Unrelated Parallel Machines Research Articles

Evolving many-objective dispatching rule pairs for unrelated parallel machine scheduling with sequence-dependent setup times

The real-world problem of unrelated parallel machine scheduling problem with sequence-dependent setup times (UPMSPSST) is investigated and focuses on two key aspects: fast solution and many-objective optimization. While dispatching rules (DRs) are effective in meeting demand, the manual design of many-objective DRs (MaODRs) is challenging. An alternative approach, based on the automatic evolution of MaODRs using hyper-heuristics, shows promise. However, limited literature exists on the automatic evolution of MaODRs specifically for UPMSPSST. In this study, a many-objective genetic programming (MaOGP) algorithm is formed by combining many-objective evolutionary algorithms (MaOEAs) with genetic programming (GP) algorithms. This enables the automatic evolution of MaODRs, leveraging the respective advantages of each approach. The exploration results demonstrate that the evolved MaODRs outperform manually designed DRs reported in prior literature. Furthermore, when considering combinations of objectives with different correlations, the MaODRs exhibit outstanding performance across multiple objectives simultaneously, surpassing even the performance of DRs trained separately for individual objectives. These findings highlight the potential of the proposed MaOGP approach in efficiently and effectively solving the UPMSPSST problem, opening avenues for further research and practical applications in related industries.

Unrelated Parallel Machine Scheduling Problem Considering Job Splitting, Inventories, Shortage, and Resource: A Meta-Heuristic Approach

This research aims to study a real-world example of the unrelated parallel machine scheduling problem (UPMSP), considering job-splitting, inventories, shortage, and resource constraints. Since the nature of the studied optimization problem is NP-hard, we applied a metaheuristic algorithm named Grey Wolf Optimizer (GWO). The novelty of this study is fourfold. First, the model tackles the inventory problem along with the shortage amount to avoid the late fee. Second, due to the popularity of minimizing completion time (Makespan), each job is divided into small parts to be operated on various machines. Third, renewable resources are included to ensure the feasibility of the production process. Fourth, a mixed-integer linear programming formulation and the solution methodology are developed. To feed the metaheuristic algorithm with an initial viable solution, a heuristic algorithm is also fabricated. Also, the discrete version of the GWO algorithm for this specific problem is proposed to obtain the results. Our results confirmed that our proposed discrete GWO algorithm could efficiently solve a real case study in a timely manner. Finally, future research threads are suggested for academic and industrial communities.

An Energy-Efficient Unrelated Parallel Machine Scheduling Problem with Batch Processing and Time-of-Use Electricity Prices

The extensive consumption of energy in manufacturing has led to a large amount of greenhouse gas emissions that have caused an enormous effect on the environment. Therefore, investigating how to reduce energy consumption in manufacturing is of great significance to cleaner production. This paper considers an energy-conscious unrelated parallel batch processing machine scheduling problem under time-of-use (TOU) electricity prices. Under TOU, electricity prices vary for different periods of a day. This problem is grouping jobs into batches, assigning the batches to machines and allocating time to the batches so as to minimize the total electricity cost. A mixed-integer linear programming model and two groups of heuristics are proposed to solve this problem. The first group of heuristics first forms batches, assigns the batches to machines and finally allocates time to the batches, while the second group of heuristics first assigns jobs to machines, batches the jobs on each machine and finally allocates time to each batch. The computational results show that the SPT-FBLPT-P1 heuristic in the second group can provide high-quality solutions for large-scaled instances in a short time, in which the jobs are assigned to the machines based on the shortest processing time rule, the jobs on each machine are batched following the full-batch longest processing time algorithm, and the time is allocated to each batch following an integer programming approach. The MDEC-FBLPT-P1 heuristic that uses the minimum difference of the power consumption algorithm to assign the jobs also performed well.

Proactive scheduling for steel plants with unrelated parallel machines and time uncertainty

This paper deals with the steel plant proactive scheduling problem with unrelated parallel machines and time uncertainty to enhance the rationality of machine assignment and processing path, improve the schedule robustness and guarantee capability of energy. First, a scheduling model is formulated with the objectives of average process time, matching degree and oxygen consumption fluctuation. Then, an improved preference-based NSGA-II is designed to solve the problem. The algorithm introduces the preference information into the optimization process and designs an individual sorting method based on the technique for order preference by similarity to ideal solution (TOPSIS) to guide the evolution direction. Besides, to improve the local search ability, variable neighborhood search is incorporated to generate new solutions with high quality. Computational experiments prove that the algorithm can effectively address the proactive scheduling problem. The sensitivity analysis and results of different scheduling models verify the robustness and superiority in machine matching and energy synergy of the model.

Dynamical Artificial Bee Colony for Energy-Efficient Unrelated Parallel Machine Scheduling with Additional Resources and Maintenance

Dynamical Artificial Bee Colony for Energy-Efficient Unrelated Parallel Machine Scheduling with Additional Resources and Maintenance

Metaheuristic Optimization for Sustainable Unrelated Parallel Machine Scheduling: A Concise Overview With a Proof-of-Concept Study

Metaheuristic Optimization for Sustainable Unrelated Parallel Machine Scheduling: A Concise Overview With a Proof-of-Concept Study

Solving an Unrelated Parallel Machines Scheduling Problem with machine- and job-dependent setups and precedence constraints considering Support Machines

Single-stage production planning problems are common in the academic literature and in real-world environments. One of the least studied scenarios in the literature for this environment is that with Unrelated Parallel Machines. In this work, this type of problem is inspired by a real station within the wind tower production process. The problem presents characteristics that have already been studied, such as mandatory precedences and setup times that depend on the machine and the job. However, a new and real feature is presented: the existence of “support machines”, which are machines that can continue to work but cannot complete jobs due to reduced capacity for some operational reason. In this case, instead of abandoning their work, support machines can still be used to assist other machines by performing partial jobs before handing them over to full-capacity machines for completion. This innovative concept of support machines, never before presented in this context of production planning, introduces a unique approach to dealing with reduced-capacity machines without sacrificing their operational potential. A Mixed-Integer Linear Programming (MILP) model is formulated to mathematically represent this problem.This work explores the impact of these support machines on production planning. For this purpose, Tabu Search and Simulated Annealing metaheuristics have been adapted for their solution, and a novel Constructive Heuristic has been developed based on the real and manual process currently performed in the aforementioned factory. These three algorithms are run and compared on a real database in order to minimise the makespan. Their analysis shows that although the use of support machines generally gives positive results, an improvement is not achieved in all cases. Furthermore, contrary to what might be expected, the use of full-capacity machines in the role of support machines sometimes improves completion times.

Learning-based two-phase cooperative optimizer for distributed machine scheduling with heterogeneous factories and order priorities

In the realm of customized manufacturing, production cycles are often compressed to capture market opportunities swiftly. The blanking system stands as the inaugural and pivotal phase in the realm of large equipment customized manufacturing. This study abstracts a novel problem from real-world blanking systems, as the distributed unrelated parallel machine scheduling with heterogeneous factories and order priorities (DUPMS-HP). The presented work formulates the bi-objective DUPMS-HP, aiming to minimize both the total weighted tardiness and the workload gap of each machine. A learning-based two-phase cooperative optimizer (LCTPO) is introduced to address this NP-hard problem, featuring: i) a cooperative evolutionary algorithm during the first stage for global search to ensure diversity; ii) the incorporation of five problem-specific local search strategies in the first stage to balance priority and due date constraints. Additionally, reinforcement learning is applied to learn and select the best neighborhood search operator for each elite solution, further enhancing diversity. The effectiveness of the proposed algorithm is validated through a comparative analysis with five state-of-the-art algorithms on 20 instances. Experimental results affirm that LCTPO is more adept at solving DUPMS-HP compared to the alternative algorithms.

A fix-and-optimize heuristic for the Unrelated Parallel Machine Scheduling Problem

This paper proposes and evaluates a matheuristic approach for the Unrelated Parallel Machine Scheduling Problem (UPMSP). The UPMSP consists of assigning jobs to unrelated parallel machines considering different processing times for the same job in different machines. Additionally, a setup time is considered between the execution of jobs in the same machine. The problem is addressed by a fix-and-optimize matheuristic that iteratively selects a subset of variables to be fixed to their current values so that the remaining variables will compose a subproblem to be optimized by a mathematical programming solver. In the proposed approach, each subproblem consists of a subset of jobs that are assigned to a subset of machines in the incumbent solution. The subproblems are solved by the state-of-the-art exact algorithm for the UPMSP. In the experiments conducted on benchmark instances, the proposed fix-and-optimize algorithm achieved remarkable results. It outperformed the standalone exact algorithm by a large margin and resulted in competitive solutions when compared to the literature’s best-performing heuristic method for the problem. The proposed algorithm obtained the best solution for 669 out of the 1000 instances addressed in this work. Among them, 338 are new best-known solutions. In general, the proposed approach excels at solving instances with a high number of jobs per machine — it resulted in the best solution for 89% of the instances with a ratio of 10 or more jobs per machine in total.

Lithography reticle scheduling in semiconductor manufacturing

The lithography process in semiconductor dynamic random-access memory (DRAM) fabrication plants (fabs) is usually a major bottleneck, and reticle scheduling is complicated by process-specific constraints such as diversity of the product mix and rapidly changing deadlines. This study proposes a three-phase scheduling framework to solve the multi-objective reticle scheduling problem, reducing capacity loss, maintaining line balance and meeting customer demand. The genetic algorithm (GA) and the technique for order preference by similarity to ideal solution (TOPSIS) are used to optimize the scheduling with a trade-off among the multiple objectives. This study tests the proposed framework based on a real semiconductor DRAM (fab) in Taiwan, which has two unrelated parallel machines in its lithography process. The study finds that the proposed framework results in better scheduling reports, reduced computation times and improvements in the overall performance of lithography equipment.

Joint Dynamic Dispatching and Preventive Maintenance for Unrelated Parallel Machines With Equipment Health Considerations

A decomposed dynamic dispatching and preventive maintenance (D-DDPM) framework is presented to overcome the computational challenges of solving large DDPM problems. Stochastic deterioration of machine health is explicitly considered. By efficient allocation of individual machines capacity under different machine health, the D-DDPM framework decomposes the global DDPM problems into single-machine DDPM problems while ensuring throughput optimality. Intelligent machine agents are then designed to solve the single-machine DDPM problems efficiently and to perform real-time decisions for individual machines. After the decomposition, the overall computational complexity grows only linearly with the number of machines and the proposed framework could be adopted in large systems. In the numerical study, the D-DDPM framework is near-optimal in small systems that have optimal DDPM solutions. In which, the computation time is reduced by 90.72% and the average cycle time is within 6% of optimal. For large systems without optimal DDPM solutions, numerical results show that the D-DDPM maintains throughput optimality and reduces average cycle time by up to 90% against other control policies.

Integrated maintenance and production scheduling for unrelated parallel machines with setup times

This paper considers jointly scheduling the production and resource-constrained maintenance activities in a manufacturing setting with unrelated parallel machines. In particular, a single maintenance activity needs to be scheduled on each machine in one of its available time windows, and the maintenance activities require a scarce resource, thereby limiting the number of maintenance activities that can be scheduled simultaneously on different machines. In addition, machine- and sequence-dependent setup times, machine eligibility constraints and job-specific release and due dates are considered. A mixed-integer linear program is formulated with objectives including the makespan and, motivated from practice, a weighted sum of total production completion times at machines and total job tardiness. Additionally, a hybrid genetic algorithm with a novel solution representation is proposed for solving industry-scale large instances. A case study is performed with real-world data from a semiconductor manufacturer, where production and maintenance are scheduled separately. The benefit of simultaneously scheduling production and maintenance is investigated. Tests with real-world data show that the proposed model results in schedules that substantially improve the current factory practice.

Multi-population genetic algorithm with greedy job insertion inter-factory neighbourhoods for multi-objective distributed hybrid flow-shop scheduling with unrelated-parallel machines considering tardiness

Distributed manufacturing is gradually becoming the future trend. The fierce market competition makes manufacturing companies focus on productivity and product delivery. The hybrid flow shop scheduling problem (HFSP) is common in manufacturing. Considering the difference of machines at the same stage, the multi-objective distributed hybrid flow shop scheduling problem with unrelated parallel machines (MODHFSP-UPM) is studied with minimum makespan and total tardiness. An improved multi-population genetic algorithm (IMPGA) is proposed for MODHFSP-UPM. The neighbourhood structure is essential for meta-heuristic-based solving algorithms. The greedy job insertion inter-factory neighbourhoods and corresponding move evaluation method are designed to ensure the efficiency of local search. To enhance the optimisation ability and stability of IMPGA, sub-regional coevolution among multiple populations and re-initialisation procedure based on probability sampling are designed, respectively. In computational experiments, 120 instances (including the same proportion of medium and large-scale problems) are randomly generated. The IMPGA performs best in all indicators (spread, generational distance, and inverted generational distance), significantly outperforming existing efficient algorithms for MODHFSP-UPM. Finally, the proposed method effectively solves a polyester film manufacturing case, reducing the makespan and total tardiness by 40% and 60%, respectively.

A cooperative adaptive genetic algorithm for reentrant hybrid flow shop scheduling with sequence-dependent setup time and limited buffers

This paper deals with a reentrant hybrid flow shop problem with sequence-dependent setup time and limited buffers where there are multiple unrelated parallel machines at each stage. A mathematical model with the minimization of total weighted completion time is constructed for this problem. Considering the complexity of the problem at hand, an effective cooperative adaptive genetic algorithm (CAGA) is proposed. In the algorithm, a dual chain coding scheme and a staged-hierarchical decoding approach are, respectively, designed to encode and decode each solution. Six dispatch heuristics and a dynamic adjustment method are introduced to define initial population. To balance the exploration and exploitation abilities, three effective operations are implemented: (1) two new crossover and mutation operators with collaborative mechanism are imposed on genetic algorithm; (2) an adaptive adjustment strategy is introduced to re-optimize better solutions after mutation operations, where ant colony search algorithm and modified greedy heuristic are intelligently switched; (3) a reset strategy with dynamic variable step strategy is embedded to re-generate some non-improved solutions. A Taguchi method of design of experiment is adopted to calibrate the parameter values in the presented algorithm. Comparison experiments are executed on test instances with different scale problems. Computational results show that the proposed CAGA is more effective and efficient than several well-known algorithms in solving the studied problem.

A variable neighborhood search algorithm for airport ferry vehicle scheduling problem

This paper formulates the airport ferry vehicle scheduling problem as unrelated parallel machine scheduling (UPMS) problem to achieve a better reduction in the weighted sum of flight tardiness. In the UPMS model, the departure time and the estimated end time of each ferry vehicle for each ferry task is simultaneously planned with the allocation of ferry vehicles, and the specific journey of each ferry vehicle for each task is arranged. A variable neighborhood search (VNS) algorithm is proposed to address the model. Three scheduling rules including random allocation, service time in turn (STT), and minimum maximum completion time (MCT) are designed to combine with VNS as comparisons, together with five neighborhood structures suited for the airport ferry vehicle scheduling problem. Comparative experiments are carried out by using two weeks of real flight data from a major international airport in China. Experimental results show the superiority of the proposed MCT initialization combined with VNS (MCT_VNS) for the airport ferry vehicle scheduling problem. The solutions obtained by MCT_VNS can provide the allocation of the airport ferry vehicles to flights that need ferry services.

A tabu search algorithm for the unrelated parallel machine scheduling problem with varied carbon emission constraints in different time intervals

The carbon emissions generated during the rapid development of the manufacturing industry have caused severe environmental pollution. Research on parallel machine scheduling problems considering carbon emission constraints has started to emerge in recent years to promote sustainable development and achieve low carbon emissions in production. In this paper, we consider an unrelated parallel machine scheduling problem with various carbon emission constraints in different time intervals. A mixed integer linear programming model with the objective of minimising the makespan is formulated to describe the problem accurately. Since the high complexity of our problem, we propose an efficient tabu search algorithm with a dedicated linked list structure to address this problem. Firstly, we generate four initial sequences according to the proposed heuristic rules and apply a greedy insertion decoding method to obtain the scheduling scheme. Then, we employ the 2-swap neighbourhood search strategy to exploit the promising solution space. The proposed model and algorithm are tested on extensive instances generated randomly. Computational results validate the correctness of the model and the effectiveness of the tabu search algorithm.

Quantum annealing solution for the unrelated parallel machine scheduling with priorities and delay of task switching on machines

Quantum computing has emerged in recent years as an alternative to classical computing, which could improve the latter in solving some types of problems. One of the quantum programming models, Adiabatic Quantum Computing, has been successfully used to solve problems such as graph partitioning, traffic routing, and task scheduling. In this paper, the focus is on the scheduling of the problem of unrelated parallel machines, where the processing time of tasks on any of the available processing elements is known. Moreover, the proposed model is extended in two relevant aspects for this kind of problem: the existence of some degree of priority of tasks, and the introduction of a delay or penalty every time a processing unit or machine changes the type of task that executes.In all cases, the problem is expressed as Quadratic Unconstrained Binary Optimization, which can be subsequently solved using quantum annealers. The quantum nonlinear programming framework discussed in this work consists of three steps: quadratic approximation of cost function, a binary representation of parameter space, and solving the resulting Quadratic Unconstrained Binary Optimization on the quantum annealer platform D-Wave. One of the novelties in tackling this problem is the compaction of the model bearing in mind the repetitions of each task, to allow solving larger scheduling problems with the quantum resources available in the experimentation platform. An estimation of the number of qubits required in relation to the scheduling parameters is analyzed. The models have been implemented on the D-Wave platform and validated with respect to other traditional methods. Furthermore, the proposed extensions to consider priorities and to switch the delay of tasks have been analyzed using a case study.

An artificial immune differential evolution algorithm for scheduling a distributed heterogeneous flexible flowshop

This paper studies a distributed heterogeneous flexible flowshop problem (DHFFP) with sequence-dependent setup and transport times, where each job has a release time and each production stage has multiple unrelated parallel machines. An integer linear programming (ILP) model and a new artificial immune differential evolution (AIDE) algorithm are proposed aiming to minimize the makespan and total tardiness simultaneously. Firstly, the AIDE employs a two-dimensional vector encoding scheme including the information of job permutation and factory allocation for solution representation. In addition, a dynamic decoding scheme is designed to construct a feasible schedule. Secondly, three distributed Nawaz–Enscore–Ham (NEH) based constructive heuristics are presented to provide the initial antibody population. Thirdly, a discrete differential evolution algorithm is introduced to mutate the cloned antibodies. Further, clonal suppression is applied by eliminating the antibodies with lower stimulation values. Simulated annealing (SA) based local search is incorporated with four problem-specific neighborhood structures to enhance the algorithm. Finally, the optimal values of the algorithmic parameters are determined by the orthogonal test. Some numerical experiments of the ILP model on small-scale instances are conducted to show the effectiveness of the proposed AIDE algorithm. The AIDE algorithm is also compared with several existing algorithms for different scale instances. The results demonstrate that the AIDE algorithm generates average relative percentage deviation of 12.51% and 7.99% respectively for small & medium-scale instances and large-scale instances, which is the best-performing among all algorithms.

Bi-objective scenario-guided swarm intelligent algorithms based on reinforcement learning for robust unrelated parallel machines scheduling with setup times

Bi-objective scenario-guided swarm intelligent algorithms based on reinforcement learning for robust unrelated parallel machines scheduling with setup times

Unrelated parallel machine scheduling problem with stochastic sequence dependent setup times

Unrelated parallel machine scheduling problem with stochastic sequence dependent setup times