Modeling and analysis of machine sharing in manufacturing systems

The issue of machine sharing arises quite frequently in the design and operation of automated manufacturing systems. It is often championed as a mechanism for enhancing the flexibility and versatility of these systems. However despite its importance, our understanding of machine sharing and of its effect on system performance has remained inadequate, relying mainly on anecdotal data or limited empirical evidence. In this paper, we present an analytical model that captures the various dimensions of machine sharing and use this model to study the effect of machine sharing on performance of manufacturing systems. In particular, we examine the relationship between machine sharing and several performance measures, such as production rate, machine utilization, flow time and work-in-process inventory, for varying assumptions of system utilization, setup times, batch sizes and demand and processing variability. These relationships are then used to identify conditions under which machine sharing is of value and to determine the corresponding optimal sharing levels.     

Inspecting the foundations of claims about cognitive demand and student learning: A citation analysis of Stein and Lane (1996)

Educational research communities bear responsibility for establishing a substantial body of evidence to support claims that drive the field. For example, one commonly accepted claim is that there is a relationship between the cognitive demand of mathematical task enactments and students’ learning. One study that is often cited in association with this claim is Stein and Lane (1996), and in 44% of those citations, Stein and Lane (1996) is the sole reference. Citation analysis reveals that many of these claims go beyond the warrants provided by the Stein and Lane study, either by granting more confidence in the relationship than the study design allows or by phrasing the claim as a causal relationship between cognitive demand and student learning. A few other studies are occasionally cited in conjunction with Stein and Lane (1996) and are summarized in this article, but there remains a need for replication studies to provide better empirical support for claims about cognitive demand and student learning and to refine our shared understanding.     

The Banzhaf index in complete and incomplete shareholding structures: A new algorithm

In this global world, many firms present a complex shareholding structure with indirect participation, such that it may become difficult to assess a firm’s controllers. Furthermore, if there are numerous dominant shareholders, the control can be shared between them. Determining who has the most influence is often a difficult task. To measure this influence, game theory allows the modeling of voting games and the computing of the Banzhaf index. This paper firstly offers a new algorithm to compute this index in all structures and then suggests some modelisations of the floating shareholder. Then, our model is applied to a real case study: the French group Lafarge. This exemplary case demonstrates how the float’s structure and hidden coalition can impact the power relationship between dominant shareholders.     

A copula approach to test asymmetric information with applications to predictive modeling

In this article, we present a copula regression model for testing asymmetric information as well as for predictive modeling applications in automobile insurance market. We use the Frank copula to jointly model the type of coverage and the number of accidents, with the dependence parameter providing for evidence of the relationship between the choice of coverage and the frequency of accidents. This dependence therefore provides an indication of the presence (or absence) of asymmetric information. The type of coverage is in some sense ordered so that coverage with higher ordinals indicate the most comprehensive coverage. Henceforth, a positive relationship would indicate that more coverage is chosen by high risk policyholders, and vice versa. This presence of asymmetric information could be due to either adverse selection or moral hazard, a distinction often made in the economics or insurance literature, or both. We calibrated our copula model using a one-year cross-sectional observation of claims arising from a major automobile insurer in Singapore. Our estimation results indicate a significant positive coverage-risk relationship. However, when we correct for the bias resulting from possible underreporting of accidents, we find that the positive association vanishes. We further used our estimated model for other possible actuarial applications. In particular, we are able to demonstrate the effect of coverage choice on the incidence of accidents, and based on which, the pure premium is derived. In general, a positive margin is observed when compared with the gross premium available in our empirical database.     

The roles of tools and models in a prospective elementary teachers’ developing understanding of multidigit multiplication

It is important for prospective elementary teachers to understand multidigit multiplication deeply; however, the development of such understanding presents challenges. We document the development of a prospective elementary teacher’s reasoning about multidigit multiplication during a Number and Operations course. We present evidence of profound progress in Valerie’s understanding of multidigit multiplication, and we highlight the roles of particular tools and models in her developing reasoning. In this way, we contribute an illuminating case study that can inform the work of mathematics teacher educators. We discuss specific instructional implications that derive from this case.     

Nonlinear behavior of the renormalization group flow and standard model parameters

The standard model for high-energy physics (SM) describes fundamental interactions between subatomic particles down to a distance scale on the order of 10⁻¹⁸ m. Despite its widespread acceptance, a consistent and comprehensive understanding of SM parameters is missing. Starting from a less conventional standpoint, our work suggests that the spectrum of particle masses, gauge couplings and fermion mixing angles may be derived from the chaotic regime of the renormalization group flow. In particular, we argue that the observed hierarchies of standard model parameters amount to a series of scaling ratios depending on the Feigenbaum constant. Leading order predictions are shown to agree well with experimental data.     

Approximate evaluation of multi-location inventory models with lateral transshipments and hold back levels

We consider a continuous-time, single-echelon, multi-location inventory model with Poisson demand processes. In case of a stock-out at a local warehouse, a demand can be fulfilled via a lateral transshipment (LT). Each warehouse is assigned a pre-determined sequence of other warehouses where it will request for an LT. However, a warehouse can hold its last part(s) back from such a request. This is called a hold back pooling policy, where each warehouse has hold back levels determining whether a request for an LT by another warehouse is satisfied. We are interested in the fractions of demand satisfied from stock (fill rate), via an LT, and via an emergency procedure from an external source. From these, the average costs of a policy can be determined. We present a new approximation algorithm for the evaluation of a given policy, approximating the above mentioned fractions. Whereas algorithms currently known in the literature approximate the stream of LT requests from a warehouse by a Poisson process, we use an interrupted Poisson process. This is a process that is turned alternatingly On and Off for exponentially distributed durations. This leads to the On/Off overflow algorithm. In a numerical study we show that this algorithm is significantly more accurate than the algorithm based on Poisson processes, although it requires a longer computation time. Furthermore, we show the benefits of hold back levels, and we illustrate how our algorithm can be used in a heuristic search for the setting of the hold back levels.     

Designing for Mathematical Abstraction

Our focus is on the design of systems (pedagogical, technical, social) that encourage mathematical abstraction, a process we refer to as designing for abstraction. In this paper, we draw on detailed design experiments from our research on children’s understanding about chance and distribution to re-present this work as a case study in designing for abstraction. Through the case study, we elaborate a number of design heuristics that we claim are also identifiable in the broader literature on designing for mathematical abstraction. Our previous work on the micro-evolution of mathematical knowledge indicated that new mathematical abstractions are routinely forged in activity with available tools and representations, coordinated with relatively na?ve unstructured knowledge. In this paper, we identify the role of design in steering the micro-evolution of knowledge towards the focus of the designer’s aspirations. A significant finding from the current analysis is the identification of a heuristic in designing for abstraction that requires the intentional blurring of the key mathematical concepts with the tools whose use might foster the construction of that abstraction. It is commonly recognized that meaningful design constructs emerge from careful analysis of children’s activity in relation to the designer’s own framework for mathematical abstraction. The case study in this paper emphasizes the insufficiency of such a model for the relationship between epistemology and design. In fact, the case study characterises the dialectic relationship between epistemological analysis and design, in which the theoretical foundations of designing for abstraction and for the micro-evolution of mathematical knowledge can co-emerge.     

Simulating prevention operations at sea against maritime piracy

Maritime piracy has been a major issue for the international community in the last decade and affected the global economy. As a reaction to this issue, international organizations have deployed naval forces to protect maritime transportation in the affected regions. In this study, we present a simulation-based analysis tool to evaluate the effectiveness of operations to prevent piracy. In our model, we consider three stakeholders’ views (pirates, maritime transporters, and naval forces) and modelled their behaviours separately, using Discrete Event Simulation (DES) and Agent-Based Simulation (ABS) approaches. Our hybrid DES and ABS model is used to simulate hypothetical scenarios on the Gulf of Aden for understanding the cause and effect relationship between naval resource allocation and piracy prevention. Our experimental results showed that, first, helicopters are most valuable in prevention and, second, either patrolling or escorting naval ships must carry a helicopter for effective prevention.     

Online time-constrained scheduling in linear and ring networks

We consider the problem of scheduling a sequence of packets over a linear network, where every packet has a source and a target, as well as a release time and a deadline by which it must arrive at its target. The model we consider is bufferless, where packets are not allowed to be buffered in nodes along their paths other than at their source. This model applies to optical networks where opto-electronic conversion is costly, and packets mostly travel through bufferless hops. The offline version of this problem was previously studied in M. Adler et al. (2002) [3]. In this paper we study the online version of the problem, where we are required to schedule the packets without knowledge of future packet arrivals. We use competitive analysis to evaluate the performance of our algorithms. We present the first online algorithms for several versions of the problem. For the problem of throughput maximization, where all packets have uniform weights, we give an algorithm with a logarithmic competitive ratio, and present some lower bounds. For other weight functions, we show algorithms that achieve optimal competitive ratios.     

Estimation,modeling, and aggregation of missing survey data for prioritizing customer voices

It is widely acknowledged that understanding and prioritizing the voice of customer is a critical step in new product development. In this work, we propose a novel approach to handle missing and incomplete data while combining information from different surveys for prioritizing customer voices. Our new approach comprises of the following stages: estimating and representing missing and incomplete data; estimating intervals for the criteria used in analyzing data; mapping data on criteria to a common scale; modeling interval data using interval belief structure; and aggregating evidence and ranking customer voices using the interval evidential reasoning algorithm. We demonstrate our approach using a case study from automotive domain with a given criteria hierarchy for analyzing data from three different surveys. We propose new optimization formulations for estimating intervals of the criteria used in our case study and logical yet pragmatic transformation functions for mapping criteria values to a common scale.     

Examining and conceptualizing the relationship between teacher praise and the co-construction of mathematical competence in classrooms

In this study we examined how teacher praise varies across and within four middle school mathematics classrooms in relationship to mathematical competence. We then conceptualized how teacher praise contributes to the co-construction of normative identity: the class’ shared understanding of what counts as being a competent learner in a mathematics classroom. Findings revealed teachers rarely used person-based praise (e.g., “you’re smart”) and frequently gave generic praise (e.g., “good”). Each teacher’s praise patterns supported different co-constructions of mathematical competence. Although some teachers taught the same lessons or ascribed to similar pedagogical approaches, findings suggest teachers’ praise patterns may contribute to the co-construction of different normative identities, some more exclusive and others more inclusive. Findings indicate praise may be a low-stakes and potentially impactful teacher practice with implications for students’ understanding of what it means to be good at math.     

Life insurance policy termination and survivorship

There has been some work, e.g. Carriere (1998), Valdez (2000b), and Valdez (2001), leading to the development of statistical models in understanding the mortality pattern of terminated policies. However, there is a scant literature on the empirical evidence of the true nature of the relationship between survivorship and persistency in life insurance. When a life insurance contract terminates due to voluntary non-payment of premiums, there is a possible hidden cost resulting from mortality antiselection. This refers to the tendency of policyholders who are generally healthy to select against the insurance company by voluntarily terminating their policies. In this article, we explore the empirical results of the survival pattern of terminated policies, using a follow-up study of the mortality of those policies that terminated from a portfolio of life insurance contracts. The data has been obtained from a major insurer which traced the mortality of their policies withdrawn, for purposes of understanding the mortality antiselection, by obtaining their dates of death from the Social Security Administration office. Using a representative sample of this follow-up data, we modeled the time until a policy lapses and its subsequent mortality pattern. We find some evidence of mortality selection and we consequentially examined the financial cost of policy termination.     

Connecting the learning of advanced mathematics with the teaching of secondary mathematics: Inverse functions,domain restrictions,and the arcsine function

Prospective secondary mathematics teachers are typically required to take advanced university mathematics courses. However, many prospective teachers see little value in completing these courses. In this paper, we present the instantiation of an innovative model that we have previously developed on how to teach advanced mathematics to prospective teachers in a way that informs their future pedagogy. We illustrate this model with a particular module in real analysis in which theorems about continuity, injectivity, and monotonicity are used to inform teachers’ instruction on inverse trigonometric functions and solving trigonometric equations. We report data from a design research study illustrating how our activities helped prospective teachers develop a more productive understanding of inverse functions. We then present pre-test/post-test data illustrating that the prospective teachers were better able to respond to pedagogical situations around these concepts that they might encounter.     

Bayesian Object Identification: Variants

We present a Bayesian theory of object identification. Here, identifying an object means selecting a particular observation from a group of observations (variants), this observation (the regular variant) being characterized by a distributional model. In this sense, object identification means assigning a given model to one of several observations. Often, it is the statistical model of the regular variant, only, that is known. We study an estimator which relies essentially on this model and not on the characteristics of the “irregular” variants. In particular, we investigate under what conditions this variant selector is optimal. It turns out that there is a close relationship with exchangeability and Markovian reversibility. We finally apply our theory to the case of irregular variants generated from the regular variant by a Gaussian linear model.     

Fractions as Subtraction: An Activity‐Oriented Perspective from Elementary Children

A sample of third‐, fourth‐, and fifth‐grade student responses to the question “What is a fraction?” were examined to gain an understanding of how children in upper elementary grades make sense of fractions. Rather than measure children's understanding of fractions relative to mathematically conventional part–whole constructions of fractions, we attempted to understand children's actions and processes. A small but nontrivial group of children used subtraction (takeaway and removal) as a framework for understanding how fractions were created and written. An analysis of the content of their responses as well as a comparison of the performance of these children with that of children who used other ways of describing fractions suggests that the use of subtraction may be a reasonable (or at least not harmful) way for children to begin to access concepts related to fractions. Also, this study suggests that attention to children's understanding through the lens of children's activity might reveal ways of thinking and insights that are masked when we compare children's thinking in more structured research settings.     

A multicast problem with shared risk cost

In this paper, we study a minimum cost multicast problem on a network with shared risk link groups (SRLGs). Each SRLG contains a set of arcs with a common risk, and there is a cost associated with it. The objective of the problem is to find a multicast tree from the source to a set of destinations with minimum transmission cost and risk cost. We present a basic model for the multicast problem with shared risk cost (MCSR) based on the well-known multicommodity flow formulation for the Steiner tree problem (Goemans and Myung in Networks 1:19–28, 1993; Polzin and Daneshmand in Discrete Applied Mathematics 112(1–3): 241–261, 2001). We propose a set of strong valid inequalities to tighten the linear relaxation of the basic model. We also present a mathematical model for undirected MCSR. The computational results of real life test instances demonstrate that the new valid inequalities significantly improve the linear relaxation bounds of the basic model, and reduce the total computation time by half in average.     

Allocating fixed costs or resources and setting targets via data envelopment analysis

In many applications of data envelopment analysis (DEA), there is often a fixed cost or input resource which should be imposed on all decision making units (DMUs). Cook and Zhu [W.D. Cook, J. Zhu, Allocation of shared costs among decision making units: A DEA approach, Computers and Operations Research 32 (2005) 2171-2178] propose a practical DEA approach for such allocation problems. In this paper, we prove that when some special constraints are added, Cook and Zhu’s approach probably has no feasible solution. The research of this paper focuses on two main aspects: to obtain a new fixed costs or resources allocation approach by improving Cook and Zhu’s approach, and to set fixed targets according to the amount of fixed resources shared by individual DMUs. When such special constraints are attached, our model is proved to be able to achieve a feasible costs or resources allocation. Numerical results for an example from the literature are presented to illustrate our approach.     

General and multiplicative non-parametric corporate performance models with interval ratio data

The increasing intensity of global competition has led organizations to utilize various types of performance measurement tools for improving the quality of their products and services. Data envelopment analysis (DEA) is a methodology for evaluating and measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. All the data in the conventional DEA with input and/or output ratios assumes the form of crisp numbers. However, the observed values of data in real-world problems are sometimes expressed as interval ratios. In this paper, we propose two new models: general and multiplicative non-parametric ratio models for DEA problems with interval data. The contributions of this paper are fourfold: (1) we consider input and output data expressed as interval ratios in DEA; (2) we address the gap in DEA literature for problems not suitable or difficult to model with crisp values; (3) we propose two new DEA models for evaluating the relative efficiencies of DMUs with interval ratios, and (4) we present a case study involving 20 banks with three interval ratios to demonstrate the applicability and efficacy of the proposed models where the traditional indicators are mostly financial ratios.