We consider the semi-on-line parallel machines scheduling problem with the known total and the largest processing times of all jobs. We develop an approximation algorithm for the problem and prove that the competitive ratio of the algorithm is not more than √<(10)/3>&ap;1.8257, regardless of the number of machines.

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Recent remarkable progresses of computer technology and solving algorisms have enabled to solve large-scale optimization problems rather easily. Correspondingly, many large-scale models of energy and environment systems have been developed. However, it has become more difficult for modelers on one side to construct, modify and upgrade the models due to their complexity and large size, and for decision-makers on the other to understand the analyses results of the complicated models. Analysis of energy and environment systems usually requires large-scale models, and constructed models occasionally need to be modified or upgraded to meet changes in assumed data and in analysis purpose or to enjoy the progress of computer technology and of solving algorithms. Thus, a new methodology is wanted to provide a high productivity in model construction and a high flexibility to model modification or upgrading. This paper presents such a new methodology to construct mathematical programming models for energy and environment systems analysis. To acquire intended productivity and flexibility, the model is divided, at first, into three kinds of modules : a database system, a matrix generator and a report generator. Secondly, all the model elements are grouped into four categories and then the equations to express inter-element relationships are also categorized : "Flow" "Conversion Process", "Stock" and "Inter-regional Transportation". In order to verify the effectiveness of the new methodology, two kinds of sample models have been developed by the new methodology and their results are shown in this article. The new methodology helps attain high productivity in modeling systems of energy and environment and also of other areas. It also facilitates for the related people such as policy analysts or policy makers to interpret the model analysis results more accurately because the model structure is more clearly understood thanks to the categorization of model elements and equations.

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In the typical type of ANP with a matrix U evaluating alternatives by criteria and a matrix W evaluating criteria by alternatives in the so-called supermatrix S, W is often said to be unstable. Here, we propose a method to revise W into a stable W and to calculate the weights of criteria and alternatives at the same time under the revised supermatrix S. Our method is formulated as an optimization problem based on Bayes Theorem which T.L. Saaty claimed to be included in ANP scheme. Concurrent Convergence method developed by Kinoshita and Nakanishi also intends to be correct W, but this method includes some contradictions. We prove that our method has no such contradiction. We introduce some eigenvalue problems, which give a lower bound of our optimal value and their special cases coincide with our problem. Furthermore, we clear what perturbations of W preserve weights of criteria and alternatives to be invariant under the concept of inactive alternatives.

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In this paper we propose a trust region sequential quadratic programming (SQP) method to solve large-scale nonlinear optimization problems. The main shortcoming of the ordinary trust region SQP method is that the QP subproblem with the trust region constraint may not be feasible when a radius of the trust region is small. The trust region SQP methods which have been proposed so far are so complicated to resolve this shortcoming. It is not desirable in view of implementation and computational time. Moreover, many of the previous trust region SQP methods have another difficulty to solve the QP subproblem which is not necessarily convex. In this paper, we propose a new trust region SQP method which eliminates these two shortcomings. In our method, we solve two types of subproblem that one is a convex QP problem and the other is a system of linear equations.

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This paper introduces a new index - the 'relative-military index, ' which is capable of evaluating a nation's dependence on military forces. We also measured this index by applying data envelopment analysis (DEA) to real-life data, and verified two inferences drawn from Dr. Kissinger's historical description of the post-Cold War world. Our study demonstrates that DEA could be useful in testing hypotheses in the social sciences, especially in the field of International Relations.

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A new methodology for reliability evaluation and optimization of non-repairable dissimilar-component cold-standby redundant systems is introduced in this paper. Each component includes some elements with series-parallel configuration. When the operating component fails, the next dissimilar component is put into operation. Therefore, the initially functioning elements are backed up by one or more cold-standby redundant elements. The lifetimes of the elements are assumed to be independent random variables with Erlang distribution. The purchase cost of each element is assumed to be an increasing function of its expected lifetime. To evaluate the system reliability, we apply shortest path technique in stochastic networks. To do that, we construct a directed stochastic network called E-network, in which each path of this network corresponds with a minimal cut of the reliability graph. Finally, we construct a multi-objective problem and apply the surrogate worth trade-off method to solve the related problem and determine the optimal allocation of reliability to the elements of the system.

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