Assembly Line production is one of the widely used basic principles in production system. The problem of Assembly Line Balancing deals with the distribution of activities among the workstations so that there will be maximum utilization of human resources and facilities without disturbing the work sequence. Research works reported in the literature mainly deals with minimization of idle time i.e. Balancing, subject to precedence constraints. Lack of uniqueness in their optimum solutions has led to the present work where minimization of both Balancing loss and system loss has been envisaged under the usual precedence constraints. The researchers suggest a generic approach for designing of an assembly line where, with a given number of workstations, one can efficiently arrive at the desired solution under different methods of search like simulation, heuristic etc. Thus, the main aim of this paper is to redefine the objective of the Assembly Line Balancing Problem and sequentially handle Balancing Loss and System Loss. A numerical example has been added to demonstrate the generic nature of the researcher's approach and improvement in the solution set when compared with different standard line Balancing methods available so far in the literature.

The main goal of this paper is to develop a new generalization of Balancing and Lucas-Balancing sequences namely Balancing and Lucas-Balancing p-numbers and derive several identities related to them. Some combinatorial forms of these numbers are also presented.

Balancing has been an important element of Saudi Arabia's foreign policy towards Iran following the Islamic Revolution in this country. This approach of the Kingdom of Saudi Arabia has been mainly influenced by the threat that its leaders perceive the Islamic Republic of Iran poses to them, a perception that has been reproduced almost continuously for four decades for various reasons. The type of Balancing strategy, though, has been subject to change over time between internal and external Balancing in different periods. This descriptive-analytical study was conducted to answer the question: "Why has the type of Saudi Arabia's Balancing strategy against the Islamic Republic of Iran changed over the past four decades?" Drawing on the dynamic Balancing theory, and given the persistent threat that the leaders of Saudi Arabia perceive the Islamic Republic of Iran poses to them, the findings of this research  suggest that the change in Saudi Arabia's Balancing strategy against the Islamic Republic of Iran is  caused  by the change in the  polarity in  the international system. Moreover, the tendency toward internal Balancing has grown as multipolarity has arrived in this system.

The main of multi-depot vehicle scheduling problem (MDVSP) is to schedule the timetabled trips using limited resources, optimally. The problem is very important in the management of the transportation systems. One of the most useful ways to better manage these systems is to consider the real conditions including depot Balancing constraints. To normalize the number of vehicles departed from each depot and the number of drivers assigned to each depot, new constraints are proposed in this paper. This normalization prevents excessive accumulation of vehicles in one or more depots and it balances labor between depots. We suggest a new mathematical formulation for MDVSP in which the Balancing constraints are considered as soft constraints. To solve the problem with the new constraints an auction-based heuristic algorithm with decompositions ideas is proposed. The CPLEX software is used to evaluate the proposed model and the presented method in order to compare the results. The computational results show that the proposed algorithm solves the problem in appropriate time.

With the growth in customers demand diversification, mixed-model U-lines (MMUL) have acquired increasing importance in the area of assembly systems. There are generally two different approaches in the literature for Balancing such systems. Some researchers believe that since the types of models can be very diverse, a Balancing approach without simultaneously sequencing of models will not yield an optimum con guration. On the other hand, another group of researchers point to the high cost of Balancing systems and prefer to do it only one time regardless of the models sequences. In this paper, we aim to compare these two approaches by introducing an economic indicator. To do so, two models as representatives of the two different viewpoints are taken from the literature. To check the validity of this methodology, it is implemented by Lingo 11.0, for small scale, and GA, for a large scale. The obtained results indicate that, from the proposed economic indicator point of view, mixed-model U-lines Balancing and sequencing (MMUL/BS) is preferred to its counterpart, mixed-model U-lines Balancing (MMULB).This paper offers economic guidelines for managers to choose between only Balancing and implementing it by sequencing at the same time.

Sex selection for non-medical reasons is a major controversy in around the world. Here in this paper, we presented the ethical arguments about sex selection for non-medical reasons and discuss about them in Islamic context. Significant arguments about sex selection relate to sexism and sex discrimination, sex disproportion, human dignity, playing God, psychological pressure on unselected children and other ethical issues. Main responses includes: parental autonomy, compare with their authority in using contraceptive methods or cosmetic surgery; utilitarianism and consequentialism that practically prefers sex selection that abortion; sex ratio can be protected by some legislations. Islam underscores the will of God in any human action so no one can play God and unlike Christians, the vision of Islam to the pre-implantation embryo is not a human. Our conclusion from religious, legal and ethical survey is: sex selection in family Balancing type is acceptable in Islamic context with the following conditions: only for married couples, only one successful time, not for the first child not for same sex. Detail counseling should be performed with the couple about the risks and success rate. If both genders exist in family, sex selection should not be performed. If the selected child dies with any reasons, another attempt is acceptable. Sex selection clinics should act under supervision of health care authorities.