A hybrid of genetic algorithm and particle swarm optimization for solving bi-level linear programming problem – A case study on supply chain model

The main goal of supply chain management is to coordinate and collaborate the supply chain partners seamlessly. On the other hand, bi-level linear programming is a technique for modeling decentralized decision. It consists of the upper level and lower level objectives. Thus, this paper intends to apply bi-level linear programming to supply chain distribution problem and develop an efficient method based on hybrid of genetic algorithm (GA) and particle swarm optimization (PSO). The performance of the proposed method is ascertained by comparing the results with GA and PSO using four problems in the literature and a supply chain distribution model.     

Value of supplier’s capacity information in a two-echelon supply chain

In traditional supply chain models it is generally assumed that full information is available to all parties involved. Although this seems reasonable, there are cases where chain members are independent agents and possess different levels of information. In this study, we analyze a two-echelon, single supplier-multiple retailers supply chain in a single-period setting where the capacity of the supplier is limited. Embedding the lack of information about the capacity of the supplier in the model, we aim to analyze the reaction of the retailers, compare it with the full-information case, and assess the value of information and the effects of information asymmetry using game theoretic analysis. In our numerical studies, we conclude that the value of information is highly dependent on the capacity conditions and estimates of the retailers, and having information is not necessarily beneficial to the retailers.     

Dynamic conformance and design quality in a supply chain: an assessment of contracts’ coordinating power

We consider a two-echelon supply chain involving one manufacturer and one supplier who collaborate on improving both design and conformance quality. Design quality is supposed to increase product desirability, and therefore market demand, while conformance quality should reduce the proportion of defective items, and therefore increase the manufacturer’s sales revenue. We investigate how the supply chain parties allocate effort between design and conformance quality under both cooperative and non-cooperative settings in an intertemporal framework. Furthermore, we evaluate wholesale price contracts and revenue-sharing contracts in terms of their performance and coordination power. We show that although a revenue-sharing contract enables the manufacturer to effectively involve the supplier in quality improvement, neither contract type allows for perfect coordination resulting in the quality that can be achieved by a cooperative supply chain. We thus suggest a reward-based extension to the revenue-sharing contract, to ensure system-wide optimal quality performance. Importantly, we find that the supplier would be better off adopting a reward-based revenue sharing contract and refusing a standard revenue-sharing contract, while the opposite would be true for the manufacturer.     

Exact asymptotics for the stationary distribution of a Markov chain: a production model

We derive rough and exact asymptotic expressions for the stationary distribution π of a Markov chain arising in a queueing/production context. The approach we develop can also handle “cascades,” which are situations where the fluid limit of the large deviation path from the origin to the increasingly rare event is nonlinear. Our approach considers a process that starts at the rare event. In our production example, we can have two sequences of states that asymptotically lie on the same line, yet π has different asymptotics on the two sequences.     

A steepest-descent Krasnosel’skii–Mann algorithm for a class of variational inequalities in Banach spaces

In this paper, in order to solve a variational inequality problem over the fixed point set of a nonexpansive mapping on uniformly smooth or reflexive and strictly convex Banach spaces with a uniformly Gâteaux differentiable norm, we investigate an explicit iteration method, based on the steepest-descent and Krasnosel’skii–Mann algorithms. We also show that some modifications of the last and Halpern-type algorithms are special cases of our result.     

‘Experimental pedagogy’ in Germany,elaborated for mathematics – a case study in searching the roots of PME

PME, the International Group for the Psychology of Mathematics Education, was founded in 1976, at the Third International Congress on Mathematical Education in Karlsruhe, organised by the International Commission on Mathematics Instruction (ICMI). While PME is thus beyond coming of age and is reflecting its further orientation – due to the present “social turn” – the origins of investigating psychological aspects of mathematics learning have not yet been systematically studied. I am undertaking here a first such approach, concentrating on Germany, where the first pertinent monographs were published in 1913 and 1916. Different endeavours, focussing in particular on the notion of error, merged into the characteristic approach of ‘experimental pedagogy’. Given the key function of ICMI for founding PME, an additional aspect is whether the forerunner of ICMI: the Internationale Mathematische Unterrichtskommission (IMUK), founded in 1908, had an impact upon promoting research into the psychology of mathematics education. The pertinent research was effected by psychology; doing research themselves was still outside the horizon of mathematics educators. Perspectives of future research, in particular comparative ones, are outlined.     

Algorithmic contexts and learning potentiality: a case study of students’ understanding of calculus

The study explores the nature of students’ conceptual understanding of calculus. Twenty students of engineering were asked to reflect in writing on the meaning of the concepts of limit and integral. A sub-sample of four students was selected for subsequent interviews, which explored in detail the students’ understandings of the two concepts. Intentional analysis of the students’ written and oral accounts revealed that the students were expressing their understanding of limit and integral within an algorithmic context, in which the very ‘operations’ of these concepts were seen as crucial. The students also displayed great confidence in their ability to deal with these concepts. Implications for the development of a conceptual understanding of calculus are discussed, and it is argued that developing understanding within an algorithmic context can be seen as a stepping stone towards a more complete conceptual understanding of calculus.     

Erratum to “A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling” [Appl. Math. Modell. 34 (2010) 655–670]

This study analyzes Mixed Integer Linear Program (MILP) proposed by G. Kannan, P. Sasikumar M. Devika, (2010) in their paper titled ‘A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling’, Applied Mathematical Modelling, (34, 655–670). The model in Kannan et al. (2010) is found to be inadequate for the problem described. It is erroneous/infeasible in terms of constraints, objective and variables. In this work, we list down the flaws in the published work and propose modifications to rectify the flaws. The revised model is presented and illustrated using hypothetical problems.     

A case study: assessment of preservice secondary mathematics teachers’ metacognitive behaviour in the problem-solving process

The purpose of the present study was to investigate preservice secondary mathematics teachers’ metacognitive behaviour in the mathematical problem-solving process. The case study methodology was employed with six preservice mathematics teachers, enrolled at one university in Ankara, Turkey. We collected data by using the think aloud method, which lasted for two sessions. It was found that there was no relationship between academic achievement and frequencies of metacognitive behaviour. However, the types of problems could affect these frequencies. Furthermore, there was no pattern in metacognitive behaviour with respect to achievement and type of problem.     

Identifying authority structures in mathematics classroom discourse: a case of a teacher’s early experience in a new context

We explore a conceptual frame for analyzing mathematics classroom discourse to understand the way authority is at work. This case study of a teacher moving from a school where he is known to a new setting offers us the opportunity to explore the use of the conceptual frame as a tool for understanding how language practice and authority relate in a mathematics classroom. This case study illuminates the challenges of establishing disciplinary authority in a new context while also developing the students’ sense of authority within the discipline. To analyze the communication in the teacher’s grade 12 class in the first school and grade 9 class early in the year at the new school, we use the four categories of positioning drawn from our earlier analysis of pervasive language patterns in mathematics classrooms—personal authority, discourse as authority, discursive inevitability, and personal latitude.     

Transfer in chemistry: a study of students’ abilities in transferring mathematical knowledge to chemistry

It is recognized that there is a mathematics problem in chemistry, whereby, for example, undergraduate students appear to be unable to utilize basic calculus knowledge in a chemistry context – calculus knowledge – which would have been taught to these students in a mathematics context. However, there appears to be a scarcity of literature addressing the possible reasons for this problem. This dearth of literature has spurred the following two questions: (1) Can students transfer mathematical knowledge to chemistry?; and (2) What are the possible factors associated with students being able to successfully transfer mathematical knowledge to a chemistry context? These questions were investigated in relation to the basic mathematical knowledge which chemistry students need for chemical kinetics and thermodynamics, using the traditional view of the transfer of learning. Two studies were undertaken amongst two samples of undergraduate students attending Dublin City University. Findings suggest that the mathematical difficulties which students encounter in a chemistry context may not be because of an inability to transfer the knowledge, but may instead be due to insufficient mathematical understanding and/or knowledge of mathematical concepts relevant to chemical kinetics and thermodynamics.     

Validating a concept inventory for measuring students’ probabilistic reasoning: The case of reasoning within the context of a raffle

Assessing students’ conceptions related to independence of events and determining probabilities from a sample space has been the focus of research in probability education for over 40 years. While we know a lot from past studies about predictable ways students may reason with well-known tasks, developing a diagnostic assessment that can be used by teachers to inform instruction demands the use of familiar and unfamiliar contexts. This paper presents the current work of a research team whose aim is to create a formative concept inventory with strong evidence of validity that uses a psychometric model to confidently predict whether a student exhibits one or more misconception across many items. We illustrate this process in this paper using a particular item with a context of a raffle aimed to measure whether a student reasons with misconceptions related to independence or equiprobability. The results of two aspects of the validity process: cognitive interviews to assess response processes on individual items, and a large-scale administration to examine internal structure of the concept inventory revealed difficulties in assessing students’ reasoning about these key probability concepts and trends in the prevalence of misconceptions across grades. Results can provide guidance for others aiming to develop assessments in mathematics education and also support further possibilities for research into understanding students’ reasoning about independence and sample space.     

A criterion for the unique solvability of the dirichlet spectral problem in a cylindrical domain for a multidimensional Lavrent’ev-Bitsadze equation

We obtain a criterion for the unique solvability of the spectral problem in a cylindrical domain for a multidimensional Lavrent’ev-Bitsadze equation.     

Standing on each other’s shoulders: A case of coalescence between geometric discourses in peer interaction

In this paper we draw on the commognitive theory to examine novice students’ transition from familiar mathematics meta-rules to less familiar ones during peer interaction. To pursue this goal, we focused on a relatively symmetric interaction between two middle-school students given a geometric task. During their dyadic problem-solving, the students transitioned from configural procedures to deductive ones. We found that this transition included an interactive coalescence pattern in which one student “borrowed” her partner’s configural sub-procedures and built on them to develop a new deductive procedure. Furthermore, we found that during their peer interaction, the students oscillated between configural, coalesced and deductive procedures. Several patterns in the students’ interpretation of the task-situation contributed to these oscillations. We discuss the contribution of our findings to commognitive research, to geometry learning research and to peer learning research.     

GIS-based optimization for the locations of sewage treatment plants and sewage outfalls – A case study of Nansha District in Guangzhou City,China

Based on GIS technology, eco-suitability evaluation method integrating economic, social and ecological factors is employed to optimize the locations of the sewage treatment plants and outfalls in this paper. The ecological indices considering eco-sensitivity areas as key elements of the integrated evaluation system are allotted to the water subsystem, riparian zone subsystem, and land subsystem. A novel integrated eco-suitability evaluation index system encompassing ten criteria and fifteen indices is established to generate the distributed eco-suitability map of the concerned areas and determine the possible locations of sewage treatment plants and sewage outfalls according to the eco-suitability levels. With the case study of Nansha District in Guangzhou City, China, 212 km² areas of land are found to be suitable for locating the sewage treatment plants, 87 km² areas of water suitable for sewage release, and 6 km² area of riparian zone unsuitable for sewage outfalls.     

Optimal sensor placement for modal identification of structures using genetic algorithms—a case study: the olympic stadium in Cali,Colombia

Adequate sensor placement plays a key role in such fields as system identification, structural control, damage detection and structural health monitoring of flexible structures. In recent years, interest has increased in the development of methods for determining an arrangement of sensors suitable for characterizing the dynamic behavior of a given structure. This paper describes the implementation of genetic algorithms as a strategy for optimal placement of a predefined number of sensors. The method is based on the maximization of a fitness function that evaluates sensor positions in terms of natural frequency identification effectiveness and mode shape independence under various occupation and excitation scenarios using a custom genetic algorithm. A finite element model of the stadium was used to evaluate modal parameters used in the fitness function, and to simulate different occupation and excitation scenarios. The results obtained with the genetic algorithm strategy are compared with those obtained from applying the Effective Independence and Modal Kinetic Energy sensor placement techniques. The sensor distribution obtained from the proposed strategy will be used in a structural health monitoring system to be installed in the stadium.