This paper focuses on the appropriate selection of suppliers and assigning order quantities to them. This problem contains multiple objectives and their related constraints and utilizes fuzzy decision making in its solution approach. In the proposed model, goals, constraints, variables and coefficients are all fuzzy. It is shown that with the application of the fuzzy methodology, the multiy objective problem is converted to a single one that can be solved easily.

In this paper, a review of multiple objective Flowshop Scheduling Problems is introduced. Different version of the problem are classified according to different multi objective optimization approaches, flowshop assumptions, solving methods, and also objective functions terms. This paper can be considered as a complete and valuable reference for researchers in the field of scheduling, especially multiple objective ones.

Inventory classification is one of important techniques in inventory control context. Managers have to classify inventories because of their variety and high volume. So a stream of research has been to attempt to find methods that increase the management control by determining the number of inventory classes. In this paper the multiple objective particle swarm optimization algorithm has been used. This algorithm has been presented by Chi-Yang Tsai and Szu-Wei Yeh in 2008. multiple objective particle swarm optimization algorithm is an evolutionary algorithm that enables the management to optimize multiple objectives simultaneously. Minimizing costs of inventory holding and ordering and maximizing inventory turnover ratios are this model’s objectives. We write the software program of this model and then test it on a sample of 100 items. Results show that this algorithm can decrease costs of holding & ordering and also increase the inventory turnover ratios significantly.

In this paper, we establish a proof for a necessary condition for multiple objective fractional pro-gramming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we present the related semi parametric model.

multiple objective Programming (MOP) problems have become famous among many researchers due to more practical and realistic implementations. There have been a lot of methods proposed especially during the past four decades. In this paper, we develop a new algorithm based on a new approach to solve MOP problems by starting from a utopian point (which is usually infeasible) and moving towards the feasible region via stepwise movements and a plain continuous interaction with Decision Maker (DM). We consider the case where all objective functions and constraints are linear. The implementation of the proposed algorithm is demonstrated with two numerical examples.

A utility function is an important tool for representing a DM’s preference. We adjoin utility functions tomulti objective optimization problems. In current studies, usually one utility function is used for each objective function. Situations may arise for a goal to have multiple utility functions. Here, we consider a constrained multi-objective problem with each objective having multiple utility functions. We induce the probability of the utilities for each objective function using Bayesian theory. Illustrative examples considering dependence and independence of variables are worked through to demonstrate the usefulness of the proposed model.

A B S T R A C T Green city is one of the approaches to sustainable development. “green city” is an environmentally friendly city compatible with the concept of sustainable development and can be used for the welfare and security of its inhabitants. Based on the concept of a “green city,” urban managers try to have the least destructive effect on the ecosystems upon which cities rely. Green city is one of the sustainable development approaches that reduce the environmental footprint of cities. The purpose of this study is to evaluate the situation of Mashhad metropolis in terms of the objective characteristics of the green city. In this study, 14 indicators of electricity consumption per capita, green space per capita, population density, water availability, sewage availability, superior public transportation network, urban mass transportation, traffic reduction, annual production waste per capita, carbon monoxide, concentration nitrogen dioxide, sulfur dioxide concentration, particulate matter concentration, and air quality were exerted. To determine the importance of research indicators, the Shannon entropy method, and the status of Mashhad city areas in terms of green city indicators, the VIKOR multi-criteria decision-making method has been applied. The results showed that most areas of Mashhad are average and below average in terms of green city characteristics, and only District 9 is in very good condition (0.636). Also, based on the results of this part of the research, District 5, with the value of VIKOR index of 0.969, is in the last rank in terms of objective characteristics of the green city Extended Abstract Introduction Green city is one of the approaches to sustainable development. A “Green city” is an environmentally friendly city compatible with the concept of sustainable development and can be used for the welfare and security of its inhabitants. Based on the concept of a “green city,” urban managers try to have the least destructive effect on the ecosystems upon which cities rely. Green cities constantly try to manage their environmental effects by reducing waste, increasing recycling, reducing air pollution, increasing population density, developing open urban spaces, and encouraging the development of sustainable local businesses. Green cities were first used to evaluate 30 European cities by the Economist Intelligence Unit (EIU) in 2009 with the financial support of Siemens and the aim of reducing the environmental effects of human activities in cities. In that study, eight indices of carbon dioxide, energy, construction, transportation, water, recycling and land use, air quality, and environmental governance were used. Later, the Economist Intelligence Unit, with the financial support of Siemens, evaluated the status of the green city index in 17 Latin American cities, 15 African cities, 22 major Asian cities, and 27 cities in United States, Canada, Australia, and New Zealand. In recent years, even some Western Islamic scholars have, in various publications, shown that Islam is an ecological religion. In Iran, the issue of protecting the environment has not received much attention regardless of its rich cultural and religious background and its confirmation in Article 50 of the Constitution of the Islamic Republic of Iran. Mashhad is the second metropolis of Iran, located in North-East of Iran, and is one of the counties of Khorasan Razavi Province. According to the 2016 Iranian Population and Housing Census, its population was 3057679 people (The Vice-Presidency of Planning and Development of Mashhad Municipality). In Mashhad, due to several reasons including the presence of Imam Reza Shrine (PBUH) and arrival of millions of pilgrims per year, population growth, increased garbage production (production of 896534 tons of garbage in 2016 (The Vice-Presidency of Planning and Development of Mashhad Municipality), air pollution (increased number of unhealthy days from 46 days per year in 2015 to 88 days in 2016 for sensitive groups and 4 days of unhealthy air for all groups in 2016 (Center for Monitoring Environmental Pollutants of Mashhad Municipality) the 2025 vision of the city has paid attention to the environment in the form of five general objectives; however, just like the national level, no specific pattern for environmentally-compatible urban development, such as green city, is determined. Analysis of the green city index in Mashhad metropolis can considerably contribute to urban managers and planners in addition to providing a pattern for evaluating the present situation in other cities of Iran and improving the quality of life regardless of the current status of the urban environment in Iranian cities; we can preserve these environments as parts of the natural environment for future generations.   Methodology In terms of its goal, the present study is an applied one; in the study, drawing upon other studies and library sources and considering the conditions of Iran and the metropolis of Mashhad in terms of green city, 14 quantitative indices were exerted. To this end, the required data for the quantitative indices was gathered by library research from the relevant institutions. Next, the weights of quantitative indices were determined using Shannon's entropy. Then, using the VIKOR method of multi-criteria decision-making, the status of various districts of the metropolis of Mashhad in terms of quantitative indices of green city was determined. Finally, the map of the spatial distribution of quantitative indices was drawn using the ARC GIS software package.   Results and discussion In this study, to analyze the status of the metropolis of Mashhad in terms of green city features, 14 quantitative indices were used. Considering the value of the VIKOR index ranges from 0 to 1, various districts of Mashhad can be classified into five categories; very satisfactory, satisfactory, average, unsatisfactory, and very unsatisfactory in terms of quantitative indices of green city. The results of the current situation of Mashhad showed that in terms of objective indicators of the green city, District 9 of Mashhad metropolis with a value of VIKOR index of 0.056 is in first place, and the seventh region with a value of VIKOR index of 0.433 is in second place. Also, based on the results of this part of the research, District 5, with the value of VIKOR index of 0.969, is in the last rank in terms of objective characteristics of the green city.   Conclusion Similarly, the results of studies by Afshar (2011) and Shabani et al. (2017) on Tehran metropolis are indicative of the unsatisfactory situation of Tehran (the biggest metropolis of Iran) in terms of green city features. Comparing the results of the studies by Afshar (2011) and Shabani et al. (2017) with the present study on Mashhad (the second biggest metropolis of Iran) reveals the necessity for a comprehensive plan toward achieving green cities. It should be mentioned that, due to the specific conditions of Mashhad metropolis and availability or unavailability of the required data, the indices used in the present study are somewhat different from the ones used by Afshar (2011) and Shabani et al. (2017).   Funding There is no funding support.   Authors’ Contribution All of the authors approved the content of the manuscript and agreed on all aspects of the work.     Conflict of Interest Authors declared no conflict of interest.   Acknowledgments We are grateful to all the scientific

Background and objectives: Applications and systems software that are running constantly become obsolete due to the accumulation of error conditions or the depletion of resources like physical memory or performance degradation. In this regard, software rejuvenation has been proposed to deal with such a phenomenon and prevent software failure in the future. This paper proposes a multiple objective of software rejuvenation models with several policies. The purpose is to identify the right rejuvenation policy in practical situations. Methods: We model software system with four policies using the Markov process. These policies are: (a) Software system without rejuvenation; (b) Software system with partial rejuvenation; (c) Software system with partial and full rejuvenation; and (d) Software system with four different types of rejuvenation. In the models and each policy, we consider assigning the level of performance on which the availability and operating costs are calculated. Results: To evaluate the models with the four policies, many numerical experiments were performed. For each policy, we evaluated and compared three objectives, namely performance, availability and operating costs. The experimental results states that for Software System with the policy of four different type of rejuvenation have about 18 and 16 percent improvement in performance and availability, respectively, compared with those other policies. Moreover, the operating cost of the software system with partial rejuvenation policy is lower and more efficient than other policies. Conclusion: According to the calculated objectives and the results of the policies, it can be concluded that in systems with lower operational costs, the most appropriate policy is the software system with four different types of rejuvenation because this policy bring the maximum possible value for the performance and availability. The result of this study showed that the combined method is not always a suitable method because its operating cost is higher than other methods and in systems that are more important in terms of cost, this policy is not appropriate.