the sum of three consecutive numbers and to explain why they think these are true, thereby giving students the opportunity to engage in structural reasoning. The teaching sequence had four phases designed to allow students to make, share and develop their observations and reasoning, and we found a clear improvement in the quality of students’ responses. As far as students’ reasoning is concerned, this suggests limitations may stem at least in part from a lack of familiarity with the nature of mathematical reasoning.     

Conceptualising, investigating and stimulating representational flexibility in mathematical problem solving and learning: a critical review

Based on Verschaffel et al.’s conceptualisation of flexible strategy choice, this article provides a critical review on the literature concerning flexible representational choice in mathematical learning. We argue that, while flexibility in the selection of a representation to complete a mathematical task has traditionally been understood as choosing the representation(s) that match(es) the characteristics of the to-be-solved task, research evidence suggests that it also includes the ability to take into account the characteristics of the subjects interacting with the representations, as well as the context in which such interaction takes place. The instructional and research implications of acknowledging the subjectivity and contextuality of flexible representational choice are examined.     

Student-Invented Numeration Systems: Pattern-Analysis and Mathematical Understanding

Thirteen fifth graders were given an assignment to invent their own numeration systems, following a unit on bases and a look at early events in the history of numbers. The task presented options that required the students to make decisions (such as whether to use a base, which base to use, design of symbols, etc.), and build a rationale for the elements of their system. Analyses of patterns embedded in their invented systems provided an assessment of student understanding of numeration. The progression of more and less complex thinking related to the student's choice of a base other than 10, consistency of logic throughout the system in words and symbols, rationale for change, and perception of real life examples that would change if the system was adopted. The invention task is presented as another way to make connections.     

The sugar production factory—A dynamic decision task

This article describes the Sugar Production Factor and its structural equivalent, the Personal Interaction task. These are two simple, individual dynamic decision-making tasks in which subjects make interdependent decisions to reach a goal, and receive feedback on the outcome of their efforts along the way. An important result from human learning experiments using these two tasks and their variants is that subjects reliably improve their ability to reach the goal over a moderate number of training trials (40–90) but do not show consistent improvement in other measures of task knowledge. These other measures focus on subjects' ability to accurately predict the task environment's response to their actions and subjects' ability to produce useful heuristics. This pattern of results runs counter to the idea that decision makers' performance in dynamic decision tasks depends critically on the predictive accuracy their internal models of the task environment. Variants of both tasks have been used to manipulate this pattern of results and explore more deeply the nature of the internal models that subjects form of the task environment. These variants are discussed in the context of other relevant findings in the dynamic decision making literature.     

Stability Analysis of an Orbiting Plate with Finite Elements

This paper contributes to the analysis of rotating equilibria of non–driven systems (sometimes called relative equilibria), which are characterized by the fact that their angular momentum is conserved and non–zero. Interesting applications are usually found in space dynamics, in particular if large earth orbiting structures such as the space elevator are considered. For flexible structures relative equilibria can be found with Finite Element software packages. However, in this case the stability analysis is a non–trivial task since one usually has only limited account to the internal data of commercial FE solvers. Therefore, in [5] a new finite element based stability test was developed and applied to one–dimensional structural elements. Here, we consider a large–scale flexible plate orbiting around the earth in order to demonstrate that this method works well also for two dimensional shell–elements. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vibration surveillance during milling of flexible details with a use of the optimal control

The paper concerns vibration surveillance during ball end milling of curved flexible details. Here is explained dynamic analysis of non-stationary vibrating system, from which are separated subsystems: modal, structural and connective. An assessment of coincidence of the calculation model results with those from investigation on milling machine is performed. Ball end milling of flexible details is observed very frequently in case of modern machining centres. It is obvious that tool-workpiece relative vibration plays principal role during cutting process. The most important task is to create a FE-model of machined flexible detail and obtain its good correlation with the results of experimental modal analysis. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

旋转刚柔耦合系统的模型及控制

旋转刚柔耦合系统在航空航天、机器人、高速机构以及车辆等领域有着广泛的应用,主要描述负载在旋转刚体上的柔性梁的运动。对旋转刚柔耦合系统施加控制使得整个闭环系统达到:1)旋转刚体以预期的旋转角速度运动;2)负载在刚体上的柔性梁镇定。本文将从控制器设计的角度出发,介绍目前在旋转刚柔耦合系统控制方面取得的主要研究成果。     

Multipurpose Professional Growth Sequence: The catwalk problem as a paradigmatic example

An important concern in mathematics teacher education is how to create learning opportunities for prospective and practicing teachers that make a difference in their professional growth as educators. The first purpose of this article is to describe one way of working with prospective and practicing teachers in a graduate mathematics education course that holds promise for positively influencing the way teachers think about mathematics, about student learning, and about mathematics teaching. Specifically, I use the “catwalk” task as an example of how a single problem can serve as the basis for a coherent sequence of professional learning experiences. A second purpose of this article is to provide background information that contextualizes the subsequent two articles, each of which details the positive influence of the catwalk task sequence on the authors’ professional growth.     

Developing flexible procedural knowledge in undergraduate calculus

Mathematics experts often choose appropriate procedures to produce an efficient or elegant solution to a mathematical task. This flexible procedural knowledge distinguishes novice and expert procedural performances. This article reports on an intervention intended to aid the development of undergraduate calculus students’ flexible use of procedures. Two sections of the same course were randomly assigned to treatment and control conditions. Treatment students completed an assignment on which they resolved derivative-finding problems with alternative methods and compared the two resulting solutions. Control students were assigned a list of functions to differentiate. On the post-intervention test, treatment students were more likely to use a variety of solution methods without prompting than the control. Moreover, the set of treatment section solutions were closer to those of a group of mathematics experts. This study presents evidence that not only is flexible procedural knowledge a key skill in tertiary mathematics, it can be taught.     

Log-gamma motion as flexible model for generalized interest rates

Negative, oscillating, and near zero interest rates are changing financial modeling completely. To address this situation, we introduce novel, flexible, and estimable model of interest rate. This model is based on recent developments of so-called Inv-Log-Gamma process. This model is much easier to be estimated as the continuous time models for interest rates with dampings, where interest rate r_t possesses a martingale property. Even though the estimation of continuous time interest rates is a difficult task. Therefore, more flexible and estimable model for interest rate is needed, which motivates our developments. Simulation and real data examples illustrate usefulness of our development.     

Dynamics modelling and Hybrid Suppression Control of space robots performing cooperative object manipulation

Dynamics modelling and control of multi-body space robotic systems composed of rigid and flexible elements is elaborated here. Control of such systems is highly complicated due to severe under-actuated condition caused by flexible elements, and an inherent uneven nonlinear dynamics. Therefore, developing a compact dynamics model with the requirement of limited computations is extremely useful for controller design, also to develop simulation studies in support of design improvement, and finally for practical implementations. In this paper, the Rigid–Flexible Interactive dynamics Modelling (RFIM) approach is introduced as a combination of Lagrange and Newton–Euler methods, in which the motion equations of rigid and flexible members are separately developed in an explicit closed form. These equations are then assembled and solved simultaneously at each time step by considering the mutual interaction and constraint forces. The proposed approach yields a compact model rather than common accumulation approach that leads to a massive set of equations in which the dynamics of flexible elements is united with the dynamics equations of rigid members. To reveal such merits of this new approach, a Hybrid Suppression Control (HSC) for a cooperative object manipulation task will be proposed, and applied to usual space systems. A Wheeled Mobile Robotic (WMR) system with flexible appendages as a typical space rover is considered which contains a rigid main body equipped with two manipulating arms and two flexible solar panels, and next a Space Free Flying Robotic system (SFFR) with flexible members is studied. Modelling verification of these complicated systems is vigorously performed using ANSYS and ADAMS programs, while the limited computations of RFIM approach provides an efficient tool for the proposed controller design. Furthermore, it will be shown that the vibrations of the flexible solar panels results in disturbing forces on the base which may produce undesirable errors and perturb the object manipulation task. So, it is shown that these effects can be significantly eliminated by the proposed Hybrid Suppression Control algorithm.     

Prescriptive analytics for human resource planning in the professional services industry

In this paper, we examine human resource planning decisions made at firms that sell contract-based consulting projects. High levels of uncertainty in deals and revenue forecasts make it challenging for consulting firms to hire the right people to staff their projects. We present a human resource planning model using concepts from robust optimization to allow companies to dynamically make hiring decisions that maximize profit while remaining as flexible as possible, and demonstrate potential profit improvements through simulation on real data.     

Scheduling of multistage fast-moving consumer goods plants

Fast-moving consumer goods (FMCG) plants are required to be highly flexible due to their multiproduct nature and frequent portfolio changes with seasons or consumer preferences. The multipurpose nature of equipment units usually results in changeover activities which can increase the production scheduling model’s size significantly. The objective of this paper is to present two approaches to decrease the number of changeover activities. The first approach aims to reduce unit flexibility by reducing the allowable task to unit allocations. The second approach emphasises sequencing operations on units. By limiting the set of possible task sequences in the scheduling problem, the number of allowable activities (especially changeovers) is decreased and the optimisation procedure has a smaller search space. The results of these approaches, tested against realistically sized instances indicate their effectiveness in reducing the model size and the solution time, enabling the solution of industrial examples which previously could not be solved.     

Part-whole number knowledge in preschool children

Ability to reflect on a number as an object of thought, and to isolate its constituent parts, is basic to a deep knowledge of arithmetic, as well as much practical and applied mathematical problem solving. Part-whole reasoning and counting are closely related in children’s numerical development. The mathematical behavior of young children in part-whole problem settings was examined by using a dynamic problem situation, in which a small set of items was partitioned such that one of the subsets remained perceptually inaccessible. Issues addressed include the problem solving strategies successful children used, adaptations children make in response to successive administrations of the task over time, and characterizations of children’s mathematical thinking based on their responses to the task.     

Robust observer-based frequency-shaping optimal vibration control of uncertain flexible linkage mechanisms

Based on the state-space model of the flexible linkage mechanism equipped with piezoelectric materials, a robust observer-based frequency-shaping optimal feedback (OBFSOF) control methodology is presented for actively suppressing the elastodynamic responses of the high-speed flexible linkage mechanism with linear structured time-varying parameter perturbations. The advantage of the proposed OBFSOF control methodology is that it can make the controlled closed-loop system to obtain both good robustness at high frequencies and good performance at low frequencies. Besides, this paper also presents two robust stability criteria to guarantee that the designed OBFSOF controller can make the controlled flexible linkage mechanism system to avoid the possibilities of both spillover-induced instability and time-varying-parameter-perturbation-induced instability. Numerical simulation of a slider–crank mechanism example is performed to evaluate the improvement of the elastodynamic responses.     

Flexible <Emphasis Type="Italic">versus</Emphasis> fixed timetabling: a case study

This case study presents the timetabling problem of the Flight Training Department at Embry-Riddle Aeronautical University. The problem consists of scheduling the flight resources to students to various time blocks. This problem represents a well-studied field in operations research, mainly adopting variations of mathematical programming models. This paper initially presents the efforts towards developing a fixed timetable using optimization models for the case under study. It is, however, demonstrated that implementation of optimum solutions obtained using this approach cannot be sustained, mainly because of the dynamic nature of the governing parameters. A flexible and dynamic timetable utilizing the university computer network, allowing the instructors and students to make their own decentralized flexible timetables, is proposed. A simulation study is initiated to compare the performance measures under both timetables. The analysis shows that implementation of a flexible system generates higher utilization of flight resources as well as improving key performance measures.     

Control concepts for a parallel manipulator with flexible links

Light-weight robots are advantageous considering the low energy consumption and the low material cost. However, in light-weight structures significant oscillations can occur which make the control very challenging. Objective of this research is end-effector trajectory tracking of a parallel manipulator with flexible links. Hereby, only the manipulator's drives are used, and no additional actuation on the flexible bodies is considered. For accurate trajectory tracking, feedforward control of the manipulator is used based on inverse dynamics and servo-constraints, combined with feedback control of the drive positions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)