Parallel Machine Scheduling Problem Research Articles

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.

A K-means-Teaching Learning based optimization algorithm for parallel machine scheduling problem

With the continuous increase of workshop production scale, traditional heuristic algorithms in solving the scheduling problem have the defects of unsatisfactory computing time and insufficient stability of the solution result. However, data mining has a good performance in solving large-scale scheduling problems. A data mining method was proposed for industrial big data to solve the problem of large-scale parallel machines scheduling. This methodology can obtain an effective initial solution for single-operation parallel machine scheduling problem by exploring the effective information in the historical scheduling data. Based on historical customer orders, the offline learning was used to continuously generate simulated data for learning, which makes up for the shortcomings of insufficient data. A TLBO framework (teaching-learning-based optimization) hybrid K-means algorithm was redesigned to enhance the accuracy of offline learning and the efficiency of data searching. In the online operation part, according to the optimal solutions for high-similarity manufacturing orders are the approximate solutions, the new customer order will be quickly matched with the most similar manufacturing order through similarity calculation, and then and then local search is performed. Finally, the globally optimal solution is obtained after screening. Experimental results show that the hybrid teaching–learning methodology can solve the large-scale parallel machines scheduling problem with a better learning performance and computational efficiency.

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%.

A novel exact formulation for parallel machine scheduling problems

Machine scheduling is one of the most studied problems due to its technical challenges and prevalence in real life. In the literature, continuous- and discrete-time formulations are the two most known formulations for scheduling problems. However, continuous-time formulations often suffer from weak linear relaxations, while discrete-time formulations struggle with large numbers of variables. In contrast, the bucket-indexed formulation is an alternative that mitigates both issues by working with partial time discretization. We propose a mixed-integer linear programming model based on a bucket-indexed formulation to solve a nonpreemptive scheduling problem of identical parallel machines considering release dates, deadlines, precedence, eligibility, and machine availability constraints. We evaluate the proposed formulation against real-world instances comprising more than 400 jobs and 100 machines, comparing its performance against equivalent continuous- and discrete-time formulations. Remarkably, our formulation can be solved to optimality for all instances, outperforming both continuous- and discrete-time formulations.

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.

Minimizing total completion time with machine-dependent priority lists

We consider a natural, yet challenging variant of the parallel machine scheduling problem in which each machine imposes a preferential order over the jobs and schedules the jobs accordingly once assigned to it. We study the problem of minimizing the total completion time, distinguishing between identical and unrelated machines, machine-dependent and identical priority lists, or a constant number of different priority classes. Additionally, we consider the setting in which the priority list on a machine must satisfy longest processing time first. We resolve the computational complexity of the problem and provide a clear distinction between problems that are polynomial time solvable and APX-hard.

Scheduling parallel extrusion lines

This paper introduces the problem of scheduling jobs on parallel plastic extrusion lines where each line is composed of one or more than one extruder. Although there are some similarities between the introduced problem and the non-identical parallel machines scheduling problems with sequence-dependent setup times, limited additional resources and machine eligibility restrictions, the problem considered in this paper is a generalization of the parallel machine scheduling problem. This is because in parallel machines scheduling each job requires only one machine but in our case some jobs require more than one machine. Thus, our problem reduces to the parallel machine scheduling problem if all jobs require only one machine. This paper describes the problem of scheduling parallel extrusion lines, its industrial context, and develops a mixed-linear formulation to model the problem. This formulation allowed solving instances of up to 15 jobs. In addition, we developed four metaheuristics: a simulated annealing algorithm, a tabu search heuristic, a genetic algorithm, and a greedy randomized adaptive search procedure. These metaheuristics can be used to solve real-life instances of the problem. A numerical experiment shows that the proposed metaheuristics produce excellent solutions. Some of the proposed simulated annealing adaptations and of the tabu search heuristics obtained solutions with less than 2% deviation from the optimum.

A Metaheuristic Framework for Energy-Intensive Industries With Batch Processing Machines

Batch processing machines, which operate multiple jobs at a time, are commonly used in energy-intensive industries. A significant amount of energy can be saved in such industries using production scheduling as an approach to enhance efficiency. This study deals with an energy-aware scheduling problem for parallel batch processing machines with incompatible families and job release times. In such an environment, a machine may need to wait until all the jobs in the next batch become ready. During waiting time, a machine can be switched <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</small> or kept <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> standby for more energy-efficient scheduling. We first present a mixed-integer linear programming (MILP) model to solve the problem. However, the presented MILP model can only solve small problem instances. We therefore propose an energy-efficient tabu search (ETS) algorithm for solving larger problem instances. The proposed solution framework incorporates multiple neighborhood methods for efficient exploration of the search space. An energy-related heuristic is also integrated into the ETS for minimizing energy consumption during the waiting time. The performance of our proposed ETS algorithm is validated by comparing it with CPLEX for small problem instances and with two other heuristic algorithms for larger problem instances. The contribution of different components in ETS is also established in our experimental studies. The proposed solution framework is expected to bring many benefits in energy-intensive industries both economically and environmentally.

Metaheuristic Algorithms for Related Parallel Machines Scheduling Problem with Availability and Periodical Unavailability Constraints

Metaheuristic Algorithms for Related Parallel Machines Scheduling Problem with Availability and Periodical Unavailability Constraints

A Job Sequence Optimization Approach for Parallel Machine Scheduling Problem in Printing Manufacturing Systems

A Job Sequence Optimization Approach for Parallel Machine Scheduling Problem in Printing Manufacturing Systems

An Accurate and Robust Genetic Algorithm to Minimize the Total Tardiness in Parallel Machine Scheduling Problems

This paper uses a Genetic Algorithm (GA) to reduce total tardiness in an identical parallel machine scheduling problem. The proposed GA is a crossover-free (vegetative reproduction) GA but used for four types of mutations (Two Genes Exchange mutation, Number of Jobs mutation, Flip Ends mutation, and Flip Middle mutation) to make the required balance between the exploration and exploitation functions of the crossover and mutation operators. The results showed that use of these strategies positively affects the accuracy and robustness of the proposed GA in minimizing the total tardiness. The results of the proposed GA are compared to the mathematical model in terms of the time required to tackle the proposed problem. The findings illustrate the ability of the propounded GA to acquire the results in a short time compared to the mathematical model. On the other hand, increasing the number of machines degraded the performance of the proposed GA.

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.

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.

Exact algorithms for a parallel machine scheduling problem with workforce and contiguity constraints

We address a real-world scheduling problem where the objective is to allocate a set of tasks to a set of machines and to a set of workers in such a way that the total weighted tardiness is minimized. Our case study encompasses four types of constraints: precedence, resource, eligibility, and contiguity. While the first three constraints are common in the scheduling literature, contiguity constraints, which can be defined as a form of precedence constraints that requires both a predecessor and its successor to be processed on the same machine with no intermediate jobs in-between (but idle time is allowed), have never been studied in the literature. We present four exact methods to solve the problem: two methods use integer linear programming, one uses constraint programming, and one uses a combinatorial Benders’ decomposition. We introduce method-specific strategies to model the contiguity constraints for each of the proposed methods. We empirically evaluate, through an extensive set of computational experiments, the performance of the four methods on a heterogeneous dataset composed of real, realistic, and random instances, and outline that every method offers a competitive advantage on a targeted subset of instances. We also show that our algorithms can be generalized to solve related scheduling problems with contiguity constraints.

Self-adaptive General Variable Neighborhood Search algorithm for parallel machine scheduling with unrelated servers

This paper introduces a machine learning-augmented General Variable Neighborhood Search algorithm, termed Self-adaptive General Variable Neighborhood Search (SGVNS), for solving the two-identical parallel machine scheduling problem with unrelated servers. The studied problem is of high practical relevance in various industries and presents a significant gap in the existing literature. The motivation for this study stems from the healthcare industry, specifically surgery scheduling with limited anesthesiologists’ availability. Two mathematical formulations are presented to solve this scheduling problem. However, these formulations are limited to small-scale problems, prompting the need for an efficient metaheuristic. Therefore, a novel variant of the General Variable Neighborhood Search metaheuristic is developed, incorporating a self-adaption mechanism based on an Extreme Learning Machine (ELM) algorithm. Extensive experiments are conducted to assess the performance of the SGVNS metaheuristic on various classes of instances. The results demonstrate the effectiveness and efficiency of SGVNS in solving previously unsolved small-sized instances, outperforming both formulations while maintaining reasonable computation times.

Machine scheduling with restricted rejection: An Application to task offloading in cloud–edge collaborative computing

With the burgeoning of the Internet of everything, the amount of data generated by edge devices increases dramatically. In order to relieve the huge pressure of the could computing center, a popular computing scheme, called edge computing, is to select and process part of the computation tasks on edge servers of the network. In this paper we model the task offloading problem motivated by the popular Cloud–Edge Collaborative Computing Frame as a parallel-machine scheduling problem with restricted job rejection. We present an easy-to-implement heuristic with worst-case bound analysis and polynomial time approximation schemes for the general problem and some of the important special cases.

A Biobjective Optimization for Integrated Parallel Machine Scheduling and Location Problem: Mathematical Model and Iterative Two-Stage Heuristic

A Biobjective Optimization for Integrated Parallel Machine Scheduling and Location Problem: Mathematical Model and Iterative Two-Stage Heuristic