Dynamic Scheduling on a Single Batch Processing Machine with Split Compatibility Graphs

This paper considers online scheduling with incompatible job families on single batch processing machine and parallel batchprocessing machines. Online algorithm is developed and the performance ratio of the algorithm is analyzed for the problem under consideration, respectively.

An effective hybrid multi-objective genetic algorithm for bi-criteria scheduling on a single batch processing machine with non-identical job sizes

A new scheduling model in which both two-agent and a batch processing machine with non-identical job sizes exist is considered in this paper. Two agents compete to process their respective job sets on a common single batch processing machine. The objectives of the two agents are both to minimize the makespan. It is proved in the literature[7] that the complexity of minimizing makespan of one agent on a single batch processing machine with non-identical job sizes is NP-hard in the strong sense. We developed an improved ant colony optimal algorithm to search for the Pareto optimal solutions. The experimental results showed that the proposed algorithm could get better non-dominated solutions compared with the non-dominated sorting genetic algorithm (NSGA-II) which was widely used in solving the multi-objective optimization problem.

This paper considers the problem of minimizing makespan on a single batch-processing machine considering preventive maintenance. A mathematical model for integrating flexible preventive maintenance into the batch-processing machine scheduling is proposed. A two-stage method is proposed to solve the problem. A batching rule considering maintenance is proposed to group jobs into batches firstly. And then we improve existing heuristics to schedule production and maintenance. Computational results indicate that the two-stage method based on proposed batching rule and improved heuristics is effective.

Earliness–tardiness minimization on scheduling a batch processing machine with non-identical job sizes

This research aims to adopt two robust optimisation approaches for a real-world flow shop manufacturing system with batch processing machines, where the processing time and size of job are non-deterministic and uncertain. Each machine can process multiple jobs simultaneously as long as the machine capacity is not exceeded. Two important decisions are required: (1) grouping jobs into batches and (2) scheduling the established batches on machines. A mathematical optimisation model is presented, and then two famous robust optimisation approaches are adopted for the purpose of converting the deterministic model to the robust one. An efficient particle swarm optimisation (PSO) algorithm is developed to solve the problem in a reasonable time. In order to verify the developed model and evaluate the performance of our proposed algorithm, a set of small to large test problems are generated, and a simulation approach and a commercial optimisation solver are used to solve these problems. Analysis of the implementation of two independent robust optimisation methods is performed by the paired t-test on all of the test problems. Furthermore, the Taguchi method, as a statistical optimisation technique, is employed to investigate the appropriate level of PSO parameters.

Motivated by applications in porcelain-making companies, we consider a type of optimization problems for batch-processing operations. In production, a single batch-processing machine with a fixed capacity is used to process jobs. Several jobs can be processed together if their total size is no more than the machine capacity. Batch-position-based learning effects are considered because workers become skillful gradually after they perform the processing task repeatedly. The actual processing time of a batch is a decreasing function of its position in production. The objective is to minimize makespan and we consider three different problems. In the first problem, jobs have identical sizes and we present an algorithm which can find optimal solutions in polynomial time. In the second problem, jobs have identical processing times and we show the problem is NP-hard in the strong sense. We propose an approximation algorithm with an absolute performance guarantee of 1.5 and asymptotic performance guarantee of 1.223. In the third problem, jobs have non-identical sizes and processing times simultaneously. We propose an algorithm with an absolute and asymptotic performance guarantee of 2. Besides, we present the evolution of the performance guarantee and provide managerial insights for decision makers of manufacturing companies.

This paper aims at minimizing the total completion time for a single batch processing machine with non-identical job sizes. For this problem, each job has a corresponding processing time and size. The machine can process the jobs in batches as long as the total size of all the jobs in a batch does not exceed the machine capacity. The processing time of a batch is equal to the longest processing time among all the jobs in that batch. This problem is NP-hard and hence a chaotic ant colony optimization algorithm based on batch sequence (BCACO) is proposed. Random instances were used to test the effectiveness of the proposed approach. Computational results show that BCACO significantly outperforms other algorithms addressed in the literature.

In this paper, we consider a scheduling problem for a single batch processing machine in semiconductor wafer fabrication facilities (wafer fabs). An integrated objective function that combines the total weighted tardiness (TWT) and the electricity cost (EC) is considered. A time-of-use (TOU) tariff is assumed. A genetic programming (GP) procedure is proposed to automatically discover dispatching rules for list scheduling approaches. Results of designed computational experiments demonstrate that the learned dispatching rules lead to high-quality schedules in a short amount of computing time.

A novel algorithm called Free Search (FS) is applied to solve the scheduling problems on a single batch processing machine with non-identical job sizes (NSBM) in this paper. The concept of sensibility was introduced in FS, with which the algorithm had norestriction of the probability to zero for the parts of the search space and thus it could avoid premature convergence. In order to make it feasible to NSBM problem, we modify the parameters settings and also provide coding by vector method which makes FS proper to discrete problem. Then the algorithm of batching based FS (BFS) is proposed. In the experiment, all levels of instances are simulated and the results show that BFS has better performance on global search and outperforms other algorithm in the literature.

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.

The General Scheduling Problem (GSP) generalizes scheduling problems with sum of cost objectives such as weighted flow time and weighted tardiness. Given a set of jobs with processing times, release dates, and job dependent cost functions, we seek to find a minimum cost preemptive schedule on a single machine. The best known algorithm for this problem and also for weighted flow time/tardiness is an O(loglog P)-approximation (where P denotes the range of the job processing times), while the best lower bound shows only strong NP-hardness. When release dates are identical there is also a gap: the problem remains strongly NP-hard and the best known approximation algorithm has a ratio of e+\epsilon (running in quasi-polynomial time). We reduce the latter gap by giving a QPTAS if the numbers in the input are quasi-polynomially bounded, ruling out the existence of an APX-hardness proof unless NP\subseteq DTIME(2^polylog(n)). Our techniques are based on the QPTAS known for the UFP-Cover problem, a particular case of GSP where we must pick a subset of intervals (jobs) on the real line with associated heights and costs. If an interval is selected, its height will help cover a given demand on any point contained within the interval. We reduce our problem to a generalization of UFP-Cover and use a sophisticated divide-and-conquer procedure with interdependent non-symmetric subproblems. We also present a pseudo-polynomial time approximation scheme for two variants of UFP-Cover. For the case of agreeable intervals we give an algorithm based on a new dynamic programming approach which might be useful for other problems of this type. The second one is a resource augmentation setting where we are allowed to slightly enlarge each interval.

Batch processing machine (BPM) scheduling problem is a NP hard problem for it includes machine allocation, job grouping, and batch scheduling. In this paper, to address the BPM scheduling problem with unrelated parallel machine, a multiobjective algorithm based on multipopulation coevolution is proposed to minimize the total energy consumption and the completion time simultaneously. Firstly, the mixed integer programming model of the problem is established, and four heuristic decoding rules are proposed. Secondly, to improve the diversity and convergence of the algorithm, the population is divided into two populations: each of the populations evolves independently by using different decoding rules, and the two populations will communicate through a common external archive set every certain number of generations. Thirdly, an initialization strategy and a variable neighborhood search algorithm (VNS) are proposed to improve the overall performance of the algorithm. Finally, in order to evaluate the proposed algorithm, a large number of comparative experiments with the state-of-the-art multiobjective algorithms are carried out, and the experimental results proved the effectiveness of the proposed algorithm.

In this paper we consider a single machine preemptive scheduling problem to minimize the weighted number of late jobs. There are given n jobs and for each job we have a release date, a processing time and a due date. It is assumed that certain specified jobs have to be completed on time. The due dates for these jobs are considered as deadlines. while for the other jobs due dates may be violated. For the case of similarly ordered release and due dates (when there is no advantage to preemption) as well as for the case of embedded release and due date intervals and preemption allowed, we transform the initial problem into a reduced problem, where all jobs with deadlines are eliminated. It gives an opportunity to propose O(n log n) algorithms for some special cases of the considered problems.

This paper focuses on the scheduling problem of minimizing makespan for a given set of jobs in a two-stage hybrid flowshop subject to a product-mix ratio constraint. There are identical parallel machines at the first stage of the hybrid flowshop, while there is a single batch-processing machine at the second stage. Ready times of the jobs (at the first stage) may be different, and a given product-mix ratio of job types should be kept in each batch at the second stage. We present three types of heuristic algorithms: forward scheduling algorithms, backward scheduling algorithms, and iterative algorithms. To evaluate performance of the suggested algorithms, a series of computational experiments are performed on randomly generated test problems and results are reported.