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The purpose of this paper is to present an analysis of the difficulties faced by students when working with different representations of vectors, planes and their intersections in R[superscript 3]. Duval's theoretical framework on semiotic representations is used to design a set of evaluating activities, and later to analyze student work. The analysis covers three groups of undergraduate students taking introductory courses in linear algebra. Different types of treatments and conversions are required to solve the activities. One important result shows that, once students choose a register to solve a task, they seldom make transformations between different registers, even though this facilitates solving the task at hand. Identifying these difficulties for particular transformations may help teachers design specific activities to promote students cognitive flexibility between representation registers.

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2006.01.044 Byline: Thomas W. Archibald (a), Lyn C. Thomas (b), Edgar Possani (b) Keywords: Inventory; Markov processes; Dynamic programming Abstract: Start-up companies are considered an important factor in the success of a nation's economy. We are interested in the decisions for long-term survival of these firms when they have considerable cash restrictions. In this paper we analyse several inventory control models to manage inventory purchasing and return policies. The Markov decision models are formulated for both established companies that look at maximising average profit and start-up companies that look at maximising their long-term survival probability. We contrast both objectives, and present properties of the policies and the survival probabilities. We find that start-up companies may need to be riskier if the return price is very low, but there is a period where a start-up firm becomes more cautious than an established company and there is a point, as it accumulates capital, where it starts behaving as an established firm. We compare the various models and give conditions under which their policies are equivalent. Author Affiliation: (a) University of Edinburgh Management School, 50 George Square, Edinburgh EH8 9JY, UK (b) School of Management, University of Southampton, Southampton SO17 1BJ, UK Article History: Received 26 November 2003; Accepted 30 January 2006

In this article we consider the advantages of applying lot streaming in a multiple job flow-shop context. The lot streaming process of splitting jobs into sublots to allow overlapping between successive operations has been shown to reduce makespan and thus increase customer satisfaction. Efficient algorithms are available in the literature for solving the problem for a single job. However, for multiple jobs, job sequencing, as well as lot sizing, is involved, and the problem is therefore NP-hard. We consider two special cases for which we provide polynomial time solutions. In one case, we eliminate diversity of the jobs, and hence the job sequencing decision, and in the other we restrict the number of machines. We show that for jobs with identical processing times and number of sublots, no advantage is obtained by allowing inconsistency in sublot sizing of consecutive jobs. For the two-machine case, we also explain why the sequencing and sublot size decision can be approached independently, and supply a polynomial time algorithm for minimising makespan, taking account of attached set-ups on the first machine and transportation times. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present an analysis of the difficulties faced by students when working with different representations of vectors, planes and their intersections in $\mathbb {R}^{3}$. Duval's theoretical framework on semiotic representations is used to design a set of evaluating activities, and later to analyze student work. The analysis covers three groups of undergraduate students taking introductory courses in linear algebra. Different types of treatments and conversions are required to solve the activities. One important result shows that, once students choose a register to solve a task, they seldom make transformations between different registers, even though this facilitates solving the task at hand. Identifying these difficulties for particular transformations may help teachers design specific activities to promote students cognitive flexibility between representation registers. [ABSTRACT FROM AUTHOR]

The cross entropy method was initially developed to estimate rare event probabilities through simulation, and has been adapted successfully to solve combinatorial optimization problems. In this paper we aim to explore the viability of using cross entropy methods for the vehicle routing problem. Published implementations to this problem have only considered a naive route-splitting scheme over a very limited set of instances. In addition of presenting a better route-splitting algorithm we designed a cluster-first/route-second approach. We provide computational results to evaluate these approaches, and discuss its advantages and drawbacks. The innovative method, developed in this paper, to generate clusters may be applied in other settings. We also suggest improvements to the convergence of the general cross entropy method. [ABSTRACT FROM AUTHOR]

This paper deals with component commonality in start-up manufacturing firms. We present a two-product Markov decision model that examines the implications of the inventory and production strategies for the survival probability of the firm. The advantage of using component commonality is studied for varying costs, demand correlations and order replenishment lead times. Optimal policies are derived, and minimum stock levels for survival are obtained. Moreover, we state the conditions under which simplified production decisions can be made. It is shown that commonality is not only useful as a way of dealing with demand uncertainty, but that its increased use is preferred for strongly substitutable products, and shorter replenishment lead times. [ABSTRACT FROM AUTHOR]