Task graph Scheduling is a multi-objective optimization and NP-hard problem. In this paper a new algorithm on homogeneous multiprocessors systems is proposed. Basically, Scheduling algorithms are targeted to balance the two parameters of time and energy consumption. These two parameters are up to a certain limit in contrast with each other and improvement of one causes reduction in the other one. The problem is to achieve the trade-off between these two parameters. Pre-Scheduling algorithms are mainly aimed at modifying the structure of task graph to gain optimal Scheduling.In the proposed algorithm the suitable number of processors for Scheduling the task graph is computed. The idea of Nash equilibrium is mainly applied to compute the appropriate number of processors in such a way that the idle time of the processors is reduced while their processing power is increased. Also, considering the communication costs and interdependencies, the tasks are merged as their earliest start time is reduced. In this way, the length of the critical path is reduced while the degree of parallelism is increased and ultimately the completion time is reduced. Our experimental result on a number of known benchmark graphs demonstrates the effect of our proposed algorithm.

We study the order acceptance, Scheduling, and pricing problem (OASP) in a parallel machine environment. Each order is characterized by due date, release date, deadline, controllable processing time, sequence-dependent setup time, and price in MTO system. An MILP formulation is used to maximize the net profit. Then, under a joint optimization approach, the pricing decisions are set for the unrelated parallel machine environment. The results show that the proposed model can solve the Scheduling decision problems based on different levels of products’ prices. Thus, the model solves these two categories of decisions, simultaneously. Moreover, the changes in accepted orders in pricing levels can be analyzed regarding their dependency on price elasticity of items for future research.

Flow shop Scheduling problem has a wide application in the manufacturing and has attracted much attention in academic fields. From other point, on time delivery of products and services is a major necessity of companies’ todays; early and tardy delivery times will result additional cost such as holding or penalty costs. In this paper, just-in-time (JIT) flow shop Scheduling problem with preemption and machine idle time assumptions is considered in which objective function is minimizing the sum of weighted earliness and tardiness. A new non-linear mathematical model is formulated for this problem and due to high complexity of the problem meta-heuristic approaches have been applied to solve the problem for finding optimal solution. The parameters of algorithms are set by Taguchi method. Each parameter is tested in three levels. By implementation of many problems with different sizes these levels are determined. Genetic algorithm, imperialist competitive algorithm and hybrid of these algorithms are applied to solve the problem and the performance of the proposed algorithms are evaluated by many test problems. The Computational results indicate the superiority of the performance of hybrid approach than GA and ICA in finding the best solution in reasonable computational time.

With the changes in the workplace and the added element of competition, it is apparent that the efficient Scheduling of resources such as machines, labor and material is extremely important. Scheduling covers a broad array of topics, such as machine Scheduling and sequencing, vehicle and fleet Scheduling, crew Scheduling, employee Scheduling, project Scheduling, lot-size Scheduling, interval (or reservation) Scheduling and timetabling. This article reviews the literature to identify the state-of-the-art research on Scheduling and routing problems.