Job Release Times Research Articles

A simplified swarm optimization algorithm to minimize makespan on non-identical parallel machines with unequal job release times under non-renewable resource constraints

A simplified swarm optimization algorithm to minimize makespan on non-identical parallel machines with unequal job release times under non-renewable resource constraints

Approximation of the Objective Function of Single-Machine Scheduling Problem

The problem of the approximation of the coefficients of the objective function of a scheduling problem for a single machine is considered. It is necessary to minimize the total weighted completion times of jobs with unknown weight coefficients when a set of problem instances with known optimal schedules is given. It is shown that the approximation problem can be reduced to finding a solution to a system of linear inequalities for weight coefficients. For the case of simultaneous job release times, a method for solving the corresponding system of inequalities has been developed. Based on it, a polynomial algorithm for finding values of weight coefficients that satisfy the given optimal schedules was constructed. The complexity of the algorithm is O(n2(N+n)) operations, where n is the number of jobs and N is the number of given instances with known optimal schedules. The accuracy of the algorithm is estimated by experimentally measuring the function ε(N,n)=1n∑j=1n∣wj−wj0∣wj0, which is an indicator of the average modulus of the relative deviation of the found values wj from the true values wj0. An analysis of the results shows a high correlation between the dependence ε(N,n) and a function of the form α(n)/N, where α(n) is a decreasing function of n.

Single Machine Scheduling Proportionally Deteriorating Jobs with Ready Times Subject to the Total Weighted Completion Time Minimization

In this paper, we investigate a single machine scheduling problem with a proportional job deterioration. Under release times (dates) of jobs, the objective is to minimize the total weighted completion time. For the general condition, some dominance properties, a lower bound and an upper bound are given, then a branch-and-bound algorithm is proposed. In addition, some meta-heuristic algorithms (including the tabu search (TS), simulated annealing (SA) and heuristic (NEH) algorithms) are proposed. Finally, experimental results are provided to compare the branch-and-bound algorithm and another three algorithms, which indicate that the branch-and-bound algorithm can solve instances of 40 jobs within a reasonable time and that the NEH and SA are more accurate than the TS.

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.

Mathematical models for multi-stage hybrid assembly flow-shop scheduling with preventive maintenance and release times

Effective job scheduling is crucial in production to reduce costs, improve customer satisfaction, enhance efficiency, and boost competitiveness, leading to transformative impacts in production environments. This article presents a pioneering approach that addresses assembly and processing at multiple stages in the scheduling process. Specifically, we introduce the first formulation of mixed integer linear programs (MILP) for a Multi-stage Hybrid Assembly Flow-shop with identical parallel machines. The models incorporate considerations for job release times and service tasks to implement preventive maintenance and effectively captures the intricacies of a Multistage Assembly flow-shop. Existing literature in Assembly flow-shop scheduling primarily focuses on the two-stage assembly flow-shop scheduling problem (TSAFSP) and its extensions, such as the three-stage assembly flow-shop scheduling problem, the Distributed two-stage assembly flow-shop scheduling problem (DTSAFSP), the Distributed assembly permutation flow-shop Scheduling Problem (DAPFSP), and the multi-stage assembly flow shop (MSAF). Our work deals with a challenging NP-hard problem. Inspired by a real-life production site dedicated to manufacturing heavy machinery, we validate our proposed mathematical models by solving various instances of the problem using exact methods. The experimental results confirm the effectiveness and robustness of our approach in tackling multi-stage hybrid assembly flow shop scheduling challenges.

A Trajectory-Based Immigration Strategy Genetic Algorithm to Solve a Single-Machine Scheduling Problem with Job Release Times and Flexible Preventive Maintenance

This paper considers the single-machine problem with job release times and flexible preventive maintenance activities to minimize total weighted tardiness, a complicated scheduling problem for which many algorithms have been proposed in the literature. However, the considered problems are rarely solved by genetic algorithms (GAs), even though it has successfully solved various complicated combinatorial optimization problems. For the problem, we propose a trajectory-based immigration strategy, where immigrant generation is based on the given information of solution extraction knowledge matrices. We embed the immigration strategy into the GA method to improve the population’s diversification process. To examine the performance of the proposed GA method, two versions of GA methods (the GA without immigration and the GA method with random immigration) and a mixed integer programming (MIP) model are also developed. Comprehensive experiments demonstrate the effectiveness of the proposed GA method by comparing the MIP model with two versions of GA methods. Overall, the proposed GA method significantly outperforms the other GA methods regarding solution quality due to the trajectory-based immigration strategy.

A SIMULATED ANNEALING PROCEDURE TO MINIMIZE TOTAL WEIGHTED TARDINESS ON A SINGLE MACHINE WITH UNEQUAL JOB RELEASE TIME, SEQUENCE DEPENDENT SETUP TIME, AND MACHINE DOWN TIME

ABSTRACT In this study, we explored a scheduling problem with machine down time, unequal job release time, and sequence dependent setup time to minimize the total weighted tardiness on a single machine. The ATCS rule (Apparent Tardiness Cost with Setup time Rule, Lee et al. 1997) was modified first and then presented with a simulated annealing procedure. Experimental results revealed that the performance of the new simulated annealing procedure outperformed the modified Lin''s simulated annealing method (Lin and Ying, 2007) in the total weighted tardiness reduction. Keywords single machine, simulated annealing, dependent setup time, release time, machine down time.

Application of a Non-Dominated Sorting Genetic Algorithm to Solve a Bi-Objective Scheduling Problem Regarding Printed Circuit Boards

An unrelated parallel machine scheduling problem motivated by the scheduling of a printed circuit board assembly (PCBA) under surface mount technology (SMT) is discussed in this paper. This problem involved machine eligibility restrictions, sequence-dependent setup times, precedence constraints, unequal job release times, and constraints of shared resources with the objectives of minimizing the makespan and the total job tardiness. Since this scheduling problem is NP-hard, a mathematical model was first built to describe the problem, and a heuristic approach using a non-dominated sorting genetic algorithm (NSGA-II) was then designed to solve this bi-objective problem. Multiple near-optimal solutions were provided using the Pareto front solution and crowding distance concepts. To demonstrate the efficiency and effectiveness of the proposed approach, this study first tested the proposed approach by solving test problems on a smaller scale. It was found that the proposed approach could obtain optimal solutions for small test problems. A real set of work orders and production data was provided by a famous hardware manufacturer in Taiwan. The solutions suggested by the proposed approach were provided using Gantt charts to visually assist production planners to make decisions. It was found that the proposed approach could not only successfully improve the planning time but also provide several feasible schedules with equivalent performance for production planners to choose from.

Model for Selecting Optimal Dispatching Rules Based Real-time Optimize Job Shop Scheduling Problem

Owing to the randomness of the job release time, it is not possible to obtain all job information in real time during the operation of a manufacturing system. Generating a suitable scheduling strategy at the correct moment is the focus of addressing this disturbance. In this study, the flow time of the job in the manufacturing system was used as a criterion for evaluating the performance of the scheduling strategy. Subsequently, a model was constructed for selecting the optimal dispatching rule (DR) to actively change the scheduling strategies during the production process. The constructed model for selecting the optimal DR included an initial model for selecting the optimal DR and an evaluation model. The initial model for selecting the optimal DR outputs a DR with better performance based on the attributes of the job to be scheduled in the manufacturing system. Meanwhile, the evaluation model is responsible for evaluating the DR output of the initial model for selecting the optimal DR and determining whether the DR needs to be updated; the update process is realized based on simulation technology. Following experimental verification, the constructed model could generate scheduling strategies with superior performance in real-time and realize the update of the historical database. The results of this study will be of reference significance for solving the disturbance problem encountered by the manufacturing system in real time.

Scheduling identical parallel batch processing machines involving incompatible families with different job sizes and capacity constraints

This paper investigates the problem of scheduling jobs on parallel batch processing machines with incompatible job families, non-identical job sizes, arbitrary job release times, and machine capacity constraints. A mixed-integer linear programming (MILP) model is established to minimize makespan. A lower bound is proposed to test the solution quality obtained from heuristic and metaheuristic algorithms. Since the problem is strongly NP-hard, we propose five constructive and polynomially bounded heuristic algorithms. To improve the solutions obtained by these constructive algorithms, we describe a job family constraint-guided artificial immune system (CGAIS) based algorithm. In the proposed CGAIS algorithm, only jobs in the same family can be executed by the secondary immune response. The longest batch processing time rule is used to form the batches. The effectiveness of the proposed constructive and the CGAIS algorithms is empirically tested on the randomly generated problem instances. These computational results show that the proposed CGAIS algorithm can obtain better near-optimal solutions than the existing algorithms.

Hybrid tabu search algorithm for unrelated parallel machine scheduling in semiconductor fabs with setup times, job release, and expired times

This research is motivated by a scheduling problem arising in the ion implantation process of wafer fabrication. The ion implementation scheduling problem is modeled as an unrelated parallel machine scheduling (UPMS) problem with sequence-dependent setup times that are subject to job release time and expiration time of allowing a job to be processed on a specific machine, defined as: R|rj,eij,STsd|Cmax. The objective is first to maximize the number of processed jobs, then minimize the maximum completion time (makespan), and finally minimize the maximum completion times of the non-bottleneck machines. A mixed-integer programming (MIP) model is proposed as a solution approach and adopts a hybrid tabu search (TS) algorithm to acquire approximate feasible solutions. The MIP model has two phases and attempts to achieve the first two objectives. The hybrid TS algorithm has three phases and attempts to achieve all three objectives. In a real setting, computational results demonstrate that the maximum number of processed jobs can be acquired within a short time utilizing the hybrid TS algorithm (average 8 s). By comparing the two approaches, the TS outperforms the MIP model regarding solution quality and computational time for the second objective, minimizing the makespan. Furthermore, the third phase of the hybrid TS algorithm shows the effectiveness further to enhance the utilization of the ion implantation equipment.

Bi-objective optimization of identical parallel machine scheduling with flexible maintenance and job release times

This paper investigates an identical parallel machine scheduling problem with flexible maintenance and job release times and attempts to optimize two objectives: the minimization of the makespan and total tardiness simultaneously. A mixed-integer programming (MIP) model for solving small-scale instances is presented first, and then a modified NSGA-Ⅱ (M-NSGA-Ⅱ) algorithm is constructed for solving medium- and large-scale instances by incorporating several strategies. These strategies include: (ⅰ) the proposal of a decoding method based on dynamic programming, (ⅱ) the design of dynamic probability crossover and mutation operators, and (ⅲ) the presentation of neighborhood search method. The parameters of the proposed algorithm are optimized by the Taguchi method. Three scales of problems, including 52 instances, are generated to compare the performance of different optimization methods. The computational results demonstrate that the M-NSGA-Ⅱ algorithm obviously outperforms the original NSGA-II algorithm when solving medium- and large-scale instances, although the time taken to solve the instances is slightly longer.

Theoretical and practical issues in single-machine scheduling with two job release and delivery times

Theoretical and practical issues in single-machine scheduling with two job release and delivery times

Feature-Extraction-Based Iterated Algorithms to Solve the Unrelated Parallel Machine Problem With Periodic Maintenance Activities

This paper considers an unrelated parallel machine problem with job release times and maintenance activities, in which machines have to periodically undergo maintenance since the status of the machines will be deteriorated by job-induced dirt. The problem is inspired by a wet station for cleaning operations in a semiconductor manufacturing process. The objective is to minimize the makespan. Since the considered problem is proven to be NP-hard, obtaining optimal solutions is almost impossible in a reasonable computational time when the problem becomes large. We develop specific feature-extraction procedures to recognize important information in a job sequence and linkage encoding (LE) procedures to generate new job sequences. The two above procedures are embedded into an iterated algorithm, called a feature-extraction-based iterated algorithm (FEBIA), to obtain optimal or better solutions for the considered problem. To examine the performance of the FEBIA, the FEBIA is compared with two population-based algorithms, the particle swarm optimization (PSO) algorithm and the genetic algorithm (GA), using many test data. The results reveal that the proposed FEBIA perform better than the two population-based algorithms, demonstrating the potential of the FEBIA to solve the unrelated parallel machine problem with periodic maintenance and job release times.

Parallel machine scheduling with stochastic release times and processing times

Stochastic scheduling has received much attention from both industry and academia. Existing works usually focus on random job processing times. However, the uncertainty existing in job release times may largely impact the performance as well. This work investigates a stochastic parallel machine scheduling problem, where job release times and processing times are uncertain. The problem consists of a two-stage decision-making process: (i) assigning jobs to machines on the first stage before the realisation of uncertain parameters (job release times and processing times) and (ii) scheduling jobs on the second stage given the job-to-machine assignment and the realisation of uncertain parameters. The objective is to minimise the total cost, including the setup cost on machines (induced by job-to-machine assignment) and the expected penalty cost of jobs' earliness and tardiness. A two-stage stochastic program is proposed, and the sample average approximation (SAA) method is applied. A scenario-reduction-based decomposition approach is further developed to improve the computational efficiency. Numerical results show that the scenario-reduction-based decomposition approach performs better than the SAA, in terms of solution quality and computation time.

A robust dynamic scheduling approach based on release time series forecasting for the steelmaking-continuous casting production

In this work, the dynamic scheduling problem is investigated considering the uncertainty of the job release time in steelmaking-continuous casting production processes. In contrast to existing dynamic scheduling strategies, a novel robust dynamic scheduling approach based on release time series forecasting (RDSA_RTSF) is proposed. The proposed RDSA_RTSF consists of two stages, i.e., offline preparation and online robust dynamic scheduling. In the offline preparation stage, a release time series forecasting model is established using historical data, and the forecasting accuracy of the model is calculated. In the online robust dynamic scheduling stage, a chance constrained programming (CCP) model is built first for rescheduling based on the predicted release time series and the statistical information of the forecasting accuracy. A robust schedule is subsequently generated by using a Monte Carlo simulation and an evolutionary algorithm to solve the CCP model. The evolutionary algorithm is formulated by combining a genetic algorithm with a local search strategy based on the problem characteristics. Computational experiments based on real data from a steel plant in China show that the proposed RDSA_RTSF strategy performs better than classical approaches in obtaining robust schedule results under a dynamic environment with uncertain release times.

Dynamic Restructuring Framework for Scheduling with Release Times and Due-Dates

Scheduling jobs with release and due dates on a single machine is a classical strongly NP-hard combination optimization problem. It has not only immediate real-life applications but also it is effectively used for the solution of more complex multiprocessor and shop scheduling problems. Here, we propose a general method that can be applied to the scheduling problems with job release times and due-dates. Based on this method, we carry out a detailed study of the single-machine scheduling problem, disclosing its useful structural properties. These properties give us more insight into the complex nature of the problem and its bottleneck feature that makes it intractable. This method also helps us to expose explicit conditions when the problem can be solved in polynomial time. In particular, we establish the complexity status of the special case of the problem in which job processing times are mutually divisible by constructing a polynomial-time algorithm that solves this setting. Apparently, this setting is a maximal polynomially solvable special case of the single-machine scheduling problem with non-arbitrary job processing times.

SCHEDULING IN A SINGLE-SERVER QUEUE WITH STATE-DEPENDENT SERVICE RATES

We consider single-server scheduling to minimize holding costs where the capacity, or rate of service, depends on the number of jobs in the system, and job sizes become known upon arrival. In general, this is a hard problem, and counter-intuitive behavior can occur. For example, even with linear holding costs the optimal policy may be something other than SRPT or LRPT, it may idle, and it may depend on the arrival rate. We first establish an equivalence between our problem of deciding which jobs to serve when completed jobs immediately leave, and a problem in which we have the option to hold on to completed jobs and can choose when to release them, and in which we always serve jobs according to SRPT. We thus reduce the problem to determining the release times of completed jobs. For the clearing, or transient system, where all jobs are present at time 0, we give a complete characterization of the optimal policy and show that it is fully determined by the cost-to-capacity ratio. With arrivals, the problem is much more complicated, and we can obtain only partial results.

Machine scheduling with stochastic release and processing times

Rapid development of technology provides the foundation for the fourth industrial revolution, namely Industry 4.0. The ability to cope with unpredictable and negative events is becoming increasingly important under Industry 4.0 settings. As scheduling plays an important role in the industry system, stochastic scheduling is therefore a rather hot and interesting research topic. Most existing works assume that the job processing times are stochastic, and rarely consider the release time uncertainty. However, in practice, job release times are usually stochastic as well, due to the various factors. This work considers a parallel machine scheduling problem, in which the processing times and release times are both uncertain. The objective is to minimize the expected total weighted earliness and tardiness in a Just-in-Time (JIT) mode. For the problem, a two-stage stochastic programming formulation is first proposed, and then a classic sample average approximation (SAA) and an improved SAA, combined with scenario reduction, are developed. A case study is conducted to illustrate the applicability of the proposed methods.

An iterated greedy algorithm for total flow time minimization in unrelated parallel batch machines with unequal job release times

This paper investigates the problem of scheduling a set of jobs with arbitrary sizes and non-zero release times on a set of unrelated parallel batch machines with different capacities so as to minimize the total flow time of the jobs. The total flow time, defined as the total amount of time that the jobs spend in the system (i.e. the period between the job release dates and its completion times), is one of the most important objectives in scheduling problems, since it can lead to stable utilization of resources and reduction of working-in-process inventory. Motivated by the computational complexity of the problem, a simple and effective iterated greedy (IG) algorithm is proposed to solve it. The IG algorithm uses an efficient greedy heuristic to reconstruct solutions and a local search procedure to further enhance the solution quality. In attempting to obtain optimal solutions for small-medium size instances, a mixed integer programming model for the problem is also presented. The performance of the proposed algorithm is tested on a comprehensive set of small, medium and large benchmark of randomly generated instances, and is compared to three benchmark meta-heuristic algorithms (Discrete Differential Evolution, Ant Colony Optimization and Simulated Annealing) recently proposed for similar parallel batch machine scheduling problems. Experimental results and statistical tests show that the proposed algorithm is significantly superior in performance than the other algorithms.