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 considers the problem of scheduling parallel machines for split jobs to minimize the total tardiness. Accepting a new job, each machine needs to be set up and the setup times depend on the sequence of jobs. To solve the above problem, a new approach is suggested and a number of theorems are provided and proved regarding resource planning and job sequencing for the given problem in hand. Then, the proposed algorithm is verified and evaluated with a number of test problems. The associated results are analyzed and compared with the results obtained by the Lingo software.

In recent decade, many researches has been done on job shop scheduling problem with sequence dependent setup times (SDSJSP), but with respect to the knowledge of authors in very few of them the assumption of existing inseparable setup has been considered. Also, in attracted metaheuristic algorithms to this problem the Particle Swarm Optimization has not been considered. In this paper, the ISDSJSP with makespan minimization is considered. For this problem an MILP model has been developed and a PSO algorithm has been applied to solve it. In order to improve final solution obtained by PSO a simulated annealing algorithm has been applied. The proposed hybrid algorithm (HPSO) has been applied on some generated benchmark problems and the results indicate the effectiveness and efficiency of the proposed hybrid PSO with respect to two other algorithms.

This study presents two mixed integer programming models for scheduling hybrid flow shops with sequence dependent setup times. In the first model, we assumed the machines at each stage are identical, but in the second model the machines at each stage are different. These models may be used to determine optimal solutions for hybrid flow shop problems of moderate size, and these problems could then be used as benchmarks for testing new sequencing heuristics.

In this paper, three-stage assembly flowshop scheduling is considered with respect to minimizing bi-objectives, namely mean flow time and mean tardiness. This problem is a model of production systems, which several production operations are done simultaneously and independently, and then produced components are collected and transferred to an assembly stage for the final operation. In this model, by considering sequence-dependent setup time and components transformation times in order to make a real situation for the considered model, a lower bound (LB) is introduced to completion times of all the jobs. Further, due dates are generated randomly in a determined interval for some examples. To validate the proposed model, the Lingo 8.0 software and an enumeration technique that is coded in MATLAB are used. Comparison between the results of the Lingo 8.0 and enumeration technique shows that in larger problems (say n>8, where n is the number of jobs) the results obtained by Lingo do not have the good efficiency and cannot be compared with the enumeration technique in terms of computational time and deviation from the minimum objective function. For example, in some large problems, the objective function values obtained by the Lingo 8.0 software have 20% deviation from their minimum. Therefore, to solve such a hard problem, a meta-heuristic method is required as future research.

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 presents a new mathematical programming model for an integrated production and air transportation in supply chain management with sequence-dependent setup times in order to design an applied procedure for the production and distribution schedule. The aim of this model is to minimize the total supply chain cost consisting of the costs of distribution, production earliness and tardiness, and delivery. Because of the complexity and NP-hardness of this problem, two meta-heuristics based on genetic algorithm (GA) and variable neighborhood search (VNS) are proposed. The parameters of these algorithms and their appropriate operators are set and determined by the use of the Taguchi experimental design. Then, the quality of the results obtained by these algorithms is compared. The computational results show that the developed VNS outperforms the proposed GA.

In this paper, a flexible job shop scheduling problem (FJSP) with assembly operations and sequence dependent setup time is studied. In this problem, each product is produced from assembling a set of several different parts. At first, the parts are processed in a flexible job shop system. setup time is needed when a machine starts processing the parts or it changes items. Then in the second stage, the parts are assembled and products are produced. The assembly operation cannot be started for a product until the set of parts are completed in machining operations. In this paper, we presented a mathematical model for a flexible job shop scheduling problem with assembly operations and sequence dependent setup time. The objective is to minimize the completion time of all products (makespan). Since the problem is NP-hard, one particle swarm optimization (PSO) algorithm and two hybrid metaheuristic algorithms based on particle swarm optimization are proposed. The proposed hybrid algorithms are called, respectively, hybrid particle swarm optimization with a variable neighborhood search algorithm (HPSOVNS) and hybrid particle swarm optimization with a simulated annealing algorithm (HPSOSA). In these hybrid algorithms, we used particle swarm optimization (PSO) algorithm for global exploration at search space and variable neighborhood search (VNS)/ simulated annealing (SA) algorithm for local search at around solutions obtained in the each iteration. In order to evaluate and validate the performance of the proposed algorithms, we are designed numerical experiments and results are compared with hybrid genetic algorithm and tabu search (HGATS) presented by Li and Gao. For this purpose, the proposed mathematical model is coded in GAMS software and the proposed metaheuristic algorithms are coded in MATLAB software. For obtaining better and more sustainable results of the metaheuristic algorithms, Minitab software was used to design the experiments and assign the best level to the size of problems. For the problems in the small size, the optimal solution is obtained by GAMS software. Then a randomized complete block design considered to compare the ability of algorithms at finding the best solution for medium and large problems. Computational results revealed that for medium and large problems the HPSOVNS algorithm outperforms the HPSOSA, PSO and HGATS algorithms.