A joint GA+DP approach for single burn-in oven scheduling problems with makespan criterion

This research is motivated by the scheduling problem found in the burn-in operation of semiconductor final testing, where jobs are associated with release times, processing times, and sizes. The burn-in ovens are modeled as batch-processing machines which can process a batch of several jobs as long as the total sizes of the jobs do not exceed the machine capacity, and the processing time of a batch is equal to the longest time among all the jobs in the batch. Moreover, this paper attempts to schedule jobs on a single batch-processing machine to minimize makespan. A joint GA+DP algorithm is proposed involving two stages: (1) the formation of job sequence by genetic algorithm operators, and (2) the formation of batches by a dynamic programming algorithm. Computational experiments are given to examine the performance of the proposed algorithm. The experimental results indicate that the joint GA+DP approach has well improved on all instances with respect to solution quality and runtime.     

A hybrid genetic algorithm to minimize makespan for the single batch machine dynamic scheduling problem

This paper considers a single batch machine dynamic scheduling problem, which is readily found in the burn-in operation of semiconductor manufacturing. The batch machine can process several jobs as a batch simultaneously, within the capacity limit of the machine, and the processing time is represented by the longest processing time among all jobs in a batch. For a single batch machine problem with arbitrary job release time, we proposed an improved algorithm (merge-split procedure) to refine the solution obtained by the LPT-BFF heuristic, and two versions of a hybrid genetic algorithm (GA) are introduced in this paper. Each version of the hybrid GA diversifies job sequences using the GA operators in stage 1, forms batches in stage 2, and finally sequence the batches in stage 3. The difference is that merge-split procedures are involved in the second version of the hybrid GA. Computational experiments showed that the hybrid GA would obtain satisfactory average solution quality and the merge-split procedures would be good at reinforcing the solution consistency of the hybrid GA.     

Flow shop scheduling with two batch processing machines and nonidentical job sizes

A batch processing machine can process several jobs simultaneously. In this research, we consider the problem of a two-stage flow shop with two batch processing machines to minimize the makespan. We assume that the processing time of a batch is the longest processing time among all the jobs in that batch and the sizes of the jobs are nonidentical. There is a limitation on batch sizes and the sum of job sizes in a batch must be less than or equal to the machine capacity. Since this problem is strongly nondeterministic polynomial time hard, we propose two heuristic algorithms. The first one is knowledge-based and the other is based on the batch first fit heuristic proposed previously. To further enhance the solution quality, two different simulated annealing (SA) algorithms based on the two constructive heuristics is also developed. Since heuristic methods for this problem has not been proposed previously, a lower bound is developed for evaluating the performance of the proposed methods. Several test problems have been solved by SAs and lower bound method and the results are compared. Computational studies show that both algorithms provide good results but the first SA (ARSA) algorithm considerably outperforms the second one (FLSA). In addition, the results of ARSA algorithm, optimal solutions, and lower bounds are compared for several small problems. The comparisons show that except for one instance, the ARSA could find the optimal solutions and the proposed lower bound provides small gaps comparing with the optimal solutions.     

Minimizing total weighted tardiness on heterogeneous batch processing machines with incompatible job families

This paper addresses a specific class of scheduling parallel batching problem, which is observed in steel casting industries. The focus of this research is to minimize the total weighted tardiness on heterogeneous batch processing machines under conditions of dynamic job arrivals, incompatible job families and non-identical job sizes. This type of parallel batching problem arises in a number of different settings, including diffusion in wafer fabrication, heat treatment operations in aircraft industries, and metal working. The problem is viewed as a three stage-decision-problem: the first stage involves selecting a machine from the heterogeneous batch processing machines for scheduling; the second stage involves the selection of a job family from the available incompatible job families; and the third stage involves the selection of a set of jobs to create a batch from the selected job family based on the capacity of the selected batch-processing machine. Since the problem is NP-hard, a few greedy heuristics are proposed. The computational experiments show that the proposed greedy heuristic algorithms are capable of consistently obtaining near-optimal solutions (statistically estimated) in very reasonable computational time on a Pentium III 650 Mz with 128 MB RAM.     

Minimizing total weighted tardiness on heterogeneous batch processing machines with incompatible job families

This paper addresses a specific class of scheduling parallel batching problem, which is observed in steel casting industries. The focus of this research is to minimize the total weighted tardiness on heterogeneous batch processing machines under conditions of dynamic job arrivals, incompatible job families and non-identical job sizes. This type of parallel batching problem arises in a number of different settings, including diffusion in wafer fabrication, heat treatment operations in aircraft industries, and metal working. The problem is viewed as a three stage-decision-problem: the first stage involves selecting a machine from the heterogeneous batch processing machines for scheduling; the second stage involves the selection of a job family from the available incompatible job families; and the third stage involves the selection of a set of jobs to create a batch from the selected job family based on the capacity of the selected batch-processing machine. Since the problem is NP-hard, a few greedy heuristics are proposed. The computational experiments show that the proposed greedy heuristic algorithms are capable of consistently obtaining near-optimal solutions (statistically estimated) in very reasonable computational time on a Pentium III 650 Mz with 128 MB RAM.     

Heuristics for makespan minimization on parallel batch processing machines with unequal job ready times

This research aims at minimizing the makespan of a set of identical batch processing machines arranged in parallel. Each job is defined by its processing time, ready time, and size. Each machine can process several jobs simultaneously as long as the machine capacity is not exceeded. The batch processing and ready times depend upon the batch composition. The batch processing time is equal to the longest processing job in the batch, and the batch ready time is equal to the largest ready time among those jobs in the batch. The problem under study is NP-hard. Consequently, a constructive heuristic is proposed and its performance with respect to solution quality and computational cost is compared against other solution approaches found in the literature. The computational experiments on a set of randomly generated instances show that the performance of the proposed heuristic is competitive with respect to solution quality and requires little computational cost.     

Scheduling identical parallel machines with machine eligibility restrictions to minimize total weighted flowtime in automobile gear manufacturing

In this paper, we address a scheduling problem for minimizing total weighted flowtime, observed in automobile gear manufacturing. Specifically, the bottleneck operation of the pre-heat treatment stage of gear manufacturing process has been dealt with in scheduling. Many real-life scenarios like unequal release times, sequence dependent setup times, and machine eligibility restrictions have been considered. A mathematical model taking into account dynamic starting conditions has been proposed. The problem is derived to be NP-hard. To approach the problem, a few heuristic algorithms have been proposed. Based on planned computational experiments, the performance of the proposed heuristic algorithms is evaluated: (a) in comparison with optimal solution for small-size problem instances and (b) in comparison with the estimated optimal solution for large-size problem instances. Extensive computational analyses reveal that the proposed heuristic algorithms are capable of consistently yielding near-statistically estimated optimal solutions in a reasonable computational time.     

Greedy randomised dispatching heuristics for the single machine scheduling problem with quadratic earliness and tardiness penalties

In this paper, we present greedy randomised dispatching heuristics for the single-machine scheduling problem with quadratic earliness and tardiness costs and no machine idle time. The several heuristic versions differ, on the one hand, on the strategies involved in the construction of the greedy randomised schedules. On the other hand, these versions also differ on whether they employ only a final improvement step or perform a local search after each greedy randomised construction. The proposed heuristics were compared with existing procedures as well as with optimum solutions for some instance sizes. The computational results show that the proposed procedures clearly outperform their underlying dispatching heuristic, and the best of these procedures provide results that are quite close to the optimum. The best of the proposed algorithms is the new recommended heuristic for large instances as well as a suitable alternative to the best existing procedure for the larger of the middle-sized instances.     

Scheduling algorithms for two-stage reentrant hybrid flow shops: minimizing makespan under the maximum allowable due dates

We consider the scheduling problem in hybrid flow shops that consist of two stages in series, each of which has multiple identical parallel machines. Each job has reentrant flow, i.e., the job visits each production stage several times. The problem is to determine the allocation of jobs to machines as well as the sequence of the jobs assigned to each machine for the objective of minimizing makespan subject to the maximum allowable due dates in the form of a constraint set with a certain allowance. To solve the problem, two types of algorithms are suggested: (a) a branch and bound algorithm that gives optimal semi-permutation schedules; and (b) heuristic algorithms that give non-permutation schedules. To show their performances, computational experiments were done on a number of test problems and the results are reported. In particular, one of the heuristics is competitive to the branch and bound algorithm with respect to the solution quality while requiring much shorter computation times.     

A heuristic algorithm for the just-in-time single machine scheduling problem with setups: a comparison with simulated annealing

This paper addresses the single machine early/tardy problem with unrestricted common due date and sequence-dependent setup times. Two algorithms are introduced to reach near-optimum solutions: the SAPT, a heuristic tailored for the problem, and a simulated annealing (SA) algorithm. It will be shown that SA provides solutions with slightly better quality; however, SAPT requires much less computational time. SAPT-SA is a hybrid heuristic that combines both approaches to obtain high quality solutions with low computational cost. Solutions provided by the three algorithms were compared to optimal solutions for problems with up to 25 jobs and to each other for larger problems.     

A branch-and-bound and heuristic algorithm for the single-machine time-dependent scheduling problem

The time-dependent scheduling problems have received considerable attention recently. However, machine availability, an important and practical consideration, is usually neglected. Motivated by this observation, we introduce a single-machine scheduling problem where deteriorating jobs and an availability constraint are considered. Our objective is to minimize the total completion time. In this paper, we derived optimal and near-optimal solutions for the problem, and we also gave a simulation study to show that our algorithm successfully yields the optimal solution for instances with less than 20 jobs in less than a minute. Our computational experiment also showed that the mean error percentage of the proposed heuristic algorithm for all test instances is less than 1.3% and drops to zero as the number of jobs increases.     

Sequencing heuristic for scheduling jobs with dependent setups in a manufacturing system

In this paper we discuss a single-machine scheduling problem with machine maintenance. In many production systems, the sequence-dependent setup time of a job cannot be ignored when a switch between two different jobs occurs. In our research, we develop a heuristic to minimize the completion time, or equivalently the total setup time subject to maintenance and due dates. The heuristic consists of three procedures: the initialization procedure, the Stinson heuristic procedure and the iterative procedure. Computational performance of the heuristic is evaluated by comparing its solution with the solution of the branch-and-bound algorithm. The performance of the heuristic on various sizes problems is provided.     

Minimization of total tardiness on unrelated parallel machines with sequence- and machine-dependent setup times under due date constraints

The unrelated parallel machine scheduling problem with sequence- and machine-dependent setup times in the presence of due date constraints represents an important but relatively less-studied scheduling problem in the literature. In this study, a simple iterated greedy (IG) heuristic is presented to minimize the total tardiness of this scheduling problem. The effectiveness and efficiency of the proposed IG heuristic are compared with existing algorithms on a benchmark problem dataset used in earlier studies. Extensive computational results indicate that the proposed IG heuristic is capable of obtaining significantly better solutions than the state-of-the-art algorithms on the same benchmark problem dataset with similar computational resources.     

Genetic algorithms for minimizing makespan in a flow shop with two capacitated batch processing machines

This paper considers a flow shop with two batch processing machines. The processing times of the job and their sizes are given. The batch processing machines can process multiple jobs simultaneously in a batch as long as the total size of all the jobs in a batch does not exceed its capacity. When the jobs are grouped into batches, the processing time of the batch is defined by the longest processing job in the batch. Batch processing machines are expensive and a bottleneck. Consequently, the objective is to minimize the makespan (or maximize the machine utilization). The scheduling problem under study is NP-hard, hence, a genetic algorithm (GA) is proposed. The effectiveness (in terms of solution quality and run time) of the GA approach is compared with a simulated annealing approach, a heuristic, and a commercial solver which was used to solve a mixed-integer formulation of the problem. Experimental study indicates that the GA approach outperforms the other approaches by reporting better solution.     

多工艺路线的批量生产调度优化

以优化生产周期为目标,研究了多工艺路线的批量调度问题,提出了一种基于工序优先级的调度算法,并将该算法嵌入到遗传算法中,得到了全局优化的批量调度算法。遗传算法搜索最佳染色体,调度算法把染色体解码为调度。在调度算法中,采用了3种提高生产率的策略,即区分批量启动时间与工序加工时间,在工件到达机床之前做好准备工作;把一批工件分成多个小生产批次,每批次独立加工:一批工件加工部分后就运向后续加工机床,缩小后续机床的等待时间。仿真表明,该调度方法能取得较好结果。     

GRASP to minimize makespan for a capacitated batch-processing machine

This paper presents a Greedy Randomized Adaptive Search Procedure (GRASP) to minimize the makespan of a capacitated batch-processing machine. Given a set of jobs and their processing times and sizes, the objective is to group these jobs into batches and schedule the batches on a single batch-processing machine such that the time taken to complete the last batch of jobs (or makespan) is minimized. The batch-processing machine can process a batch of jobs simultaneously as long as the total size of all the jobs in that batch does not exceed the machine capacity. The batch-processing time is equal to the longest processing time for a job in the batch. It has been shown that the problem under study is non-deterministic polynomial-time hard. Consequently, a GRASP approach was developed. The solution quality of GRASP was compared to other solution approaches such as simulated annealing, genetic algorithm, and a commercial solver through an experimental study. The study helps to conclude that GRASP outperforms other solution approaches, especially on larger problem instances.     

并行多机提前/拖期调度的启发式算法

准时制生产模式要求生产任务必须在交货期内完成.实际生产中这一问题受很多约束的影响变得非常复杂.文章针对任务动态到达、任务转换存在的调整时间和交货期、提前/拖期单位成本各不相同的并行多机上任务排序问题进行了分析,设计了一种解决并行多机提前/拖期调度的启发式近似求解算法.大量实验数据和应用实例充分表明文章所提的启发式算法是有效的.     

Makespan minimization in a job shop with a BPM using simulated annealing

A scheduling problem commonly observed in the metal working industry has been studied in this research effort. A job shop equipped with one batch processing machine (BPM) and several unit-capacity machines has been considered. Given a set of jobs, their process routes, processing requirements, and size, the objective is to schedule the jobs such that the makespan is minimized. The BPM can process a batch of jobs as long as its capacity is not exceeded. The batch processing time is equal to the longest processing job in the batch. If no batches were to be formed, the scheduling problem under study reduces to the classical job shop problem with makespan objective, which is known to be nondeterministic polynomial time-hard. A network representation of the problem using disjunctive and conjunctive arcs, and a simulated annealing (SA) algorithm are proposed to solve the problem. The solution quality and run time of SA are compared with CPLEX, a commercial solver used to solve the mathematical formulation and with four dispatching rules. Experimental study clearly highlights the advantages, in terms of solution quality and run time, of using SA to solve large-scale problems.     

A heuristic for a batch processing machine scheduled to minimise total completion time with non-identical job sizes

This paper studies the problem of scheduling semiconductor burn-in operations, where each job has non-identical lot sizes and an oven (a batch processing machine) that processes several jobs within its capacity limit simultaneously. We present some properties of the problem and an efficient heuristic algorithm. In a computational experiment, pairs of burning operations (,) were presented with the arrival time r_i and processing time p_i for different (,) pairs to examine the effect of arrival time and the processing time on minimising the total completion time. The result shows that a ratio of to greater than 1 was superior to other ratios, which can be a guide for schedule planners of burn-in operations. The heuristic obtains a satisfactory average performance rapidly. This revised version was published online in October 2004 with a correction to the issue number.     

Simple heuristic to minimize total tardiness in a single machine scheduling problem

This paper discusses a simple heuristic to minimize the total tardiness in a single machine scheduling problem. The problem of minimizing total tardiness in single machine scheduling is a combinatorial problem. Hence, heuristic development for such problems is inevitable. In this paper, an attempt has been made to develop a simple heuristic, alternatively called greedy heuristic, to minimize the total tardiness in a single machine scheduling problem with n independent jobs, each having its processing time and due date. Further, its solution accuracy is compared with the optimal solution of a set of randomly generated problems using an ANOVA experiment. From the ANOVA experiment, it is observed that the solution of the simple heuristic proposed in this paper does not differ significantly from the optimal solution at a significance level of 0.05.