Minimizing Makespan for Single Batch Processing Machine with Non-identical Job Sizes Using a Novel Algorithm: Free Search

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 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.

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

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

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.

Energy-efficient scheduling of a single batch processing machine with dynamic job arrival times

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.

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.

The paper addresses the problem scheduling a batch processing machine with multiple incompatible job families, non-identical job dimensions, non-identical job sizes and non-agreeable release dates to minimize makespan. The research problem is solved by proposing a mixed integer programming model that appropriately takes into account the parameters considered in the problem. The proposed is validated using a numerical example. The experiment conducted show that the model can pose significant difficulties in solving the large scale instances. The paper concludes by giving the scope for future work and some alternative approaches one can use for solving these class of problems.

We consider the problem of minimizing the makespan on a batch processing machine, in which jobs are not all compatible. Only compatible jobs can be included into the same batch. This relation of compatibility is represented by a split graph. Jobs have release dates. The capacity of the batch processing machine is finite or infinite. The processing time of a batch is given by the processing time of the longest job in the batch. We establish the NP-hardness of the general problem and present polynomial algorithms for several special cases. Relating scheduling theory and graph theory appears to be an interesting and important concept.

We consider the train delivery problem which is a generalization of the bin packing problem and is equivalent to a one dimensional version of the vehicle routing problem with unsplittable demands. The problem is also equivalent to the problem of minimizing the makespan on a single batch machine with non-identical job sizes. The train delivery problem is strongly NP-hard and does not admit an approximation ratio better than 3/2. We design the first approximation schemes for the general problem. We give an asymptotic polynomial time approximation scheme, under a notion of asymptotic that makes sense even though scaling can cause the cost of the optimal solution of any instance to be arbitrarily large. Alternatively, we give a polynomial time approximation scheme for the case where W, an input parameter that corresponds to the bin size or the vehicle capacity, is polynomial in the number of items or demands.

In this paper we study the problem of scheduling a batching machine with nonidentical job sizes. The jobs arrive simultaneously and have unit processing time. The goal is to minimize the total completion times. Having shown that the problem is NP-hard, we put forward three approximation schemes with worst case ratio 4, 2, and \(\frac{3}{2}\), respectively.

In this paper, we consider the problem of scheduling semiconductor burn-in operation, where the burn-in oven is modelled as a batch processing machine. In this study, both oven capacity and the number of boards available are taken as constraints. The objective measure of the problem is minimising the total completion time of all jobs. The computational difficulty in getting optimal solution is shown empirically. Since the problem under study is NP-hard, two variants of Tabu Search method are proposed. A series of computational experiments show that the proposed variants of Tabu Search method outperforms the existing heuristic for most system configurations in very meagre CPU times on P4 machine.

Artificial bee colony (ABC) algorithm invented by Karaboga has been proved to be an efficient technique compared with other biological-inspired algorithms for solving numerical optimization problems. Unfortunately, convergence speed of ABC is slow when working with certain optimization problems and some complex multimodal problems. Aiming at the shortcomings, a hybrid artificial bee colony algorithm is proposed in this paper. In the hybrid ABC, an improved search operator learned from Differential Evolution (DE) is applied to enhance search process, and a not-so-good solutions selection strategy inspired by free search algorithm (FS) is introduced to avoid local optimum. Especially, a reverse selection strategy is also employed to do improvement in onlooker bee phase. In addition, chaotic systems based on the tent map are executed in population initialization and scout bee's phase. The proposed algorithm is conducted on a set of 40 optimization test functions with different mathematical characteristics. The numerical results of the data analysis, statistical analysis, robustness analysis and the comparisons with other state-of-the-art-algorithms demonstrate that the proposed hybrid ABC algorithm provides excellent convergence and global search ability.

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.