Unrelated Parallel Machine Scheduling Problem Research Articles

Just-in-time scheduling of unrelated parallel machines with family setups and soft time window constraints

ABSTRACT This study addresses an unrelated parallel machine scheduling problem with family setups and soft time windows, which includes considerations for machine eligibility. The objective is to minimize the total weighted tardiness and earliness, and to maximize the number of Just-in-Time jobs. Four different metaheuristic algorithms are compared to determine which type – single-point (simulated annealing), population-based evolutionary (artificial immune system, genetic algorithm), or swarm intelligence algorithms (ant colony optimization) – is more effective in solving this problem. Two strategies, namely penalty and repair, are proposed to handle precedence constraints. Experimental results demonstrate that ant colony optimization with local search which employs the repair strategy, as a swarm intelligence-based algorithm outperforms its rivals in terms of objective function values and robustness. The performance of this algorithm has shown an improvement in objective function values ranging from 2.12% to 8.52% on average, with a relative percentage deviation of 10.35.

Combinatorial optimization methods for yarn dyeing planning

AbstractManaging yarn dyeing processes is one of the most challenging problems in the textile industry due to its computational complexity. This process combines characteristics of multidimensional knapsack, bin packing, and unrelated parallel machine scheduling problems. Multiple customer orders need to be combined as batches and assigned to different shifts of a limited number of machines. However, several practical factors such as physical attributes of customer orders, dyeing machine eligibility conditions like flotte, color type, chemical recipe, and volume capacity of dye make this problem significantly unique. Furthermore, alongside its economic aspects, minimizing the waste of natural resources during the machine changeover and energy are sustainability concerns of the problem. The contradictory nature of these two makes the planning problem multi-objective, which adds another complexity for planners. Hence, in this paper, we first propose a novel mathematical model for this scientifically highly challenging yet very practical problem from the textile industry. Then we propose Adaptive Large Neighbourhood Search (ALNS) algorithms to solve industrial-size instances of the problem. Our computational results show that the proposed algorithm provides near-optimal solutions in very short computational times. This paper provides significant contributions to flexible manufacturing research, including a mixed-integer programming model for a novel industrial problem, providing an effective and efficient adaptive large neighborhood search algorithm for delivering high-quality solutions quickly, and addressing the inefficiencies of manual scheduling in textile companies; reducing a time-consuming planning task from hours to minutes.

Unrelated Parallel Machine Considering Multi-task Simultaneous Supervision Dual Resources Constraints to Minimize Makespan

To maximize their production, many companies invest their funds into a semi-automatic machine to help them reach their fullest potential. However, many forgot to also take into account the adjustments that have to be done to the preexisting schedule because of the idle time that operators have now that the new machine has arrived. Multi-task simultaneous supervision dual resource constraints (MTSSDRC) have been the go-to method to solve that problem. Nonetheless, there is still an absence in an MTSSDRC field that involves an Unrelated Parallel Machine Scheduling Problem (UPMSP). This research proposed a model of MTSSDRC that is in line with UPMSP where the machine is a complex system and variations of machining speed can happen from a certain machine to certain jobs. This research also brought MTSSDRC closer to its real-life counterpart as a shop floor that exists in many manufacturing industries.

An energy-efficient unrelated parallel machine scheduling problem with learning effect of operators and deterioration of jobs

An energy-efficient unrelated parallel machine scheduling problem with learning effect of operators and deterioration of jobs

Imperialist competitive algorithm for unrelated parallel machine scheduling with sequence-and-machine-dependent setups and compatibility and workload constraints

In this paper, we present an in-depth analysis of the unrelated parallel machine scheduling problem (UPMSP) in the context of washing machine production at Vestel Electronics. Vestel Electronics is a leading producer of washing machines and holds a noteworthy market position in the European consumer electronics industry. The production process at Vestel Electronics is make-to-order (MTO) and requires 20 assembly lines to produce 200 different products. The decision maker must consider several important factors while forming the production schedule, including job-assembly line compatibility, the release times and due dates of the jobs, and a workload balance among the different assembly lines. This study aims to develop an algorithm to minimize the total earliness and tardiness while considering sequence-and-machine-dependent setups, unequal release times, machine-job compatibility restrictions, and workload balance requirements. To address this complex scheduling problem, we propose a novel algorithm, the imperialist competitive algorithm (ICA), which has a strong exploration–exploitation balance while mimicking real-world dynamics. Our numerical results show that the ICA significantly outperforms the current practice in Vestel by 39% and the best-performing algorithms in the literature by 23% and 12%.

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.

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.

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.

Unrelated parallel machine scheduling problem with stochastic sequence dependent setup times

Unrelated parallel machine scheduling problem with stochastic sequence dependent setup times

Sensitivity Analysis of the Unrelated Parallel Machine Scheduling Problem with Rework Processes and Machine Eligibility Restrictions

Sensitivity Analysis of the Unrelated Parallel Machine Scheduling Problem with Rework Processes and Machine Eligibility Restrictions

Minimizing tardiness and makespan for distributed heterogeneous unrelated parallel machine scheduling by knowledge and Pareto-based memetic algorithm

This work aims to deal with the distributed heterogeneous unrelated parallel machine scheduling problem (DHUPMSP) with minimizing total tardiness (TDD) and makespan. To solve this complex combinatorial optimization problem, this work proposed a knowledge and Pareto-based memetic algorithm (KPMA) which contains the following features: 1) four heuristic rules are designed including the shortest processing time rule, the minimum factory workload rule, the minimum machine finish time rule, and the earliest due date rule. Meanwhile, a hybrid heuristic initialization is developed to construct a population with great convergence and diversity; 2) four problem feature-based heuristic neighborhood structures are designed to increase the success rate of local search; and 3) a simple elite strategy is developed to enhance the usage of historical elite solutions. Finally, to evaluate the performance of KMPA, it is compared to five state-of-art and run on 20 instances with different scales. The results of numerical experiments show that the proposed hybrid heuristic initialization can efficiently save computation resources to improve the initialized convergence. In addition, the knowledge-based neighborhood structures can vastly accelerate exploration. Moreover, the elite strategy can efficiently improve the diversity of the final non-dominated solutions set. The proposed KPMA has better performance than the state-of-art and has a strong ability to solve DHUPMSP.

Review on unrelated parallel machine scheduling problem with additional resources

This study deals with an unrelated parallel machine scheduling problem with additional resources (UPMR). That is one of the important sub-problems in the scheduling. UPMR consists of scheduling a set of jobs on unrelated machines. In addition to that, a number of one or more additional resources are needed. UPMR is very important and its importance comes from the wealth of applications; they are applicable to engineering and scientific situations and manufacturing systems such as industrial robots, nurses, machine operators, bus drivers, tools, assembly plant machines, fixtures, pallets, electricity, mechanics, dies, automated guided vehicles, fuel, and more. The importance also comes from the concern about the limitation of resources that are dedicated for the production process. Therefore, researchers and decision makers are still working on UPMR problem to get an optimum schedule for all instances which have not been obtained to this day. The optimum schedule is able to increase the profits and decrease the costs whilst satisfying the customers’ needs. This research aims to review and discuss studies related to unrelated parallel machines and additional resources. Overall, the review demonstrates the criticality of resolving the UPMR problem. Metaheuristic techniques exhibit significant effectiveness in generating results and surpassing other algorithms. Nevertheless, continued improvement is essential to satisfy the evolving requirements of UPMR, which are subject to operational changes based on customer demand.

Review on unrelated parallel machine scheduling problem with additional resources

This study deals with an unrelated parallel machine scheduling problem with additional resources (UPMR). That is one of the important sub-problems in the scheduling. UPMR consists of scheduling a set of jobs on unrelated machines. In addition to that, a number of one or more additional resources are needed. UPMR is very important and its importance comes from the wealth of applications; they are applicable to engineering and scientific situations and manufacturing systems such as industrial robots, nurses, machine operators, bus drivers, tools, assembly plant machines, fixtures, pallets, electricity, mechanics, dies, automated guided vehicles, fuel, and more. The importance also comes from the concern about the limitation of resources that are dedicated for the production process. Therefore, researchers and decision makers are still working on UPMR problem to get an optimum schedule for all instances which have not been obtained to this day. The optimum schedule is able to increase the profits and decrease the costs whilst satisfying the customers’ needs. This research aims to review and discuss studies related to unrelated parallel machines and additional resources. Overall, the review demonstrates the criticality of resolving the UPMR problem. Metaheuristic techniques exhibit significant effectiveness in generating results and surpassing other algorithms. Nevertheless, continued improvement is essential to satisfy the evolving requirements of UPMR, which are subject to operational changes based on customer demand.

An evolutionary approach comprising tailor-made variation operators for rescue unit allocation and scheduling with fuzzy processing times

This paper addresses the rescue unit allocation and scheduling problem (RUASP) with fuzzy processing times through an evolutionary approach. The goal of RUASP is to efficiently assign and schedule the rescue units to process the incidents in the event of a natural disaster. This problem can be considered as a variant of the unrelated parallel-machine scheduling problem with sequence and machine-dependent setup times. A steady-state grouping genetic algorithm (SSGGA) approach is presented to minimize the total weighted completion time of the incidents, where the weights correspond to the severity levels of the incidents. The crossover and mutation operators used in this approach are designed as per the characteristics of RUASP and its objective. The proposed approach uses a combination of greedy and random heuristics while generating the initial solutions, thereby yielding superior quality diverse initial solutions. The performance of the proposed approach is compared with the state-of-the-art approach available in the literature. The proposed approach always yields better results in much shorter execution times in comparison to the state-of-the-art approach. Moreover, the robustness analysis test demonstrates the proposed approach to be more robust in comparison to the state-of-the-art approach.

Unrelated parallel machine scheduling models with machine availability and eligibility constraints

In this paper, we address the unrelated parallel machine scheduling problem with calendar, which consists of a generic intermittent availability scheme with non-regular active and inactive time windows in sequence. The problem additionally considers machine eligibility and release date constraints, as well as the possibility of pausing or not the processing of the jobs between successive active time windows. This problem is quite frequent and relevant in several practical settings in which it is necessary to schedule parallel resources with different calendars, such as different weekly and daily shifts, non-regular not worked days, holidays, and preventive maintenance periods, among others, while considering the resources eligibility. We present novel mixed integer linear programming models for this problem with the aim of minimizing the makespan. Basic formulations of these models are presented as well as tight lower bounds for the objective, including enhanced formulations. To the best of our knowledge, there are no other works that tackled this problem and that proposed optimization models with the level of detail and generality here considered. The models presented are evaluated using a state-of-the-art general-purpose solver, and the computational tests are performed on a variety of instances. The results validate the models and show that they are can handle instances in realistic situations where the problem occurs. The results also show that the enhanced formulations are able to find several optimal solutions, and that within acceptable computational times they are able to sharply reduce the optimality gaps when compared to the more basic formulations.

A shuffled frog-leaping algorithm with Q-learning for unrelated parallel machine scheduling with additional resource and learning effect

Unrelated parallel machine scheduling problem (UPMSP) with additional resources and UPMSP with learning effect have attracted some attention; however, UPMSP with additional resources and learning effect is seldom studied and meta-heuristics for UPMSP hardly possess reinforcement learning as new optimization mechanism. In this study, a shuffled frog-leaping algorithm with Q-learning (QSFLA) is presented to solve UPMSP with one additional resource and learning effect. A new solution presentation is presented. Two populations are obtained by division. A Q-learning algorithm is constructed to dynamically decide search operator and search times. It has 12 states depicted by population quality evaluation, four actions defined as search operators, a new reward function and a new action selection. Extensive experiments are conducted. Computational results demonstrate that QSFLA has promising advantages for the considered UPMSP.

Hybridizing genetic algorithm and single-based metaheuristics to solve unrelated parallel machine scheduling problem with scarce resources

<span lang="EN-US">This paper focuses on solving unrelated parallel machine scheduling with resource constraints (UPMR). There are </span><em><span lang="EN-US">j</span></em><span lang="EN-US"> jobs, and each job needs to be processed on one of the machines aim at minimizing the </span><em><span lang="EN-US">makespan</span></em><span lang="EN-US">. Besides the dependence of the machine, the processing time of any job depends on the usage of a rare renewable resource. A certain number of those resources R</span><em><span lang="EN-US">max</span></em><span lang="EN-US"> can be disseminated to jobs for the purpose of processing them at any time, and each job j needs units of resources (</span><em><span lang="EN-US">rjm</span></em><span lang="EN-US">) when processing in machine m. When more resources are assigned to a job, the job processing time minimizes. However, the number of resources available is limited, and this makes the problem difficult to solve for a good quality solution. Genetic algorithm shows promising results in solving UPMR. However, genetic algorithm suffers from premature convergence, which could hinder the resulting quality. Therefore, the work hybridizes genetic algorithm with a single-based metaheuristics (SBH) to handle the premature convergence in the genetic algorithm with the aim to escape from the local optima and improve the solution quality further. The single-based metaheuristics replaces the mutation in the genetic algorithm. The evaluation of the algorithm performance was conducted through extensive experiments. </span>