DEA-R:ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications

We propose a new mathematical model for efficiency analysis, which combines DEA methodology with an old idea-Ratio Analysis. Our model, called DEA-R, treats all possible ratios "output/input" as outputs within the standard DEA model. Although DEA and DEA-R generate different summary measures for efficiency, the two measures are comparable. Our mathematical and empirical comparisons establish the validity of DEA-R model in its own right. The key advantage of DEA-R over DEA is that it allows effective integration of the model with experts' opinions via flexible restrictive conditions on individual "output/input" pairs. © 2007 Springer Science+Business Media, LLC.

A mathematical model for assembly line balancing model to consider disordering sequence of workstations

Purpose – A binary integer programming model for the simple assembly line balancing problem (SALBP), which is well known as SALBP-1, was formulated more than 30 years ago. Since then, a number of researchers have extended the model for the variants of assembly line balancing problem.The model is still prevalent nowadays mainly because of the lower and upper bounds on task assignment. These properties avoid significant increase of decision variables. The purpose of this paper is to use an example to show that the model may lead to a confusing solution. Design/methodology/approach – The paper provides a remedial constraint set for the model to rectify the disordered sequence problem. Findings – The paper presents proof that the assembly line balancing model formulated by Patterson and Albracht may lead to a confusing solution. Originality/value – No one previously has found that the commonly used model is incorrect.

An integrated scheduling problem of PCB components on sequential pick-and-place machines:mathematical models and heuristic solutions

This paper formulates several mathematical models for determining the optimal sequence of component placements and assignment of component types to feeders simultaneously or the integrated scheduling problem for a type of surface mount technology placement machines, called the sequential pick-andplace (PAP) machine. A PAP machine has multiple stationary feeders storing components, a stationary working table holding a printed circuit board (PCB), and a movable placement head to pick up components from feeders and place them to a board. The objective of integrated problem is to minimize the total distance traveled by the placement head. Two integer nonlinear programming models are formulated first. Then, each of them is equivalently converted into an integer linear type. The models for the integrated problem are verified by two commercial packages. In addition, a hybrid genetic algorithm previously developed by the authors is adopted to solve the models. The algorithm not only generates the optimal solutions quickly for small-sized problems, but also outperforms the genetic algorithms developed by other researchers in terms of total traveling distance.

A mathematical model for dynamic efficiency using data envelopment analysis

In this paper we propose a data envelopment analysis (DEA) based method for assessing the comparative efficiencies of units operating production processes where input-output levels are inter-temporally dependent. One cause of inter-temporal dependence between input and output levels is capital stock which influences output levels over many production periods. Such units cannot be assessed by traditional or 'static' DEA which assumes input-output correspondences are contemporaneous in the sense that the output levels observed in a time period are the product solely of the input levels observed during that same period. The method developed in the paper overcomes the problem of inter-temporal input-output dependence by using input-output 'paths' mapped out by operating units over time as the basis of assessing them. As an application we compare the results of the dynamic and static model for a set of UK universities. The paper is suggested that dynamic model capture the efficiency better than static model. © 2003 Elsevier Inc. All rights reserved.

An action research study with low proficiency learners in Japan to promote the learning of vocabulary through collocations.

This action research (AR) study explores an alternative approach to vocabulary instruction for low-proficiency university students: a change from targeting individual words from the general service list (West, 1953) to targeting frequent verb + noun collocations. A review of the literature indicated a focus on collocations instead of individual words could potentially address the students’ productive challenges with targeted vocabulary. Over the course of four reflective cycles, this thesis addresses three main aspects of collocation instruction. First, it examines if the students believe studying collocations is more useful than studying individual lexical items. Second, the thesis investigates whether a focus on collocations will lead to improvements in spoken fluency. This is tested through a comparison of a pre-intervention spoken assessment task with the findings from the same task completed 15 weeks later, after the intervention. Third, the thesis explores different procedures for the instructing of collocations under the classroom constraints of a university teaching context. In the first of the four reflective cycles, data is collected which indicates that the students believe a focus on collocations is superior to only teaching individual lexical items, that in the students’ opinion their productive abilities with the targeted structures has improved, and that delexicalized verb collocations are problematic for low-proficiency students. Reflective cycle two produces evidence indicating that productive tasks are superior to receptive tasks for fluency development. In reflective cycle three, productively challenging classroom tasks are investigated further and the findings indicate that tasks with higher productive demands result in greater improvements in spoken fluency. The fourth reflective cycle uses a different type of collocation list: frequent adjective + noun collocations. Despite this change, the findings remain consistent in that certain types of collocations are problematic for low-proficiency language learners and that the evidence shows productive tasks are necessary to improve the students’ spoken ability.

A mathematical model of coal-fired fluidised bed boilers

A mathematical model of a large coal-fired fluidized bed boiler for power generation is synthesised. The effect of variations in the main parameters of the model on variables such as the background carbon concentrations in the bed, and the transient response of heat evolution are studied. The mechanisms of solids mixing within the bed, combustion and the flow of heat to the boiler tubes are shown to result in a characteristic dynamic response, knowledge of which is essential for the proper control and regulation of a practical system.