Dynamic Job Arrivals Research Articles

Metaheuristics to minimise makespan on parallel batch processing machines with dynamic job arrivals

Batch processing machines that can process a group of jobs simultaneously are often encountered in semiconductor manufacturing and metal heat treatment. This research investigates the scheduling problem on parallel batch processing machines in the presence of dynamic job arrivals and non-identical job sizes. The processing time and ready time of a batch are equal to the largest processing time and release time among all jobs in the batch, respectively. This problem is NP-hard in the strong sense, and hence two lower bounds were proposed to evaluate the performance of approximation algorithms. An ERT-LPT heuristic rule was next presented to assign batches to parallel machines. Two metaheuristics, a genetic algorithm (GA) and an ant colony optimisation (ACO) are further proposed using ERT-LPT to minimise makespan. The performances of the two approaches, along with a BFLPT-ERTLPT (BE) heuristic were compared by computational experiments. The results show that both metaheurisitcs outperform BE. GA is able to obtain better solutions when dealing with small-job instances compared to ACO, whereas ACO dominates GA in large-job instances.

A memetic algorithm for minimizing total weighted tardiness on parallel batch machines with incompatible job families and dynamic job arrival

This paper addresses a scheduling problem motivated by scheduling of diffusion operations in the wafer fabrication facility. In the target problem, jobs arrive at the batch machines at different time instants, and only jobs belonging to the same family can be processed together. Parallel batch machine scheduling typically consists of three types of decisions—batch forming, machine assignment, and batch sequencing. We propose a memetic algorithm with a new genome encoding scheme to search for the optimal or near-optimal batch formation and batch sequence simultaneously. Machine assignment is resolved in the proposed decoding scheme. Crossover and mutation operators suitable for the proposed encoding scheme are also devised. Through the experiment with 4860 problem instances of various characteristics including the number of machines, the number of jobs, and so on, the proposed algorithm demonstrates its advantages over a recently proposed benchmark algorithm in terms of both solution quality and computational efficiency.

A PTAS for parallel batch scheduling with rejection and dynamic job arrivals

In the parallel batch scheduling model, a group of jobs can be scheduled together as a batch while the processing time of this batch is the greatest processing time among its members; in the model of scheduling with rejection, any job can be rejected with a corresponding penalty cost added to the objective value. In this paper, we present a PTAS for the combined model of the above two scheduling models where jobs arrive dynamically. The objective is to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected ones. Our basic approaches are dynamic programming and roundings.

New dispatching rules to minimize rejection and tardiness costs in a dynamic flexible flow shop

This paper studies a flexible flow shop system considering dynamic arrival of jobs and the ability of acceptance and rejection of new jobs. The problem objective is to determine a schedule that minimizes sum of the tardiness and rejection costs of jobs. A 0–1 mixed integer model of the problem is formulated. Since this problem class is NP-hard, four dispatching rules have been developed to solve the problem approximately. Moreover, a discrete event simulation model of the flexible flow shop system is developed for the purpose of experimentation. Four dispatching rules from the literature and four new dispatching rules proposed in this paper are incorporated in the simulation model. Simulation experiments have been conducted under various experimental conditions characterized by factors such as shop utilization level, due date tightness and number of stages in flexible flow shop. The results indicate that proposed dispatching rules provide better performance under problem assumptions.

ACO-based multi-objective scheduling of parallel batch processing machines with advanced process control constraints

This research was motivated by a scheduling problem in the dry strip operations of a semiconductor wafer fabrication facility. The machines were modeled as parallel batch processing machines with incompatible job families and dynamic job arrivals, and constraints on the sequence-dependent setup time and the qual-run requirements of advanced process control. The optimization had multiple objectives, the total weighted tardiness (TWT) and makespan, to consider simultaneously. Since the problem is NP-hard, we used an Ant Colony Optimization (ACO) algorithm to achieve a satisfactory solution in a reasonable computation time. A variety of simulation experiments were run to choose ACO parameter values and to demonstrate the performance of the proposed method. The simulation results showed that the proposed ACO algorithm is superior to the common Apparent Tardiness Cost-Batched Apparent Tardiness Cost rule for minimizing the TWT and makespan. The arrival time distribution and the number of jobs strongly affected the ACO algorithm’s performance.

Heuristic algorithms for scheduling heat-treatment furnaces of steel casting industries

This paper addresses a research problem of scheduling parallel, non-identical batch processors in the presence of dynamic job arrivals, incompatible job-families and non-identical job sizes. We were led to this problem through a real-world application involving the scheduling of heat-treatment operations of steel casting. The scheduling of furnaces for heat-treatment of castings is of considerable interest as a large proportion of the total production time is the processing times of these operations. In view of the computational intractability of this type of problem, a few heuristic algorithms have been designed for maximizing the utilization of heat-treatment furnaces of steel casting manufacturing. Extensive computational experiments were carried out to compare the performance of the heuristics with the estimated optimal value (using the Weibull technique) and for relative effectiveness among the heuristics. Further, the computational experiments show that the heuristic algorithms proposed in this paper are capable of obtaining near (statistically estimated) optimal utilization of heat-treatment furnaces and are also capable of solving any large size real-life problems with a relatively low computational effort.

A Complete Multiagent Framework for Robust and Adaptable Dynamic Job Shop Scheduling

This paper presents a complete multiagent framework for dynamic job shop scheduling, with an emphasis on robustness and adaptability. It provides both a theoretical basis and some experimental justifications for such a framework: a job dispatching procedure for a completely reactive scheduling approach, combining real-time and predictive decision making. It resolves various disruptions as flexibly as dispatching rules while providing more stability. It is ready to be implemented in a distributed environment where agents have minimum global information thereby improving system fault tolerance. Computational experiments on dynamic job arrivals provide the experimental justification of the framework. First, a comparison of computational results on unpredictable job arrivals among the presented framework and commonly used dispatching rules is presented to show the effectiveness and robustness of the developed framework. Then, a comparison of the computational results among four cases of dynamic job arrivals is presented to demonstrate the effects of making full use of available uncertain information about disruptions using this framework for the enhancement of scheduling robustness.

Using genetic algorithms (GA) and a coloured timed Petri net (CTPN) for modelling the optimization-based schedule generator of a generic production scheduling system

The semiconductor manufacturing industry is one of the most complicated manufacturing systems in the world. Considering its complex problem nature, such as the unrelated parallel machine environment, dynamic job arrival, non-pre-emption, inseparable sequence-dependent set-up time, multiple-resource requirements, general precedence constraint, and job recirculation, this study proposed the optimization-based schedule generator (OptSG) for solving the generalized scheduling problems arising from the semiconductor manufacturing environment. The separation of the problem structure and problem configuration in OptSG contributes to the structural independence, making OptSG robust and convenient in analysis and problem-solving in real settings with changing properties. Meanwhile, an MILP model was proposed as a benchmark to estimate the validity of OptSG. Inseparable sequence-dependent set-up time and multiple-resource requirements that have not been addressed simultaneously in the literature were considered in this model. By using different evaluation criteria, including makespan, total completion time and maximum tardiness, experiments were conducted to compare the solutions of the MILP model, OptSG and dispatching rule-based heuristics (DRBH). The results validated the solution quality of OptSG.

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.

A genetic algorithm for minimizing maximum lateness on parallel identical batch processing machines with dynamic job arrivals and incompatible job families

We consider the problem of minimizing maximum lateness on parallel identical batch processing machines with dynamic job arrivals. We propose a family of iterative improvement heuristics based on previous work by Potts [Analysis of a heuristic for one machine sequencing with release dates and delivery times. Operations Research 1980;28:1436–41] and Uzsoy [Scheduling batch processing machines with incompatible job families. International Journal for Production Research 1995;33(10):2685–708] and combine them with a genetic algorithm (GA) based on the random keys encoding of Bean [Genetic algorithms and random keys for sequencing and optimization. ORSA Journal on Computing 1994;6(2):154–60]. Extensive computational experiments show that one of the proposed GAs runs significantly faster than the other, providing a good tradeoff between solution time and quality. The combination of iterative heuristics with GAs consistently outperforms the iterative heuristics on their own.

Predictive, Stochastic and Dynamic Extensions to Aversion Dynamics Scheduling

Schedulers' decisions in real factories deal with perceived risks and impacts. They proactively anticipate and reactively mitigate risky events by altering what would be considered a normal schedule to minimize associated impacts. These risk mitigation concepts are called aversion dynamics (AD). Aversion dynamics describes the aversion that jobs exhibit to impacts resulting from risky events in dynamic and unstable production environments. The aversion manifests itself in either advancing or delaying the work to avoid the risky period. This paper extends the first AD heuristic, Averse-1, to capture additional real-world dynamics and to make the heuristic predictive (proactive) as to when the perceived risky event may happen. In particular, predictive and stochastic elements are incorporated within a dynamic job arrival framework to create an extended heuristic called Averse-2.

SCHEDULING ALGORITHMS AND SENSITIVITY ANALYSIS FOR HETEROGENEOUS BATCH PROCESSORS WITH INCOMPATIBLE JOB FAMILIES

We consider the problem of scheduling heterogeneous batch processor under the conditions non-identical job sizes, dynamic job arrivals and incompatible job families. The problem studied in this paper is motivated by heat-treatment operations in the pre-casting stage of steel casting manufacturing. We proposed a few heuristic algorithms with maximizing the average utilization of batch processors as scheduling objective. From the computational experiments carried out, it appears that all the proposed heuristics are yielding very close to the optimum (estimated optimum) average utilization of the batch processors. Further, we carried out a few simple sensitivity analyses. From sensitivity analysis, in general, it appears that there is an influence on the performance of the proposed heuristic algorithms when the input parameter changes. The influence observed is further verified statistically. Finally, it is observed that with respect to the scheduling objective, the choice of the best algorithm(s) do not significantly affected due to changes in the parameters considered.

SCHEDULING ALGORITHMS AND SENSITIVITY ANALYSIS FOR HETEROGENEOUS BATCH PROCESSORS WITH INCOMPATIBLE JOB FAMILIES

ABSTRACT We consider the problem of scheduling heterogeneous batch processor under the conditions non-identical job sizes, dynamic job arrivals and incompatible job families. The problem studied in this paper is motivated by heat-treatment operations in the pre-casting stage of steel casting manufacturing. We proposed a few heuristic algorithms with maximizing the average utilization of batch processors as scheduling objective. From the computational experiments carried out, it appears that all the proposed heuristics are yielding very close to the optimum (estimated optimum) average utilization of the batch processors. Further, we carried out a few simple sensitivity analyses. From sensitivity analysis, in general, it appears that there is an influence on the performance of the proposed heuristic algorithms when the input parameter changes. The influence observed is further verified statistically. Finally, it is observed that with respect to the scheduling objective, the choice of the best algorithm(s) do not significantly affected due to changes in the parameters considered.

Optimal on-line algorithms for scheduling on parallel batch processing machines

We consider the problem of scheduling jobs on-line on parallel batch processing machines with dynamic job arrivals to minimize makespan. We are given m identical batch processing machines, each of which can handle up to B (the capacity of a machine) jobs simultaneously. The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is a constant, which is independent of the number and identity of the jobs. Each job becomes available at its arrival time, which is unknown in advance. First we deal with the unbounded case where the capacity of the batch processing machines is infinite, and derive an optimal on-line algorithm with competitive ratio 1+ g m , where g m >0 is determined by (1+ g m ) m +1 = g m +2. We then consider the bounded case where the capacity B of the batch processing machines is bounded. We provide an on-line algorithm with competitive ratio (\\sqrt{5}+1)/2 (the golden ratio) and prove that the result is the best possible for all m .

Approximation Algorithms in Batch Processing

A polynomial approximation scheme for minimizing makespan in a batch processing system under dynamic job arrivals is presented. A lower bound of $${{(\sqrt 5 + 2)} \mathord{\left/ {\vphantom {{(\sqrt 5 + 2)} 2}} \right. \kern-\nulldelimiterspace} 2}$$ on the competitive ratio of any on-line algorithm is proved. This is matched by an on-line algorithm for the special case of unbounded machine capacity.

A genetic algorithm to minimize maximum lateness on a batch processing machine

We consider the problem of minimizing maximum lateness on a batch processing machine in the presence of dynamic job arrivals. The batch processing machine can process up to B jobs simultaneously, and the processing time of a batch is given by that of the job with the longest processing time in the batch. We adapt a dynamic programming algorithm from the literature to determine whether a due-date feasible batching exists for a given job sequence. We then combine this algorithm with a random keys encoding scheme to develop a genetic algorithm for this problem. Computational experiments indicate that this algorithm has excellent average performance with reasonable computational burden. Scope and purpose In this paper we address the problem of scheduling a single batch processing machine subject to dynamic job arrivals, which generalizes a number of classical single-machine models from scheduling theory (Pinedo. Scheduling theory, algorithms, and systems. Englewood Cliffs, NJ: Prentice-Hall, 1995.) Batch processing machines, where a number of jobs are processed simultaneously as a batch, are quite common in the metalworking and microelectronics industries. Although an extensive literature on several scheduling models for this type of machine has developed in the last decade, there has been relatively little work on models that consider jobs arriving at the machine dynamically over time. However, such dynamic models are an essential component of decomposition heuristics (Ovacik, Uzsoy. Decomposition methods for complex factory scheduling problems. Massachusetts: Kluwer Academic Publishers, 1997.) used to schedule the factories within which the batch processing machines form an individual workcenter. This paper builds on results developed in prior work (Lee et al. Operations Research 1992;40:764–75.) and (Uzsoy. International Journal of Production Research 1995;33:2605–708.) to develop an effective genetic algorithm (Goldberg. Genetic algorithms in search, optimization and machine learning. Reading, MA: Addison-Wesley, 1989.) for solving this provably intractable scheduling problem. Our procedure combines an optimization algorithm to evaluate job sequences with a random key representation that guarantees feasible solutions after crossover operations. Extensive computational experiments show that it consistently obtains high-quality solutions in modest CPU times.

Minimizing makespan on a single burn-in oven with job families and dynamic job arrivals

This paper considers a scheduling problem for a single burn-in oven in the semiconductor manufacturing industry where the oven is a batch processing machine and each batch processing time is represented by the largest processing time among those of all the jobs contained in the batch. Each job belongs to one of the given number of families. Moreover, the release times of the jobs are different from one another. The objective measure of the problem is the maximum completion time (makespan) of all jobs. A dynamic programming algorithm is proposed in the order of polynomial time complexity for a situation where the number of job families is given (fixed). A computational experiment is performed to compare the time complexity of the proposed algorithm with that of another exact algorithm evaluating all possible job sequences based on batching-dynamic programming (BDP). The results of the experiment show that the proposed algorithm is superior to the other. Scope and purpose This paper considers a scheduling problem on the burn-in operation in a semiconductor manufacturing process. The burn-in operation is a bottleneck process in the final testing process which is one of four major steps including wafer fabrication, wafer probe, assembly, and final testing steps. Thus, its scheduling is very important to improve the productivity of the whole manufacturing line. The objective of this paper is to find a solution technique that will find the optimal schedule that minimizes makespan for problems which are found in the semiconductor manufacturing industry.

Impact of workload and system parameters on next generation cluster scheduling mechanisms

Scheduling of processes onto processors of a parallel machine has always been an important and challenging area of research. The issue becomes even more crucial and difficult as we gradually progress to the use of off-the-shelf workstations, operating systems, and high bandwidth networks to build cost-effective clusters for demanding applications. Clusters are gaining acceptance not just in scientific applications that need supercomputing power, but also in domains such as databases, web service, and multimedia which place diverse Quality-of-Service (QoS) demands on the underlying system. Further, these applications have diverse characteristics in terms of their computation, communication, and I/O requirements, making conventional parallel scheduling solutions, such as space sharing or gang scheduling, unattractive. At the same time, leaving it to the native operating system of each node to make decisions independently can lead to ineffective use of system resources whenever there is communication. Instead, an emerging class of dynamic coscheduling mechanisms that attempt to take remedial actions to guide the system toward coscheduled execution without requiring explicit synchronization offers a lot of promise for cluster scheduling. Using a detailed simulator, this paper evaluates the pros and cons of different dynamic coscheduling alternatives while comparing their advantages over traditional gang scheduling (and not performing any coordinated scheduling at all). The impact of dynamic job arrivals, job characteristics, and different system parameters on these alternatives is evaluated in terms of several performance criteria. In addition, heuristics to enhance one of the alternatives even further are identified, classified, and evaluated. It is shown that these heuristics can significantly outperform the other alternatives over a spectrum of workload and system parameters and is thus a much better option for clusters than conventional gang scheduling.

On‐line algorithms for minimizing makespan on batch processing machines

We consider problem of scheduling jobs on-line on batch processing machines with dynamic job arrivals to minimize makespan. A batch machine can handle up to B jobs simultaneously. The jobs that are processed together from a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. Each job becomes available at its arrival time, which is unknown in advance, and its processing time becomes known upon its arrival. In the first part of this paper, we address the single batch processing machine scheduling problem. First we deal with two variants: the unbounded model where B is sufficiently large and the bounded model where jobs have two distinct arrival times. For both variants, we provide on-line algorithms with worst-case ratio (the inverse of the Golden ratio) and prove that these results are the best possible. Furthermore, we generalize our algorithms to the general case and show a worst-case ratio of 2. We then consider the unbounded case for parallel batch processing machine scheduling. Lower bound are given, and two on-line algorithms are presented. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 241–258, 2001

On‐line algorithms for minimizing makespan on batch processing machines

AbstractWe consider problem of scheduling jobs on‐line on batch processing machines with dynamic job arrivals to minimize makespan. A batch machine can handle up to B jobs simultaneously. The jobs that are processed together from a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. Each job becomes available at its arrival time, which is unknown in advance, and its processing time becomes known upon its arrival. In the first part of this paper, we address the single batch processing machine scheduling problem. First we deal with two variants: the unbounded model where B is sufficiently large and the bounded model where jobs have two distinct arrival times. For both variants, we provide on‐line algorithms with worst‐case ratio $(\sqrt{5}+1)/2$ (the inverse of the Golden ratio) and prove that these results are the best possible. Furthermore, we generalize our algorithms to the general case and show a worst‐case ratio of 2. We then consider the unbounded case for parallel batch processing machine scheduling. Lower bound are given, and two on‐line algorithms are presented. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 241–258, 2001