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Abstract. In this study, a multi-state degraded system is studied, where status of system is continuously degrading over time. As time progresses, system may either deteriorate gradually and go to lower performance state, or it may fail suddenly. If the system fails, some repairs are carried out to restore the system to the previous state. When the inspections reveal that the system has reached its last acceptable state, a PM is carried out to restore the system to the higher performance states. The goal is to nd the optimal PM level, so that the mean availability of the system is maximized and the total cost of the system is minimized. In this regard, Markov process is employed to represent di erent states of system. An integrated optimization approach is also suggested based on the desirability function of statistical approach. The suggested aggregation method is robust to the potential dependency between the total cost and the mean availability. It also ensures that both objective functions fall in decision-maker's acceptable region. In order to show the e ciency of the proposed approach, a numerical example is presented and analyzed.

In today's competitive world, it is very important for organizations to select suppliers according to price, quality, satisfactory service and timely delivery. Since a considerable portion of production costs is associated with purchasing raw materials from suppliers, selection of the right suppliers and allocation of optimal order quantities plays an important role in the success of an organization. So far, extensive research has been conducted in the context of supplier selection, and multi-criteria decision-making techniques are the common approach used to select the appropriate option. Recently, some studies in the context of supplier selection considered variable assumptions like quantity discount possibility. So, the aim of this study is modeling the supplier selection problem based on incremental and wholesale discounts and comparing the results of them like best selected supplier(s) and optimal order allocation to them. And solve a big problem with GA and NSGA algorithms and comparing with each other's for this an integrated three-stage approach has been proposed by combining fuzzy AHP and Extended Analysis Method for the supplier selection problem and develop a GA&NSGA algorithms. Finally, the performance of the proposed approach and proposed algorithms has been appraised by numerical examples.

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PurposeThe common methods for clustering time series are the use of specific distance criteria or the use of standard clustering algorithms. Ensemble clustering is one of the common techniques used in data mining to increase the accuracy of clustering. In this study, based on segmentation, selecting the best segments, and using ensemble clustering for selected segments, a multistep approach has been developed for the whole clustering of time series data.Design/methodology/approachFirst, this approach divides the time series dataset into equal segments. In the next step, using one or more internal clustering criteria, the best segments are selected, and then the selected segments are combined for final clustering. By using a loop and how to select the best segments for the final clustering (using one criterion or several criteria simultaneously), two algorithms have been developed in different settings. A logarithmic relationship limits the number of segments created in the loop.FindingAccording to Rand's external criteria and statistical tests, at first, the best setting of the two developed algorithms has been selected. Then this setting has been compared to different algorithms in the literature on clustering accuracy and execution time. The obtained results indicate more accuracy and less execution time for the proposed approach.Originality/valueThis paper proposed a fast and accurate approach for time series clustering in three main steps. This is the first work that uses a combination of segmentation and ensemble clustering. More accuracy and less execution time are the remarkable achievements of this study.