Multi-machine flow shop scheduling problems with rejection using genetic algorithm

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 .The proposed model is solved by three meta-heuristic algorithms: genetic algorithm (GA), imperialist competitive algorithm (ICA) and hybrid of GA and ICA. To evaluate the performance of the proposed algorithms many test problems have been designed. The Computational results indicate the superiority of the performance of hybrid approach than GA and ICA in finding thebest solution in reasonable computational time.

Caregiver routing and scheduling is one of the challenge problems in home health care services. Efficient approaches can not only reduce the operating cost but also increase the service efficiency of caregivers. The budget of patients is a critical factor for the patients to make feasible choices among different services, especially for patients with the limited budget. However, few existing works pay attention to the budget of patients. To fill this gap, we initially formulate a novel problem for caregiver routing and scheduling in home health care services by introducing a constraint based on the budget of patients. The objective of the problem is to minimize the total cost of home health care organizations. We provide the proof for its NP-hardness, followed by an approximation algorithm (APA) for the formulated problem. The strategy of the proposed algorithm directly aims to reduce the total cost of home health care organizations, by assigning the caregiver with the minimum total cost to the patient with early time for starting service. Then, we propose two heuristic algorithms, a genetic algorithm (GA) and a tabu search algorithm (TS). Simulation results show that, the proposed algorithms outperform the existing work for various cases, on the same datasets and configuration of the state-of-art work. The total cost of home health care organizations can be reduced by 45.75%, 53.01% and 57.74% on average, by APA, GA and TS, respectively.

This paper investigates the multistage hybrid flow shop (HFS) scheduling problems using the new bat algorithm. A HFS is the generalisation of flowshop with multiple machines. HFS is one of the important scheduling problems that represent many industries like iron and steel, chemical, textile and ceramic industries. The HFS scheduling problems have been proved to be NP-hard. A recently developed bat meta-heuristic algorithm is proposed to solve the HFS problems. The proposed algorithm is validated with a well-chosen set of benchmark problems in the literature. Computational results indicate that the proposed bat algorithm is more efficient than the genetic algorithm and particle swarm optimisation.

A key challenge in production management and operational research is the flow shop scheduling problem, characterized by its complexity in manufacturing processes. Traditional models often assume deterministic conditions, overlooking real-world uncertainties like fluctuating demand, variable processing times, and equipment failures, significantly impacting productivity and efficiency. The increasing demand for more adaptive and robust scheduling frameworks that can handle these uncertainties effectively drives the need for research in this area. Existing methods do not adequately capture modern manufacturing environments’ dynamic and unpredictable nature, resulting in inefficiencies and higher operational costs; they do not employ a fuzzy approach to benefit from human intuition. This study successfully demonstrates the application of Hexagonal Type-2 Fuzzy Sets (HT2FS) for the accurate modeling of the importance of jobs, thereby advancing fuzzy logic applications in scheduling problems. Additionally, it employs a novel Multi-Criteria Decision-Making (MCDM) approach employing Proportional Picture Fuzzy AHP (PPF-AHP) for group decision-making in a flow shop scheduling context. The research outlines the methodology involving three stages: group weight assessment through a PPF-AHP for the objectives, weight determination using HT2FS for the jobs, and optimization via Genetic Algorithm (GA), a method that gave us the optimal solution. This study contributes significantly to operational research and production scheduling by proposing a sophisticated, hybrid model that adeptly navigates the complexities of flow shop scheduling. The integration of HT2FS and MCDM techniques, particularly PPF-AHP, offers a novel approach that enhances decision-making accuracy and paves the way for future advancements in manufacturing optimization.

Two-agent scheduling problems under rejection budget constraints

A well-planned schedule is essential to any organization’s growth. Thus, it is important for the literature to cover a more comprehensive range of scheduling problems. In this paper, energy-efficient hybrid flow shop (EEHFS) scheduling problems are considered. Researchers have developed several techniques to deal with EEHFS scheduling problems. Also, researchers have recently proposed several metaheuristics. Honey Badger Algorithm (HBA) is one of the most recent algorithms proposed to solve various optimization problems. The objective of the present work is to solve EEHFS scheduling problems using the Hybrid Honey Badger Algorithm (HHBA) to reduce the makespan (Cmax) and total energy cost (TEC). In the HHBA, a constructive heuristic known as the NEH heuristic was incorporated with the Honey Badger Algorithm. The suggested algorithm’s performance was verified using an actual industrial scheduling problem. The company’s results are compared with those of the HHBA. The HHBA could potentially result in an 8% decrease in total energy cost. Then, the proposed algorithm was applied to solve 54 random benchmark problems. The results of the proposed HHBA were compared with the FIFO dispatching rule, the NEH heuristic, and other metaheuristics such as the simulated annealing (SA) algorithm, the genetic algorithm (GA), the particle swarm optimization (PSO) algorithm, Honey Badger Algorithm, and the Ant Colony Optimization (ACO) algorithms addressed in the literature. Average percentage deviation (APD) was the performance measure used to compare different algorithms. The APD of the proposed HHBA was zero. This indicates that the proposed HHBA is more effective in solving EEHFS scheduling problems.

In this paper, first, the problem of dynamic two-machine flow shop scheduling with the objective of minimizing the number of tardy jobs is investigated. Second, a hybrid algorithm based on genetic algorithm and parallel simulated annealing algorithm is presented. In order to solve large scale instances of the problem and to generate the initial population for the hybrid approach, a heuristic algorithm is also presented. To evaluate the efficiency of the proposed algorithms, they are compared with an optimal branch-and-bound algorithm which has been already developed in the literature. Computational experiments demonstrate that the proposed hybrid algorithm can solve the entire small-sized problems and more than 95% of medium-sized problems optimally.

Scheduling is one of the many skills required for advancement in today’s modern industry. The flow-shop scheduling problem is a well-known combinatorial optimization challenge. Scheduling issues for flow shops are NP-hard and challenging. The present research investigates a two-stage flow shop scheduling problem with decoupled processing and setup times, where a correlation exists between probabilities, job processing times, and setup times. This study proposes a novel heuristic algorithm that optimally sequences jobs to minimize the makespan and eliminates machine idle time, thereby reducing machine rental costs. The proposed algorithm’s efficacy is demonstrated through several computational examples implemented in MATLAB 2021a. The results are compared with the existing approaches such as those by Johnson, Palmer, NEH, and Nailwal to highlight the proposed algorithm’s superior performance.

Focuses on the development of a learning-based heuristic for scheduling heterogeneous machines. Although list scheduling methods have been widely used for a large class of scheduling problems, including the heterogeneous machine scheduling problem, they involve designing priority rules, which usually require a fair amount of insights on the characteristics of the problem to be solved. Instead of elaborate design of priority rules in a single step, we propose an iterative list scheduling process, which refines priority rules while generating a number of schedules. The proposed iterative list scheduling is formulated as a reinforcement learning problem, with states and actions defined in list scheduling. Due to the large number of possible states, reinforcement learning algorithms which use value functions in constructing an optimal policy may not be suitable for scheduling problems. Thus, to directly work with policies rather than the values of states, we propose genetic reinforcement learning (GRL), in which the policies of reinforcement learning are encoded into the chromosomes of genetic algorithms and a near-optimal policy is searched for by genetic algorithms. A GRL-based scheduler, called evolutionary intracell scheduler (EVIS), has been developed and applied to various scheduling problems such as the heterogeneous machine scheduling, the processor scheduling, the job-shop scheduling, the flow-shop scheduling, and the open-shop scheduling problems. The proposed model of EVIS, which has a linear order of population-fitness convergence, is verified by computer experiments. Even without fine tuning EVIS, the quality of solutions achieved by EVIS is comparable to that of problem-tailored heuristics for most of the problem instances.

Genetic algorithm, as a kind of evolutionary algorithm, has the characteristics of easy operation and global search, but its stochasticity is relatively strong and highly susceptible to parameters. When facing a large-scale scheduling problem, a strategy is needed to improve the parameter adaptability to make its solution more effective. Reinforcement learning, as an optimization method, has a strong autonomous learning capability. Therefore, this paper proposes a genetic algorithm based on reinforcement learning, which uses Q-learning to self-learning the crossover probability and improve the generalization ability of genetic algorithm, so as to achieve the solution of large-scale replacement flow shop scheduling problem.

Parallel machine scheduling problem in multitasking environment plays an important role in modern manufacturing industry. Multitasking is a special scheduling method, in which each waiting job interrupts the primary job, causing an interruption time and a switching time. The existing literatures discuss the problem of multitasking scheduling, however, few studies consider credit risk into such a realm of scheduling models. In this work, we combine customer credit risk into a multitasking scheduling problem. Besides, due to the existence of credit risk and the constraint of deadline of each accepted job, we also consider the job rejection into this problem. To hedge against the worst-case performance (total profit in the worst-case), we then propose a robust stochastic mathematical model with the objective of minimising the maximum difference between total job rejection cost and total revenue. As commercial solvers cannot directly solve this robust stochastic programming model, a sample average approximation model is proposed to further solve this problem. Numerical experiments are conducted to demonstrate the effectiveness of the proposed sample average approximation approach.

The flow shop scheduling problem (FSSP) is a NP-HARD combinatorial problem with strong industrial background. Among the meta-heuristics, genetic algorithms attracted a lot of attention. However, lacking the major evolution direction, the effectiveness of regular genetic algorithm is restricted. In this paper, the particle swarm optimization algorithm (PSO) is introduced for better initial group. By combining PSO with GA, a hybrid optimization algorithm for FSSP is proposed. This method is validated on a series of benchmark datasets. Experimental results indicate that this method is efficient and competitive compared to some existing methods.

A multi-stage Hybrid Flow Shop (HFS) scheduling is characterized ‘n’ jobs ‘m’ machines with ‘M’ stages in series with unidirectional flow of work with a variety of jobs being processed sequentially in a single-pass manner. Most real world scheduling problems are NP-hard in nature. The essential complexity of the problem necessitates the use of meta-heuristics for solving hybrid flow shop scheduling problem. The paper addresses multi-stage hybrid flow shop scheduling problems with missing operations to minimize the makespan time with the specific batch size using Genetic Algorithm (GA) and Simulated Annealing algorithm (SA). It is observed that the GA algorithm yields good quality solutions than SA with lesser computational time.

Minimizing the mean weighted absolute deviation from due dates in lot-streaming flow shop scheduling

The majority of flow shop scheduling problems considers machines as the only resource. However, in most real-life manufacturing environments, jobs for their processing on machines may require additional non-renewable resources. Considering such resources, the scheduling problem is more realistic and much harder to solve. In this paper, we investigate the permutation flow shop scheduling problem subject to non-renewable resources constraints. The objective is to find a schedule that minimises the maximum completion time. An integer linear programming model is developed. Because of the computation time constraint, we propose an approximate resolution method based on genetic algorithm. To obtain better and more robust solutions, the Taguchi method is performed for tuning the parameters and operators of the algorithm. Furthermore, a local search is proposed to enhance the searching ability. Finally, computational experiments are conducted to evaluate the performance of both mathematical model and algorithm on different configurations of non-renewable resources availability.