In this paper, a new mathematical model for the problem of job scheduling in virtual manufacturing cells (VMC) is presented to minimizing the completion time of all jobs. Sequence dependent setup times of machines is considered and lot-streaming is possible. In Virtual manufacturing cells, each job has a different processing path and there is a set of machines for processing each operation. There are multiple machine types with several identical machines in each type locating in different locations in the shop floor. In this type of system, the cells are not physical and Machines can be shared between the cells. In Mixed-integer nonlinear programming model presented, the scheduling decisions involve assigning a machine to each operation, the start time at each operation, the start time of machines and sub-lot sizes of each job. Some test problems have been generated to demonstrate the implementation of the model and solved by Lingo.

This paper presents a novel, multi-objective model of a parallel machines scheduling problem that minimizes the number of tardy jobs and total completion time of all jobs. In this model, machines are considered as unrelated parallel units with different speeds. In addition, there is some precedence, relating the jobs with non-identical due dates and their ready times. Sequence-dependent setup times embedded in the proposed model may vary in different machines based on their characteristics. This paper proposes a two-level mixed-integer programming for the given problem. By solving the presented model, the associated promising results show the effectiveness of this model for small and medium-sized problems, respectively.

In the literature, the application of multi-objective dynamic scheduling problem and simple priority rules are widely studied. Although these rules are not efficient enough due to simplicity and lack of general insight, composite dispatching rules have a very suitable performance because they result from experiments. In this paper, a dynamic flexible flow line problem with Sequence-dependent setup times is studied. The objective of the problem is minimization of mean flow time and mean tardiness.A 0–1 mixed integer model of the problem is formulated.Since the problem is NP-hard, four new composite dispatching rules are proposed to solve it by applying genetic programming framework and choosing proper operators.Furthermore, a discrete-event simulation model is made to examine the performances of scheduling rules considering four new heuristic rules and the six adapted heuristic rules from the literature. It is clear from the experimental results that composite dispatching rules that are formed from genetic programming have a better performance in minimization of mean flow time and mean tardiness than others.

This paper addresses an unrelated multi-machine scheduling problem with Sequence-dependent setup time, release date and processing set restriction to minimize the sum of weighted earliness/tardiness penalties and the sum of completion times, which is known to be NP-hard. A Mixed Integer Programming (MIP) model is proposed to formulate the considered multi-criteria problem. Also, to solve the model for real-sized applications, a Pareto-based algorithm, namely controlled elitism nondominated sorting genetic algorithm (CENSGA), is proposed. To validate its performance, the algorithm is examined under six performance metric measures, and compared with a Pareto-based algorithm, namely NSGA-II. The results are statistically evaluated by the Mann– Whitney test and t-test methods. From the obtained results based on the t-test, the proposed CENSGA significantly outperforms the NSGA-II in four out of six terms. Additionally, the statistical results from Mann– Whitney test show that the performance of the proposed CENSGA is better than the NSGA-II in two out of six terms. Finally, the experimental results indicate the effectiveness of the proposed algorithm for different problems.

We consider an open shop scheduling problem with setup and processing times separately such that not only the setup times are dependent on the machines, but also they are dependent on the Sequence of jobs that should be processed on a machine. A novel bi-objective mathematical programming is designed in order to minimize the total tardiness and the makespan. Among several multi-objective decision making (MODM) methods, an interactive one, called the TH method is applied for solving small-sized instances optimally and obtaining Pareto-optimal solutions by the Lingo software. To achieve Pareto-optimal sets for medium to large-sized problems, an improved non-dominated sorting genetic algorithm II (NSGA-II) is presented that consists of a heuristic method for obtaining a good initial population. In addition, by using the design of experiments (DOE), the efficiency of the proposed improved NSGA-II is compared with the efficiency of a well-known multi-objective genetic algorithm, namely SPEAII.Finally, the performance of the improved NSGA-II is examined in a comparison with the performance of the traditional NSGA-II.