Performance of Two-Component Systems with Imperfect Repair

Operational systems deteriorate over time and eventually fail by the failure of one or more of their components. Failed components are either replaced or repaired, and replacement is usually expensive. This article examines the behavior of repairable systems with imperfect repair, where a failed component is repaired once or more depending on factors such as repair cost, level of deterioration, and criticality of the component. When these systems are subjected to a customer use environment, their performance must endure different conditions. In imperfect repair, the performance of the system lessens after each failure. Three models of a two-component system studied are the series, parallel, and standby configurations, and the components are identical and independent. A closed form analytical expression for steady state operational probability is derived for different configurations under exponential distribution time to failure and repair time. Two examples are then discussed thoroughly.

Automatic Partitioning of Large Scale Simulation in Grid Computing for Run Time Reduction

Simulating large-scale systems usually entails exhaustive computational powers and lengthy execution times. The goal of this research is to reduce execution time of large-scale simulations without sacrificing their accuracy by partitioning a monolithic model into multiple pieces automatically and executing them in a distributed computing environment. While this partitioning allows us to distribute required computational power to multiple computers, it creates a new challenge of synchronizing the partitioned models. In this article, a partitioning methodology based on a modified Prim’s algorithm is proposed to minimize the overall simulation execution time considering 1) internal computation in each of the partitioned models and 2) time synchronization between them. In addition, the authors seek to find the most advantageous number of partitioned models from the monolithic model by evaluating the tradeoff between reduced computations vs. increased time synchronization requirements. In this article, epoch- based synchronization is employed to synchronize logical times of the partitioned simulations, where an appropriate time interval is determined based on the off-line simulation analyses. A computational grid framework is employed for execution of the simulations partitioned by the proposed methodology. The experimental results reveal that the proposed approach reduces simulation execution time significantly while maintaining the accuracy as compared with the monolithic simulation execution approach.

A New Hybrid Inexact Logarithmic-Quadratic Proximal Method for Nonlinear Complementarity Problems

In this paper, the authors present and analyze a new hybrid inexact Logarithmic-Quadratic Proximal method for solving nonlinear complementarity problems. Each iteration of the new method consists of a prediction and a correction step. The predictor is produced using an inexact Logarithmic-Quadratic Proximal method, which is then corrected by the Proximal Point Algorithm. The new iterate is obtained by combining predictor and correction point at each iteration. In this paper, the authors prove the convergence of the new method under the mild assumptions that the function involved is continuous and monotone. Comparison to another existing method with numerical experiments on classical NCP instances demonstrates its superiority.

Fuzzy Multi-Choice Goal Programming for Supplier Selection

Supplier selection decision is an important issue of purchasing management in supply chain management involving multiple objectives; however, it is difficult to solve because objectives are often conflicting in nature. This study integrates multi-choice goal programming (MCGP) and fuzzy approaches as decision aids to help decision makers to choose better suppliers by considering multiple aspiration levels and vague goal relations. According to the function of multiple aspirations provided by the fuzzy MCGP (FMCGP), decision makers can set fuzzy relations among multiple supplier goals with linguistic quantifiers according to their different strategies. Also, decision makers can define the membership function for each linguistic quantifier to describe their ambiguous selection preference in supplier selection. With the FMCGP method, decision makers can obtain the order quantities for suitable suppliers based on different organizations’ supply chain strategies. To demonstrate the usefulness of the proposed method, a real-world case of a Liquid Crystal Display (LCD) monitor and acrylic sheet manufacturer is presented.

Polynomial Approximation for Two Stage Stochastic Programming with Separable Objective

In this paper, the authors solve the two stage stochastic programming with separable objective by obtaining convex polynomial approximations to the convex objective function with an arbitrary accuracy. Our proposed method will be valid for realistic applications, for example, the convex objective can be either non-differentiable or only accessible by Monte Carlo simulations. The resulting polynomial is constructed by Bernstein polynomial and norm approximation models. At a given accuracy, the necessary degree of the polynomial and the replications are properly determined. Afterward, the authors applied the first gradient type algorithms on the new stochastic programming model with the polynomial objective, resulting in the optimal solution being attained.

Discrete Combat Models

Lanchester’s equations and their solutions, as continuous differential equations, have been studied for years. This article introduces a new approach with the use of the discrete form of Lanchester’s equations, using dynamical systems or difference equations. It begins with Lanchester’s square law and develops a generalized analytical solution for the discrete model that can be built by knowing only the kill rates and the initial force sizes of the combatants. It then forms the condition of parity (a draw) to develop a simple relationship of these variables to determine who wins the engagement. This article illustrates these models and their solutions using historic combat examples. It also illustrates that current counter-insurgency combat models can be built and solved using various forms of difference equations.

Security Constrained Economic Dispatch

The main objective of electric power dispatch is to provide electricity to the customers at low cost and high reliability. Transmission line failures constitute a great threat to the electric power system security. We use a Markov decision process (MDP) approach to model the sequential dispatch decision making process where demand level and transmission line availability change from hour to hour. The action space is defined by the electricity network constraints. Risk of the power system is the loss of transmission lines, which could cause involuntary load shedding or cascading failures. The objective of the model is to minimize the expected long-term discounted cost (including generation, load shedding, and cascading failure costs). Policy iteration can be used to solve this model. At the policy improvement step, a stochastic mixed integer linear program is solved to obtain the optimal action. We use a PJM network example to demonstrate the effectiveness of our approach.

Optimizing Cash Management for Large Scale Bank Operations

The Federal Reserve System (Fed) provides currency services to banks, including sorting currency into fit and non-fit bills and repackaging bills for redistribution. To reduce the cost of currency management operations, many banks make Fed deposits and withdrawals of the same denomination each week. In July 2007, the Fed introduced fees for making both deposits and withdrawals during a given Monday through Friday. Recognizing an opportunity, Fiserv Corporation initiated a project to optimize bank vault inventories across time and space. This article presents the integer programming model developed to assist Fiserv clients reduce the logistics cost component of cash management. The model is implemented in software using OPL. The underlying configuration is a time-space multi-commodity network with a fixed-charge cost structure. The authors report on a successful pilot study and present an efficient heuristic procedure that can be used to reduce computational solution times from hours to a few minutes.

A Graph-Search Based Navigation Algorithm for Traversing A Potentially Hazardous Area with Disambiguation

The authors consider the problem of navigating an agent to safely and swiftly traverse a two dimensional terrain populated with possible hazards. Each potential hazard is marked with a probabilistic estimate of whether it is indeed true. In proximity to any of these potential hazards, the agent is able to disambiguate, at a cost, whether it is indeed true or false. The method presented in this paper is to discretize the terrain using a two dimensional grid with 8-adjacency and approximately solve the problem by dynamically searching for shortest paths using the A* algorithm in the positively weighted grid graph with changing weight function.

Decision-Making Elements for the Design of Emerging Multi-Dimensional Auctions

Auctions have known considerable and continuous growth during the past decades due to their logic and efficiency in price formation when the value of goods traded is not known or varies. Although earlier research has been based mainly on Microeconomics and Games Theory, recent advances extended relevant research in Operational Research and Information Technology. Today, auctions and their applications form a challenging topic not only for economists but for operational researchers, marketers, logisticians and management engineers. This paper examines contemporary emerging auction formats, including auctions in which bids consist of many other parameters. The study of these emerging auction formats proceeds through the analysis of critical auction parameters that directly affect the decision-making process and the problems that auction participants face. This paper presents, with a presentation in graphical form, the decision framework for the majority of approaches presented in contemporary literature to highlight the association between decision elements and auction design.