The constrained two-dimensional cutting problem involves maximising the sum of the profits obtained from small rectangular pieces cut from a large rectangular plate where the number of each type of cut piece cannot exceed a prescribed quantity. This paper proposes a best-first branch-and-bound algorithm to find the optimal solution to the problem. The proposed algorithm uses an efficient method to remove the duplicate patterns, and it improves the existing upper bounds. It also prevents the construction of dominated patterns and introduces a new bounding strategy that can prune more than one node at a time. Computational results are compared with a well-known exact algorithm to demonstrate the efficiency of the proposed algorithm. The proposed algorithm is as fast as or faster than the existing algorithm and reduces the average computing time by up to 99% for benchmark problems. For some problems, it can also find optimal solutions that existing algorithms are not able to find.

This study deals with the preventive maintenance optimization problem based on a reliability threshold. The conditional reliability threshold is used instead of the system reliability threshold. Then, the difference between the two thresholds is discussed. The hybrid failure rate model is employed to represent the effect of imperfect preventive maintenance activities. Two maintenance strategies are proposed under two types of reliability constraints. These constraints are set to consider the cost-effective maintenance strategy and to evaluate the balancing point between the expected total maintenance cost rate and the system reliability. The objective of the proposed maintenance strategies is to determine the optimal conditional reliability threshold together with the optimal number of preventive maintenance activities that minimize the expected total maintenance cost per unit time. The optimality conditions of the proposed maintenance strategies are also investigated and shown via four propositions. A numerical example is provided to illustrate the proposed preventive maintenance strategies. Some sensitivity analyses are also conducted to investigate how the parameters of the proposed model affect the optimality of preventive maintenance strategies.

The work proposed a reliability demonstration test (RDT) process, which can be employed to determine whether a finite population is accepted or rejected. Bayesian and non-Bayesian approaches were compared in the proposed RDT process, as were lot and sequential sampling. One-shot devices, such as bullets, fire extinguishers, and grenades, were used as test targets, with their functioning state expressible as a binary model. A hypergeometric distribution was adopted as the likelihood function for a finite population consisting of binary items. It was demonstrated that a beta-binomial distribution was the conjugate prior of the hypergeometric likelihood function. According to the Bayesian approach, the posterior beta-binomial distribution is used to decide on the acceptance or rejection of the population in the RDT. The proposed method in this work could be used to select item providers in a supply chain, who guarantee a predetermined reliability target and confidence level. Numerical examples show that a Bayesian approach with sequential sampling has the advantage of only requiring a small sample size to determine the acceptance of a finite population.

In general, during decision making or negotiations, the investor and the investee may often have different opinions which result in conflicts. So, an objective standard to mitigate potential conflicts between investors and investees should be provided since it is highly important that rational decisions must be made when choosing investments from various options. However, the models currently used come with some problems for several reasons, for instance, the arbitrariness of the evaluator, the difficulty in understanding the relationships that exist among the various investment options (that is, alternatives to investments), inconsistency in priorities, and simply providing selection criteria without detailing the proportion of investment in each option or evaluating only a single investment option at a time without considering all options. Thus, in this research, we present a project selection model which can enable reasonable resource allocation or determination of return rates by considering the core competencies for various investment options. Here, core competency is based on both performance and ability to create a competitive advantage. For this, we deduce issue-specific structural power indicators and analyze quantitatively the resource allocation results based on negotiation power. Through this, it is possible to examine whether the proposed project selection model considers core competencies or not by comparing several project selection models currently used. Furthermore, the proposed model can be used on its own, or in combination with other methods. Consequently, the presented model can be used as a quantitative criterion for determining behavioral tactics, and also can be used to mitigate potential conflicts between the investor and the investee who are considering idiosyncratic investments, determined by an interplay between power and core competency.

With the advent of the fourth industrial revolution in recent years, engineering systems require prognostics and health management techniques that can accurately diagnose and prognose the state of the system. In this study, we developed a state-of-the-art fault diagnostics model using real-time vibration signals in the engineering systems. We established a degradation model that follows the Weibull hazard function and performed Bayesian estimation based on Markov chain Monte Carlo simulation to develop a fault diagnostics model. From the fault diagnostics model, we developed a data-driven fault prognostics model by monitoring the condition of the system continuously. In the experiment, this model is applied in the actual Intelligent Maintenance System bearing data provided by the University of Cincinnati. Compared with the previous methods, the results showed better performance.