In real world scheduling applications, machines might not be available during certain time periods due to deterministic or stochastic causes. In this article, the machine scheduling with AVAILABILITY CONSTRAINTs for both deterministic and stochastic cases with different environments, CONSTRAINTs and performance measures will be discussed. The existing body of research work in the literature will be completely reviewed and the NP-complete models will be identified.

Scheduling problems have been considered by researchers from different aspects, and it has been widely addressed in the literature. Most scheduling problems, and almost all that arise in real-world applications, are NP-hard, therefore finding a proper and feasible solution, a solution that is performed in a reasonable time (polynomial time), is difficult. Approximation scheme, among different methods, is one approach that can overcome difficulties. Polynomial-time approximation and differential approximation schemes are categorized as approximation approaches based on comparing the proposed algorithm with optimum and worst-case solutions. As the first attempt, the paper investigates differential approximation schemes for the minimization of maximum delivery time. In this paper, the main methods and tools for proofing the existence of an approximation scheme are presented. To do so, a differential approximation scheme is proposed by employing a polynomial-time approximation scheme (PTAS). The paper also reviews efficient approximation schemes on single machine problems with objective functions minimization of maximum delivery time, and minimizing the total weighted completion time.

Scheduling problems have been considered by researchers from different aspects, and it has been widely addressed in the literature. Most scheduling problems, and almost all that arise in real-world applications, are NP-hard, therefore finding a proper and feasible solution, a solution that is performed in a reasonable time (polynomial time), is difficult. Approximation scheme, among different methods, is one approach that can overcome difficulties. Polynomial-time approximation and differential approximation schemes are categorized as approximation approaches based on comparing the proposed algorithm with optimum and worst-case solutions. As the first attempt, the paper investigates differential approximation schemes for the minimization of maximum delivery time. In this paper, the main methods and tools for proving the existence of an approximation scheme are presented. To do so, a differential approximation scheme is proposed by employing a polynomial-time approximation scheme (PTAS). The paper also reviews efficient approximation schemes on single machine problems with objective functions minimization of maximum delivery time, and minimizing the total weighted completion time. Also, in this paper, using the polynomial time approximation scheme (PTAS), a differential approximation scheme has been studied for the problem of minimizing the maximum delivery time of works, which has not been investigated so far.

In this paper an uncertain multi objective closed-loop supply chain is developed. The first objective function is maximizing the total profit. The second objective function is minimizing the use of row materials. In the other word, the second objective function is maximizing the amount of remanufacturing and recycling. Genetic algorithm is used for optimization; and for finding the pareto optimal line, Epsilon-CONSTRAINT method is used. Finally a numerical example is solved with proposed approach and performance of the model is evaluated in different sizes. The results show that this approach is effective and useful for managerial decisions.

Constrain is the condition of driven by necessity. The principle of CONSTRAINT determines the duties of the person constrained. In jurisprudence, it includes a range of activities from cleanness to blood compensation. However, jurisprudents have discussed it mainly with regard to those that can be eaten and drunk, and presented three different interpretations: fear of losing one"s life; fear in general, including fear of losing one"s life, or one"s limb, etc.; and fear of things not related to oneself but to others. The roots of CONSTRAINT are compulsion, precautionary concealment, loss and necessity. The present article deals with a kind of CONSTRAINT whose source is necessiy. The Qur"an has explicitly excused the person constrained from duties provided that the oppressor shows no inclination to sin. Tradition says that "there is so unlawful act that God Almighty has not made it permissible under CONSTRAINT." The intellect also knows it permissible to give up necessary duties and to do the unlawful acts under CONSTRAINT. Finally, the writer presents the conditions under which the application of the principle of constrain is made permissible.

The problem of scheduling with multi agent has been studied for more than one decade and significant advances have been made over the years. However, most work has paid more attention to the condition that machines are available during planning horizon. Motivated by the observations, this paper studies a two-agent scheduling model with multiple AVAILABILITY CONSTRAINT. Each agent aims at minimizing a function which depends only on the completion times of its jobs. The problem is to find a schedule that minimizes the objective function of one agent, subject to the objective function of the other agent does not exceed a given threshold Q. some new dominance properties for this problem percent and next, using these properties, we develop a genetic algorithm with modified crossover for the problem. Computational results are also presented to determine the performance of the proposed genetic algorithms.