# American Institute of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

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## Journal of Industrial & Management Optimization

2008 , Volume 4 , Issue 3

Special Issue Dedicated to Professor Yacov Y. Haimes

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2008, 4(3): i-iv doi: 10.3934/jimo.2008.4.3i +[Abstract](370) +[PDF](76.3KB)
Abstract:
We are very pleased to dedicate this Special Issue of the Journal of Industrial and Management Optimization to Professor Yacov Y. Haimes for his pioneering and significant contributions over forty years to various aspects of systems engineering and risk management including planning, design, management and operation of water resources, transportation and other interdependent infrastructure systems, multiple objective optimization and hierarchical analysis of large-scale systems, as a scholar and educator.
2008, 4(3): 407-423 doi: 10.3934/jimo.2008.4.407 +[Abstract](390) +[PDF](270.3KB)
Abstract:
A novel procedure having strategic flexibility is designed to handle multiple criteria sorting problems such that a decision maker (DM) can adjust the group count and fine-tune group numbers to improve sorting efficiency. Its unique features include interactive control, so that the DM can adjust the number of groups and other sorting characteristics; the capacity to aggregate cardinal and ordinal criteria using concepts from data envelopment analysis; and the integration of approximate information about criterion weights, which may help to ensure that the sorting results more closely reflect the DM's intrinsic preferences. A case study in inventory classification is carried out to demonstrate the efficacy of the proposed method.
2008, 4(3): 425-452 doi: 10.3934/jimo.2008.4.425 +[Abstract](434) +[PDF](1037.1KB)
Abstract:
Most previous Cournot-Nash models of competition among electricity generators have assumed a static perspective, resulting in finite dimensional variational and quasi-variational inequality formulations. However, these models' system costs and constraints fail to capture the dynamic nature of power networks. In this paper we propose a more general and complete model of Cournot-Nash competition on power networks that accounts for these features by including ($i$) explicit intra-day dynamics that describe the market's evolution from one Generalized Cournot-Nash Equilibrium to another for a 24 hour planning horizon, ($ii$) ramping constraints and costs for changing the power output of generators, and ($iii$) joint constraints that include variables from other generating companies within the profit maximization problems for individual generators. These joint constraints yield a generalized Nash equilibrium problem which can be represented as a differential quasi-variational inequality (DQVI); such generalized Nash equlibrium problems can have multiple solutions. The resulting formulation poses computational challenges that can cause traditional algorithms for DVIs to fail. A restricted formulation is proposed that can be solved by an implicit fixed point algorithm. A numerical example is provided.
2008, 4(3): 453-475 doi: 10.3934/jimo.2008.4.453 +[Abstract](487) +[PDF](932.1KB)
Abstract:
Radiation therapy (RT) is a non-invasive and highly effective treatment option for Prostate cancer. The goal is to deliver the prescription dose to the tumor (prostate) while minimizing the damages to the surrounding healthy organs namely bladder, rectum, and femoral heads. One major drawback of the conventional RT is that organ positions and shapes vary from day to day and that the original plan that is based on pre-treatment CT images may no longer be appropriate for treatment in subsequent sessions. The usual remedy is to include some margins surrounding the target when planning the treatment. Though this image guided radiation therapy technique allows in-room correction and can eliminate patient setup errors, the uncertainty due to organ deformation still remains. Performing a plan re-optimization will take about 30 minutes which makes it impractical to perform an online correction. In this paper, we develop an Adaptive Radiation Therapy (ART) system for online adaptive IMRT planning to compensate for the internal motion during the course of the prostate cancer treatment. It allows the treatment plan to be quickly modified based on the anatomy-of-the-day.
2008, 4(3): 477-487 doi: 10.3934/jimo.2008.4.477 +[Abstract](515) +[PDF](126.2KB)
Abstract:
Systems engineering concepts are directly applicable to the development and integration of management and technological processes that support all of the major lifecycle functions needed to produce high quality and trustworthy systems in a total quality fashion. Information is the glue that holds together such processes as: research and development, test and evaluation (RDT&E); system acquisition; and planning and marketing. Systems management deals with such issues as program and project management, technical direction of development, and quality and configuration management of the evolving system such as to achieve risk management. Risk issues abound in many contemporary systems management situations. Often, these situations emerge from behavior of many independent agents who attempt to achieve both individual organizational objectives and objectives of the larger organizational unit seeking to attain an interoperable system of systems or system family from the efforts of the individual organizations. A complex system of systems will often exhibit evolutionary, emergent, and adaptive behavior when the individual systems are architected, engineered and integrated to achieve the composite system of systems. Of course, evolutionary, emergent, and adaptive behavior may well exist even when systems are not consciously architected, engineered, and integrated. But this behavior may well be not at all desired. Complex adaptive system behavior manifests itself at the level of both the individual system and the composite system family. These changes are generally experienced as emergent or evolutionary processes. It is for this reason that emergence has been defined as system behavior that evolves from interaction of many participants, and cannot be predicted or even envisioned from knowledge of the isolated behavior of each system or each individual design team. Modeling and simulation are essential in the engineering of large systems of all types, especially those that are subject to evolutionary and path dependent results. Whether we are dealing with human-made systems, human systems, or organizational systems; there is a need to organize and manage for complexity, and associated knowledge and enterprise integration, ultimately for the betterment of all concerned. In this paper, we examine these risk management issues for a system of systems, especially one operating in a federated environment.
2008, 4(3): 489-510 doi: 10.3934/jimo.2008.4.489 +[Abstract](400) +[PDF](318.9KB)
Abstract:
The increasing degree of interdependencies among sectors of the economy can likely make the impacts of natural and human-caused disruptive events more pronounced and far-reaching than before. An extended input-output model is implemented in this paper to analyze risk scenarios to a particular sector and to estimate the resulting ripple effects to other sectors. The proposed extension is capable of combining likelihood and consequence estimates from multiple experts, which incorporates traditional expected value and extreme-event measures of risk. The probability densities of ripple effects are generated via Monte Carlo simulation; hence, providing estimates of the mean and extreme values of economic losses and corresponding levels of sector disruptions. In investing for additional airline security, for example, the breakeven level of investment cost should be optimized with respect to both average and worst-case consequences. Ultimately, the ranking of the sectors that are most critically affected by a given disruptive event can provide guidance in identifying resource allocation and other risk management strategies to minimize the overall impact on the economy. The methodology is demonstrated through an air transportation sector case study.
2008, 4(3): 511-533 doi: 10.3934/jimo.2008.4.511 +[Abstract](452) +[PDF](386.0KB)
Abstract:
A number of quantitative methods have emerged to identify and track precursors to risk for engineering systems. While data mining and statistical inference identify patterns from information of historical events, they may not address features of extreme events that have never occurred. While, event and fault-tree analyses synthesize important information on basic and initiating risk events, they fall short of addressing incident data in real time. Accident precursor analyses refine event and fault tree analyses by considering near-misses or precursors from system operational data. Complementing precursor analysis is an existing method of detecting anomalies in a sequence of risk incident reports to (a) identify and count patterns in the reports, (b) measure and track the complexity of the reports with univariate statistical process control, and (c) identify specific periods of instability. This paper extends the existing method to (d) introduce two additional measurements of patterns, (e) apply multiple criteria statistical process control to track the multiple measurements of the reports, and (f) use optimal search parameters to generate a watch list of system components for input to accident precursor analyses. The extension is demonstrated for a sequence of four observation periods of incident reports in a power distribution system.
2008, 4(3): 535-552 doi: 10.3934/jimo.2008.4.535 +[Abstract](823) +[PDF](221.6KB)
Abstract:
It is often the case that some unexpected event may force an investor to terminate her investment and leave the market. We consider in this paper the mean-variance formulation of multi-period portfolio optimization for asset-liability management with an uncertain investment horizon. Under the assumption that exit time follows a given distribution, the problem under investigation with uncertain investment horizon can be translated into one with deterministic exit time. By making use of the embedding technique of Li and Ng (2000), we derive an analytical optimal strategy and an analytical expression of the mean-variance efficient frontier for the mean-variance formulation of the problem.
2008, 4(3): 553-563 doi: 10.3934/jimo.2008.4.553 +[Abstract](303) +[PDF](345.1KB)
Abstract:
This paper develops the available transfer capability (ATC) concept to available transfer capability region (ATCR). Based on the steady-state security, the ATC of a single-contract is reformulated to a system of semismooth equations. Along the line of the methodology, the ATC of a combination of multi-contracts is presented. The combination coefficients forms a region, which is defined as ATC region (ATCR) in this paper. According to the messages of ATCs of each single-contract, the boundary of ATCR is approximated by a set of quadratic functions via a patching technology. The approximation of the ATCR and the visualization take a novelly practical approach called offline-online calculation. IEEE 30-bus system is chosen to test the method with respect to point-to-point transfers and area-to-area transfers. The computing results are visualized through a class of graphs. The virtue of ATCR is that it can provide the global message of possible increasing transfer in the system. The characteristic of the proposed method in this paper is its behave of online calculation. Numerical tests show the effect of the new approach.
2008, 4(3): 565-579 doi: 10.3934/jimo.2008.4.565 +[Abstract](478) +[PDF](214.2KB)
Abstract:
In this paper, we proposed two modified PRP conjugate gradient methods. It is a interesting feature that these new methods possess the sufficient descent property without assuming any line search condition and reduce to the standard PRP method when exact line search is used. Under some reasonable conditions, the global convergence is achieved for these methods. Preliminary numerical results show that these methods are efficient.
2008, 4(3): 581-609 doi: 10.3934/jimo.2008.4.581 +[Abstract](505) +[PDF](355.4KB)
Abstract:
In this paper we will propose a new classifier design based on the AFS fuzzy theory. First, we will briefly review the current researches in data classification based on fuzzy and rough set theories and then present the AFS framework. Second, we will present new membership functions for fuzzy sets with their logic operations in the AFS framework and then tackle some theoretical and computational problems related to classifier design. Third, we will develop a new approach for fuzzy classifier design based on the proposed membership functions and their logic operations. Finally, a well-known example is used to illustrate its effectiveness. The advantage of this classifier is in two-folds. One is that it can mimic the human reasoning comprehensively and offers a far more flexible and effective way for the study of large-scale intelligent systems. The other is its simplicity in methodology and mathematical beauty in fuzzy theory.
2008, 4(3): 611-616 doi: 10.3934/jimo.2008.4.611 +[Abstract](456) +[PDF](109.8KB)
Abstract:
Ghaffari-Hadigheh and Terlaky's methodology for finding support set invariancy sensitivity analysis intervals for general form linear optimization problems needs another condition to correctly identifying those intervals. This condition is complementarity condition. We show that this nonlinear complementarity condition can be eliminated by an extra assumption and the auxiliary problems become linear.
2008, 4(3): 617-630 doi: 10.3934/jimo.2008.4.617 +[Abstract](514) +[PDF](333.9KB)
Abstract:
In order to accurately simulate the game behaviors of market participants, a new dynamic Cournot game model of power market considering the constraints of power network is proposed in this paper. The model is represented by a discrete difference equations embedded with the maximization problem of the social benefit of power market. Compared with those existing dynamic models, the proposed one has the following remarkable characteristics: it adopts a dynamic adjustment where the limit point is the Nash equilibrium of power market, and the system of discrete difference equations embedded with the maximization problem considers the inherent physical characteristics of power network, i.e., the complex network constraints. Both of the properties show that the proposed model is much closer to the practical market. By using the nonlinear complementarity function to reformulate the Karush-Kuhn-Tucker (KKT) system of maximization problem, the Nash equilibrium of power market and its stability are quantitatively analyzed. Numerical simulations are carried out to evaluate the dynamic behaviors of market participants with different market parameters, especially the periodic and chaotic dynamic behaviors when the market parameters are beyond the stability region of Nash equilibrium.
2008, 4(3): 631-646 doi: 10.3934/jimo.2008.4.631 +[Abstract](383) +[PDF](179.5KB)
Abstract:
Machine layout and material flow between machines are crucial considerations for improving productivity in any manufacturing environment. The machine layout and the operations assignment problems are both known to be NP hard problems. In this paper, we consider a combined machine layout and job assignment problem and introduce an evolutionary algorithm to solve this combined problem. The usefulness of our approach is demonstrated through numerical examples.

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