Islamic Azad University, Rasht BranchIranian Journal of Optimization2588-572305220130701On Bottleneck Product Rate Variation Problem with Batching477491514134ENShree RamKhadkaCentral Department of Mathematics, Tribhuvan University, Kathmandu, NepalTanka NathDhamalaCentral Department of Mathematics, Tribhuvan University, Kathmandu, NepalJournal Article20150430The product rate variation problem minimizes the variation in the rate at which different models of a common base product are produced on the assembly lines with the assumption of negligible switch-over cost and unit processing time for each copy of each model. The assumption of significant setup and arbitrary processing times forces the problem to be a two phase problem. The first phase determines the size and the number of batches and the second one sequences the batches of models. In this paper, the bottleneck case i.e. the min-max case of the problem with a generalized objective function is formulated. A Pareto optimal solution is proposed and a relation between optimal sequences for the problem with different objective functions is investigated. http://ijo.iaurasht.ac.ir/article_514134_66aee2e924eb1b0beb59235054f07992.pdfIslamic Azad University, Rasht BranchIranian Journal of Optimization2588-572305220130701Mapping Sequence diagram in Fuzzy UML to Fuzzy Petri Net492505514136ENE. AkbariDepartment of Mathematics, Islamic Azad University, Sari Branch, Sari, IranR. Noorian TalookiDepartment of Computer Engineering, Islamic Azad University, Sari Branch, Sari, IranH. MotameniDepartment of Computer Engineering, Islamic Azad University, Sari Branch, Sari, IranJournal Article20100430<span>This ability in fuzzy UML, practically leaves the customers and market’s need without response in this important and vital area. Here, the available sequence diagrams in fuzzy UML will map into fuzzy Petri net. However, the formal models ability will be added to the Semi-formal fuzzy UML. This formalization will add the automatic processing ability to the Semi-formal fuzzy UML. </span> <br /><span>Further more, the other advantages of this mapping is: access to non-functional parameters such as reliability automatically to the considering systems, study the verification of the designed plan and also decrease the expenses because of satiety to make lab sample before its implementation. Using the fuzzy UML mapping into fuzzy Petri net in control, critical and real-time systems will be more applicable. </span>http://ijo.iaurasht.ac.ir/article_514136_8e2d23e5ff6ba2e807b4dbea0b3bd9b1.pdfIslamic Azad University, Rasht BranchIranian Journal of Optimization2588-572305220130701On the averaging of differential inclusions with Fuzzy right hand side with the average of the right hand side is absent506517514137ENAndrej V.PlotnikovOdessa State Academy of Civil Engineering and Architecture, Odessa, UkraineTatyana A.KomlevaOdessa State Academy of Civil Engineering and Architecture, Odessa, UkraineLilia I.PlotnikovaOdessa National Polytechnic University, Odessa, UkraineJournal Article20150830<span>In this article we consider the averaging method for differential inclusions with fuzzy right-hand side for the case when the limit of a method of an average does not exist. </span>http://ijo.iaurasht.ac.ir/article_514137_d97144096845e36718c73422f2f61fec.pdfIslamic Azad University, Rasht BranchIranian Journal of Optimization2588-572305220130701Analytic-Approximate Solution For An Integro- Differential Equation Arising In Oscillating Magnetic Fields Using Homotopy Analysis Method518535514138ENH. Saberi-NikDepartment of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.S. EffatiDepartment of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.R. BuzhabadiDepartment of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.Journal Article20100430<span>In this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The homotopy analysis method (HAM) is used for solving this equation. Several examples are given to reconfirm the efficiency of these algorithms. The results of applying this procedure to the integro-differential equation with time-periodic coefficients show the high accuracy, simplicity and efficiency of this method. </span>http://ijo.iaurasht.ac.ir/article_514138_83b91e496581c65b2416ec737b16ac35.pdf