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The purpose of this paper is to propose a procedure to construct the membership functions for a one-unit repairable system, which has both active and standby redundancy. The coverage factor is the same for the operating and standby unit failure.

The α-cut approach is used to extract a family of conventional crisp intervals from the fuzzy repairable system for the desired system characteristics. This can be determined with a set of non-linear parametric programing using the membership functions.

When system characteristics are governed by the membership functions, more information is provided to use by management. On the other hand, fuzzy theory is applied for the redundant system; therefore, the results are more useful for designers and practitioners.

Different from other studies, the authors’ model provides more accurate estimation compared to uncertain environments based on fuzzy theory. The research would help managers and manufactures to make a better decision in order to have the optimal maintenance strategy based on the desired mean time to failure and availability of the systems.

The purpose of this study is to develop Markovian model to obtain the transient probabilities to determine mean-time-to-failure and reliability function and further steady state availability of the repairable system. As the system parameters are uncontrollable factors; thus the life times, repair times and recovery/reboot time are assumed to be as uncertain or fuzzified distributions.

The fuzzy approach is introduced to investigate the reliability measures of load sharing repairable system which consists of two operating units and one standby unit. On the failure of an operating component, it is instantly spotted, located and sent for recovery procedures with coverage probability. In case of imperfect recovery, reboot takes place.

On the basis of extension principle and mathematical programming approach, the authors establish membership functions for system characteristics with the help of α-cuts. To demonstrate the practical validity of the proposed fuzzified model, numerical illustrations are performed.

The model proposed for reliability analysis may cheer up the continuance of the work towards more applications in repairable systems. Therefore, the reader is provided with useful intuition into the nature of fuzzy computations and practical amendments while measuring ambiguous data.

The purpose of this paper is to study the impact of learning effect and demand uncertainty on aggregate production planning (APP), provide practitioners with some important managerial implications for improving production planning and productivity.

Motivated by the background of one labour-intensive manufacturing firm – a mosquito expellant factory – an APP model considering workforce learning effect and demand uncertainty is established. Numerical example and comparison with other two models without considering learning and uncertainty of demand are conducted.

The result shows that taking into account the uncertain demand and learning effect can reduce total production cost and increase flexibility of APP.

Managerial implications are provided for practitioners with four propositions on improving workforce learning effect, i.e. emphasizing employee training, combing individual and organizational learning and reduction of forgetting effect.

This paper has practice value in improving APP in labor-intensive manufacturing.

To solve the multi‐period portfolio management problem under transactions costs.

We apply a recently designed super genetic hybrid algorithm (SuperGHA) – an integrated optimisation system for simultaneous parametric search and non‐linear optimisation – to a recursive portfolio management decision support system (SHAREX). The parametric search machine is implemented as a genetic superstructure, producing tentative parameter vectors that control the ultimate optimisation process.

SHAREX seems to outperform the buy and hold‐strategy on the Finnish stock market. The potential of a technical portfolio system is best exploitable under favorable market conditions.

A number of robust engines for matrix algebra, mathematical programming and numerical calculus have been integrated with SuperGHA. The engines expand its scope as a general‐purpose algorithm for mathematical programming.

To discuss a new parallel algorithmic platform (minlp_machine) for complex mixed‐integer non‐linear programming (MINLP) problems.

The platform combines features from classical non‐linear optimization methodology with novel innovations in computational techniques. The system constructs discrete search zones around noninteger discrete‐valued variables at local solutions, which simplifies the local optimization problems and reduces the search process significantly. In complicated problems fast feasibility restoration may be achieved through concentrated Hessians. The system is programmed in strict ANSI C and can be run either stand alone or as a support library for other programs. File I/O is designed to recognize possible usage in both single and parallel processor environments. The system has been tested on Alpha, Sun and Linux mainframes and parallel IBM and Cray XT4 supercomputer environments. The constrained problem can, for example, be solved through a sequence of first order Taylor approximations of the non‐linear constraints and feasibility restoration utilizing Hessian information of the Lagrangian of the MINLP problem, or by invoking a nonlinear solver like SQP directly in the branch and bound tree. minlp_machine( ) has been tested as a support library to genetic hybrid algorithm (GHA). The GHA(minlp_machine) platform can be used to accelerate the performance of any linear or non‐linear node solver. The paper introduces a novel multicomputer partitioning of the discrete search space of genuine MINLP‐problems.

The system is successfully tested on a small sample of representative MINLP problems. The paper demonstrates that – through concurrent nonlinear branch and bound search – minlp_machine( ) outperforms some recent competing approaches with respect to the number of nodes in the branch and bound tree. Through parallel processing, the computational complexity of the local optimization problems is reduced considerably, an important aspect for practical applications.

This paper shows that binary‐valued MINLP‐problems will reduce to a vector of ordinary non‐linear programming on a suitably sized mesh. Correspondingly, INLP‐ and ILP‐problems will require no quasi‐Newton steps or simplex iterations on a compatible mesh.

Introduction Operations research, i.e. the application of scientific methodology to operational problems in the search for improved understanding and control, can be said to have started with the application of mathematical tools to military problems of supply bombing and strategy, during the Second World War. Post‐war these tools were applied to business problems, particularly production scheduling, inventory control and physical distribution because of the acute shortages of goods and the numerical aspects of these problems.

Revealed preference axioms provide a simple way of testing data from consumers or firms for consistency with optimizing behavior. The resulting non-parametric tests are very attractive, since they do not require any ad hoc functional form assumptions. A weakness of such tests, however, is that they are non-stochastic. In this paper, we provide a detailed analysis of two non-parametric approaches that can be used to derive statistical tests for utility maximization, which account for random measurement errors in the observed data. These same approaches can also be used to derive tests for separability of the utility function.

To propose a new algorithmic platform (minlp_machine) for complex mixed‐integer non‐linear programming (MINLP) problems.

The platform combines features from classical non‐linear optimization methodology with novel innovations in computational techniques. The system constructs discrete search zones around non‐integer discrete‐valued variables of local solutions, which reduces the search process significantly. In complicated problems fast feasibility restoration is achieved through concentrated Hessians. The system is programmed in strict ANSI C and can be run either stand alone or as a support library for other programs. File I/O is designed to recognize possible usage in both single and parallel processor environments.

The system has been tested on Alpha and Sun mainframes and – as a support library for a Genetic Hybrid Algorithm (GHA()) – in Linux and IBM parallel supercomputer environments. The constrained problem can, for example, be solved through a sequence of first order Taylor approximations of the non‐linear constraints and occasional feasibility restoration through Hessian information of the Lagrangian of the MINLP problem, or by invoking a nonlinear solver like SQP directly in the branch and bound tree. The system has been successfully tested on a small sample of representative continuous‐valued non‐linear programming problems.

It is demonstrated that – through zone‐constrained search – minlp_machine() outperforms some recent competing approaches with respect to the number of nodes in the branch and bound tree.

The purpose of this paper is to measure the financial risk and optimal capital structure of a corporation.

Irregular disjunctive programming problems arising in firm models and risk management can be solved by the techniques presented in the paper.

Parallel processing and mathematical modeling provide a fruitful basis for solving ultra-scale non-convex general disjunctive programming (GDP) problems, where the computational challenge in direct mixed-integer non-linear programming (MINLP) formulations or single processor algorithms would be insurmountable.

The test is limited to a single firm in an experimental setting. Repeating the test on large sample of firms in future research will indicate the general validity of Monte-Carlo-based VAR estimation.

The authors show that the risk surface of the firm can be approximated by integrated use of accounting logic, corporate finance, mathematical programming, stochastic simulation and parallel processing.

Parallel processing has potential to simplify large-scale MINLP and GDP problems with non-convex, multi-modal and discontinuous parameter generating functions and to solve them faster and more reliably than conventional approaches on single processors.

A large number of research articles have appeared in the literature during the last two decades on the subject of system reliability optimisation, each with a view to providing simple, exact and efficient techniques. Here, an efficient, fast and exact technique is proposed for solving integer‐programming problems that normally arise in optimal reliability design problems. The algorithm presented is superior to any of the earlier methods available so far, being based on functional evaluations and a limited systematic search close to the boundary of resources. Thus it can quickly solve even very large system problems. It can also be effectively used with other operations research problems involving integer‐programming formulations.