Determining the Best Performance Time Period of a System

The main purpose of this paper is to determine the best performance time period of a system, consisting some DMUs, among some sequential time periods. This aim is satised by two proposed algorithms, the rst based on global Malmquist Productivity Index and the second is based on PPS frontiers

A full investigation of the directional congestion in data envelopment analysis

One of interesting subjects in Data Envelopment Analysis (DEA) is estimation of congestion of Decision Making Units (DMUs). Congestion is evidenced when decreases (increases) in some inputs result in increases (decreases) in some outputs without worsening (improving) any other input/output. Most of the existing methods for measuring the congestion of DMUs utilize the traditional definition of congestion and assume that inputs and outputs change with the same proportion. Therefore, the important question that arises is whether congestion will occur or not if the decision maker (DM) increases or decreases the inputs dis-proportionally. This means that, the traditional definition of congestion in DEA may be unable to measure the congestion of units with multiple inputs and outputs. This paper focuses on the directional congestion and proposes methods for recognizing the directional congestion using DEA models. To do this, we consider two different scenarios: (i) just the input direction is available. (ii) none of the input and output directions are available. For each scenario, we propose a method consists in systems of inequalities or linear programming problems for estimation of the directional congestion. The validity of the proposed methods are demonstrated utilizing two numerical examples

Using convex preference cones in multiple criteria decision making and related fields

This paper reviews our own and colleagues’ research on using convex preference cones in multiple criteria decision making and related fields. The original paper by Korhonen, Wallenius, and Zionts was published in Management Science in 1984. We first present the underlying theory, concepts, and method. Then we discuss applications of the theory, particularly for finding the most preferred alternative, finding a partial and total rank ordering of alternatives, as well as developing algorithms for solving multi-objective integer and other optimization problems

A Scenario-based Model for Resource Allocation with Price Information

In this paper, we consider the problem of allocating resources among Decision Making Units (DMUs). Regarding the concept of overall (cost) efficiency, we consider three different scenarios and formulate three Resource Allocation (RA) models correspondingly. In the first scenario, we assume that overall efficiency of each unit remains unchanged. The second scenario is related to the case where none of overall efficiency scores is deteriorated. We improve the overall efficiencies by a pre-determined percentage in the last scenario. We formulate Linear Programming problems to allocate resources in all scenarios. All three scenarios are illustrated through numerical and empirical examples

A compromise programming approach for target setting in DEA

This paper presents a new data envelopment analysis (DEA) target setting approach that uses the compromise programming (CP) method of multiobjective optimization. This method computes the ideal point associated to each decision making unit (DMU) and determines an ambitious, efficient target that is as close as possible (using an lp metric) to that ideal point. The specific cases p = 1, p = 2 and p = ∞ are separately discussed and analyzed. In particular, for p = 1 and p = ∞, a lexicographic optimization approach is proposed in order to guarantee uniqueness of the obtained target. The original CP method is translation invariant and has been adapted so that the proposed CP-DEA is also units invariant. An lp metric-based efficiency score is also defined for each DMU. The proposed CP-DEA approach can also be utilized in the presence of preference information, non-discretionary or integer variables and undesirable outputs. The proposed approach has been extensively compared with other DEA approaches on a dataset from the literature

Resource allocation and target setting based on virtual profit improvement

One application of Data Envelopment Analysis (DEA) is the resource allocation and target setting among homogeneous Decision Making Units (DMUs). In this paper, we assume that all units are under the supervision and control of a central decision making unit, for instance chain stores, banks, schools, etc. The aim is to allocate available resources among units in a way that the so-called organisational overall ”virtual profit” is maximized. Our method is highly flexible in decision making to achieve the goals of the Decision Maker (DM). The resulting production plans maintain the following characteristics: (1) the virtual profit of each unit is calculated with a common set of weights; (2) the selected weights for calculating the virtual profit prevent the virtual profit of the system from getting worse; (3) the virtual profits of less profitable units are improved as much as possible. The proposed method is illustrated with a simple numerical example and a real life application

Gradual efficiency improvement through a sequence of targets

The goal in efficiency analysis is not only to evaluate a decision-making unit (DMU) performance, but also to find an efficient target which provides information on inputs reduction and outputs increment values that are necessary to remove inefficiencies for each inefficient DMU. In data envelopment analysis (DEA), the target unit is located on the efficient frontier and possibly far from the unit under assessment. Therefore, in practice performance improvement seems to be disappointing or even impossible to achieve in only one step for some inefficient DMUs. In this regard, finding intermediate targets is of great importance in benchmarking literature. In this article, we find a sequence of targets instead of a single target for each inefficient unit. In our method, the intermediate target at each step has three properties: (I) the intermediate targets and the unit under evaluation are all similar in size; (II) efficiency scores are ascending through the sequence of targets; (III) the target unit at each step is close to the special part of the efficient frontier as much as possible. These properties lead to finding a target that is more achievable in real applications

Evaluation of the Degenerative Changes of the Distal Intervertebral Discs after Internal Fixation Surgery in Adolescent Idiopathic Scoliosis

Study Design Retrospective study. Purpose Lumbar intervertebral disc degeneration is an important cause of low back pain. Overview of Literature Spinal fusion is often reported to have a good course for adolescent idiopathic scoliosis (AIS). However, many studies have reported that adjacent segment degeneration is accelerated after lumbar spinal fusion. Radiography is a simple method used to evaluate the orientation of the vertebral column. magnetic resonance imaging (MRI) is the method most often used to specifically evaluate intervertebral disc degeneration. The Pfirrmann classification is a well-known method used to evaluate degenerative lumbar disease. After spinal fusion, an increase in stress, excess mobility, increased intra-disc pressure, and posterior displacement of the axis of motion have been observed in the adjacent segments. Methods we retrospectively secured and analyzed the data of 15 patients (four boys and 11 girls) with AIS who underwent a spinal fusion surgery. We studied the full-length view of the spine (anterior-posterior and lateral) from the X-ray and MRI obtained from all patients before surgery. Postoperatively, another full-length spine X-ray and lumbosacral MRI were obtained from all participants. Then, pelvic tilt, sacral slope, curve correction, and fused and free segments before and after surgery were calculated based on X-ray studies. MRI images were used to estimate the degree to which intervertebral discs were degenerated using Pfirrmann grading system. Pfirrmann grade before and after surgery were compared with Wilcoxon signed rank test. While analyzing the contribution of potential risk factors for the post-spinal fusion Pfirrmann grade of disc degeneration, we used generalized linear models with robust standard error estimates to account for intraclass correlation that may have been present between discs of the same patient. Results The mean age of the participant was 14 years, and the mean curvature before and after surgery were 67.8 and 23.8, respectively (p<0.05). During the median follow-up of 5 years, the mean degree of the disc degeneration significantly increased in all patients after surgery (p<0.05) with a Pfirrmann grade of 1 and 2.8 in the L2–L3 before and after surgery, respectively. The corresponding figures at L3–L4, L4–L5, and L5–S1 levels were 1.28 and 2.43, 1.07 and 2.35, and 1 and 2.33, respectively. The lower was the number of free discs below the fusion level, the higher was the Pfirrmann grade of degeneration (p<0.001). Conversely, the higher was the number of the discs fused together, the higher was the Pfirrmann grade. Conclusions we observed that the disc degeneration aggravated after spinal fusion for scoliosis. While the degree of degeneration as measured by Pfirrmann grade was directly correlated by the number of fused segments, it was negatively correlated with the number of discs that remained free below the lowermost level of the fusion

A New Modified Method for Inserting Iliosacral Screw versus the Conventional Method

Study DesignMethodological study.PurposeTo our knowledge, this is the first study to introduce a new modified method for inserting iliosacral screws and to compare its results with those of a conventional method.Overview of LiteraturePrevious techniques, such as open reduction and internal fixation, are associated with perioperative hemorrhage, postoperative infection, and neurological deficits. Although percutaneous iliosacral screw insertion confers the advantage of being minimally invasive, leading to less blood loss and a low postoperative infection rate, it harbors the risk of screw malpositioning due to narrow sacral proportions and a high interindividual variability.MethodsNine cadaveric pelvises were included in this study, with one hemipelvis of each being assigned to the new modified method and the other to the conventional iliosacral screw insertion method. In the new modified method, the guidewire entry point was determined using a lateral sacral X-ray. To do so, we first identified the anterosuperior quadrant of the S1 body on one hemipelvis. The anterosuperior quadrant was further divided into four imaginary quadrants, and the guidewire was inserted into the posteroinferior quadrant. The guidewire trajectory was perpendicular to the sagittal plane so that the guidewire resembled a single point in the lateral sacral view. Guidewires were inserted into corresponding hemipelves using the conventional method as described in the literature. Subsequently, an axial computed tomography scan with 1-mm fine cuts was obtained, and sagittal and coronal views were reconstructed. The distance of the guidewire from the sacral canal, anterior sacral cortex, and first sacral foramen was measured in axial, sagittal, and coronal views. The minimum measurement among different views was defined as the safety index of the insertion methods. The conventional and new modified methods were then compared in terms of safety and duration of the procedure.ResultsThe minimum distance of the guidewire from the S1 foramen and anterior sacral cortex was not significantly different between the two methods. However, the minimum distance between the guidewire and sacral canal was significantly greater in the new modified method than in the conventional method. The duration of guidewire insertion was significantly shorter in the new modified method than in the conventional method.ConclusionsThis new modified method of iliosacral screw insertion could be safely and simply implemented while taking less surgical time than the conventional methods

Operational Research in Education

Operational Research (OR) techniques have been applied, from the early stages of the discipline, to a wide variety of issues in education. At the government level, these include questions of what resources should be allocated to education as a whole and how these should be divided amongst the individual sectors of education and the institutions within the sectors. Another pertinent issue concerns the efficient operation of institutions, how to measure it, and whether resource allocation can be used to incentivise efficiency savings. Local governments, as well as being concerned with issues of resource allocation, may also need to make decisions regarding, for example, the creation and location of new institutions or closure of existing ones, as well as the day-to-day logistics of getting pupils to schools. Issues of concern for managers within schools and colleges include allocating the budgets, scheduling lessons and the assignment of students to courses. This survey provides an overview of the diverse problems faced by government, managers and consumers of education, and the OR techniques which have typically been applied in an effort to improve operations and provide solutions