Arbitrary Release Times Research Articles

Online scheduling for jobs with arbitrary release times on uniform machines

Online scheduling for jobs with arbitrary release times on uniform machines

Minimizing total completion time on non-identical parallel batch machines with arbitrary release times using ant colony optimization

This paper considers the problem of scheduling a group of jobs with arbitrary release times, non-identical sizes, and different processing times on non-identical parallel batch processing machines to minimize the total completion time. A mixed-integer programming (MIP) model is firstly constructed in this paper to solve this problem. Then since the studied problem is strongly NP-hard, a modified elite ant system algorithm with the local search (MEASL) is also proposed to solve it, which is compared with several meta-heuristic algorithms and the commercial optimization solver (Gurobi) through extensive simulation experiments. Finally, the experimental results verify the effectiveness of the proposed algorithm.

Single machine Pareto scheduling with positional deadlines and agreeable release and processing times

<abstract><p>This paper studies the problem of scheduling $ n $ jobs on a single machine to minimize total completion time and maximum cost, simultaneously. Each job is associated with a positional deadline that indicates the largest ordinal number of this job in any feasible schedule. The jobs have agreeable release and processing times, meaning that jobs with larger release times also have larger processing times. The agreeability assumption is reasonable since both the single-criterion problems (without positional deadline constraints) of minimizing total completion time and maximum lateness on a single machine with arbitrary release and processing times are strongly NP-hard. An $ O(n^3) $-time Pareto optimal algorithm is presented. The previously known algorithms only solve two special cases of the agreeability assumption: either the case of equal release times in $ O(n^4) $ time, or the case of equal processing times (without positional deadline constraints) in $ O(n^3) $ time.</p></abstract>

Parallel batch processing machines scheduling in cloud manufacturing for minimizing total service completion time

This paper considers the integrated scheduling problem of production and delivery on parallel batch processing machines with non-identical capacities in different locations in cloud manufacturing. It is assumed that the jobs have arbitrary release times, different job sizes, unequal processing times, and unique information of customers submitting jobs. The service completion time of a job is the sum of the production completion time and the delivery duration. The objective of the studied problem is to minimize the total service completion time. A mixed-integer programming (MIP) model is presented to solve this problem. Since the problem is NP-hard, an efficient heuristic algorithm and an improved particle swarm optimization algorithm are proposed. The two proposed algorithms are compared with several state-of-the-art algorithms and the commercial optimization solver (Gurobi) through extensive experiments, verifying the effectiveness of the proposed algorithms.

On the Approximability of Related Machine Scheduling Under Arbitrary Precedence

Distributed computing systems often need to consider the scheduling problem involving a collection of highly dependent data-processing tasks that must work in concert to achieve mission-critical objectives. This paper considers the unrelated machine scheduling problem for minimizing weighted sum completion time under arbitrary precedence constraints and on heterogeneous machines with different processing speeds. The problem is known to be strongly NP-hard even in the single machine setting. By making use of Queyranne’s constraint set and constructing a novel Linear Programming relaxation for the scheduling problem under arbitrary precedence constraints, our results in this paper advance the state of the art. We develop a 2(1 + ( ${m}$ –1)/ ${D}$ )-approximation algorithm (and 2(1 + ( ${m}$ –1)/ ${D}$ ) + 1-approximation) for the scheduling problem with zero release time (and arbitrary release time), where ${m}$ is the number of servers and ${D}$ is the task-skewness product. The algorithm can be efficiently computed in polynomial time using the Ellipsoid method and achieves nearly optimal performance in practice as ${D} > {O}$ ( ${m}$ ) when the number of tasks per job to schedule is sufficiently larger than the number of machines available. Our implementation and evaluation using a heterogeneous testbed and real-world benchmarks confirms significant improvement in weighted sum completion time for dependent computing tasks.

Parallel-machine serial-batching scheduling with release times under the effects of position-dependent learning and time-dependent deterioration

This paper addresses a serial-batching scheduling problem where the jobs with arbitrary release times are scheduled on parallel machines with the objective to minimize the makespan. The effects of learning and deterioration are considered simultaneously, and each job’s actual processing time depends on the sum of previous jobs’ processing times and the position of the current job. Each machine can process up to $$ c $$ jobs in the manner of serial batch, i.e., one after another with a setup time for each batch. Structural properties are identified for the special cases of the studied problem. Based on these derived structural properties, we propose a novel hybrid SC-VNS algorithm to solve the studied problem, which combines Society and Civilization (SC) algorithm with Variable Neighborhood Search (VNS). Computational experiments are conducted to evaluate the performance of the proposed hybrid algorithm and some other well-known algorithms. The results demonstrate that the proposed hybrid SC-VNS algorithm performs quite better than the compared algorithms in terms of the solution quality and the required running time.

Better Algorithm for Order On-Line Scheduling on Uniform Machines

In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. An algorithm with competitive ratio of 7.4641 is addressed, which is better than the best existing result of 12.

Ant colony optimisation algorithms for two-stage permutation flow shop with batch processing machines and nonidentical job sizes

This paper focuses on minimising the maximum completion time for the two-stage permutation flow shop scheduling problem with batch processing machines and nonidentical job sizes by considering blocking, arbitrary release times, and fixed setup and cleaning times. Two hybrid ant colony optimisation algorithms, one based on job sequencing (JHACO) and the other based on batch sequencing (BHACO), are proposed to solve this problem. First, max-min pheromone restriction rules and a local optimisation rule are embedded into JHACO and BHACO, respectively, to avoid trapping in local optima. Then, an effective lower bound is estimated to evaluate the performances of the different algorithms. Finally, the Taguchi method is adopted to investigate and optimise the parameters for JHACO and BHACO. The performances of the proposed algorithms are compared with that of CPLEX on small-scale instances and those of a hybrid genetic algorithm (HGA) and a hybrid discrete differential evolution (HDDE) algorithm on full-scale instances. The computational results demonstrate that BHACO outperforms JHACO, HDDE and HGA in terms of solution quality. Besides, JHACO strikes a balance between solution quality and run time.

A modified particle swarm optimization algorithm for a batch-processing machine scheduling problem with arbitrary release times and non-identical job sizes

Abstract This paper presents a modified particle swarm optimization (MPSO) algorithm to minimize the maximum lateness for the single batch-processing machine problem with non-identical job sizes and release dates. The MPSO algorithm incorporated a diversification and a local search strategy into a basic particle swarm optimization algorithm. This incorporation enables the proposed algorithm to have a good balance between exploration and exploitation that yields high search efficiency. Additionally, a dynamic programming method is proposed to calculate a relevant value for each particle. The MPSO algorithm was tested in problems from the literature without release dates and newly generated problems with release dates. Computational results show the advantages of combining the diversification strategy, and local search methods. The performance of the proposed MPSO is competitive. For the problems without release dates, the MPSO algorithm could find 80 optimal solutions and improve 68 solutions for all benchmark instances. For the problems with job release dates, the MPSO algorithm also significantly outperformed the other two algorithms with respect to solution quality within the same computational time.

A random-keys genetic algorithm for scheduling unrelated parallel batch processing machines with different capacities and arbitrary job sizes

A batch processing machine (BPM) can simultaneously process several jobs and has wide applications in various industrial environments. This paper studies the problem of minimizing makespan on unrelated parallel BPMs with non-identical job sizes and arbitrary release times. In the environment of unrelated machines, each machine has a processing speed for each job. The unrelated BPM problem is the most general case of parallel BPM problems and is closer to actual production conditions. The problem under study is NP-hard. We present two lower bounds for the problem. Then a genetic algorithm based on random-keys encoding is proposed to solve the problem. The performance of the proposed algorithm is compared with a commercial solver (ILOG CPLEX) and two meta-heuristics published in the literature: a recent iterated greedy algorithm and a particle swarm optimization algorithm. Computational experiments show that the proposed algorithm produces better solutions compared to the other methods. The quality of the proposed lower bounds is evaluated as well.

Ordinal Semi On-Line Scheduling for Jobs with Arbitrary Release Times on Identical Parallel Machines

In this paper, we investigate the problem of semi-on-line scheduling n jobs on m identical parallel machines under the assumption that the ordering of the jobs by processing time is known and the jobs have arbitrary release times. Our aim is to minimize the maximum completion time. An ordinal algorithm is investigated and its worst case ratio is analyzed.

Distance matrix based heuristics to minimize makespan of parallel batch processing machines with arbitrary job sizes and release times

Batch scheduling is prevalent in many industries such as burn-in operations in semiconductor manufacturing and heat treatment operations in metalworking. In this paper, we consider the problem of minimizing makespan on parallel batch processing machines in the presence of non-identical job sizes and arbitrary release times. Since the problem under study is strongly NP-hard (non-deterministic polynomial-time hard), we develop a number of efficient heuristics. In the proposed heuristics, several distance matrix based approaches are first developed to form batches and a scheduling technique is devised to assign the batches to parallel machines. The performance of the proposed heuristics is evaluated by comparing their results to a set of existing heuristic and meta-heuristic algorithms in the literature. The computational experiments show that the proposed heuristics are competitive with respect to solution quality. Moreover, the computational costs of the proposed heuristics are very little.

On-Line Scheduling for Jobs with Arbitrary Release Times on Parallel Related Uniform Machines

A parallel related uniform machine system consists of m machines with different processing speeds. The speed of any machine is independent on jobs. In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. The jobs appear over list in terms of order. An order includes the processing size and releasing time of a job. For this model, an algorithm with competitive ratio of 12 is addressed in this paper.

Energy-efficient multiprocessor scheduling for flow time and makespan

We consider energy-efficient scheduling on multiprocessors, where the speed of each processor can be individually scaled, and a processor consumes power sα when running at speed s, for α>1. A scheduling algorithm needs to decide at any time both processor allocations and processor speeds for a set of parallel jobs with time-varying parallelism. The objective is to minimize the sum of the total energy consumption and certain performance metric, which in this paper includes total flow time and makespan. For both objectives, we present instantaneous parallelism-clairvoyant (IP-clairvoyant) algorithms that are aware of the instantaneous parallelism of the jobs at any time but not their future characteristics, such as remaining parallelism and work. For total flow time plus energy, we present an O(1)-competitive algorithm, which significantly improves upon the best known non-clairvoyant algorithm. In the case of makespan plus energy, we present an O(ln1−1/α⁡P)-competitive algorithm, where P is the total number of processors. We show that this algorithm is asymptotically optimal by providing a matching lower bound. In addition, we study non-clairvoyant scheduling for total flow time plus energy, and present an algorithm that is O(ln⁡P)-competitive for jobs with arbitrary release time and O(ln1/α⁡P)-competitive for jobs with identical release time. Finally, we prove an Ω(ln1/α⁡P) lower bound on the competitive ratio of any non-clairvoyant algorithm.

A hybrid differential evolution algorithm for a two-stage flow shop on batch processing machines with arbitrary release times and blocking

Batch processing machines (BPMs) have important applications in a variety of industrial systems. This paper considers the problem of scheduling two BPMs in a flow shop with arbitrary release times and blocking such that the makespan is minimised. The problem is formulated as a mixed integer programming model. Subsequently, a hybrid discrete differential evolution (HDDE) algorithm is proposed. In the algorithm, individuals in the population are first represented as discrete job sequences, and mutation and crossover operators are applied based on the representation. Second, after using the first-fit rule to form batches, a novel least idle/blocking time heuristic is developed to schedule the batches in the flow shop. Furthermore, an effective local search technique is embedded in the algorithm to enhance the exploitation ability. The performance of the proposed algorithm is evaluated by comparing its results to a commercial solver (CPLEX), a genetic algorithm and a simulated annealing algorithm. Computational experiments demonstrate the superiority of the HDDE algorithm in terms of solution quality, robustness and run time.

Online scheduling for jobs with nondecreasing release times and similar lengths on parallel machines

In this paper, we consider semi-online scheduling problems on parallel identical machine system which result from the online scheduling problem for jobs with arbitrary release times by knowing part information of the release times or processing sizes. The conditions are informed that the release times are nondecreasing sequence and the processing lengths are similar in with . An upper bound of the competitive ratio of List Scheduling (LS) algorithm is given and it is proved that the LS schedule is optimal when for any . Furthermore, for we present a tight bound when . We also show that the competitive ratio of the LS algorithm is improved when additional information is known by letting each job have release time zero. However, if the processing lengths are arbitrary, then no impact on the competitive ratio of the LS algorithm occurs after imposing the additional information.

The Geometry of Scheduling

We consider the following general scheduling problem. The input consists of $n$ jobs, each with an arbitrary release time, size, and monotone function specifying the cost incurred when the job is completed at a particular time. The objective is to find a preemptive schedule of minimum aggregate cost. This problem formulation is general enough to include many natural scheduling objectives, such as total weighted flow time, total weighted tardiness, and sum of flow time squared. We give an $O(\log \log P )$ approximation for this problem, where $P$ is the ratio of the maximum to minimum job size. We also give an $O(1)$ approximation in the special case of identical release times. These results are obtained by reducing the scheduling problem to a geometric capacitated set cover problem in two dimensions.

The Bell Is Ringing in Speed-Scaled Multiprocessor Scheduling

This paper investigates the problem of scheduling jobs on multiple speed-scaled processors, i.e., we have constant ?>1 such that running a processor at speed s results in energy consumption s ? per time unit. We consider the general case where each job has a monotonously increasing cost function that penalizes delay. This includes the so far considered cases of deadlines, flow time, and weighted flow time. For any type of delay cost functions, we obtain the following results: Any β-approximation algorithm for a single processor yields a randomized βB ? -approximation algorithm for multiple processors, where B ? is the ?th Bell number, that is, the number of partitions of a set of size ?. The generated schedule is without migration, but we compare it to an optimal schedule with migration. Hence, this result holds for migratory and non-migratory schedules. Analogously, we show that any β-competitive online algorithm for a single processor yields a βB ? -competitive online algorithm for multiple processors. Finally, we show that any β-approximation algorithm for multiple processors with migration yields a deterministic βB ? -approximation algorithm for multiple processors without migration. These facts improve several approximation ratios and lead to new results. For instance, we obtain the first constant factor online and offline approximation algorithm for multiple processors without migration for arbitrary release times, deadlines, and job sizes.

Online scheduling of simple linear deteriorating jobs to minimize the total general completion time

Traditional scheduling assumes that the processing time of a job is fixed. Yet there are numerous situations in which the processing time increases (deteriorates) as the start time increases. In particular, lots of work has been devoted to jobs with simple linear deterioration. The processing time pj of job Jj is a simple linear function of its start time sj, precisely, pj=bjsj, where bj is the deteriorating rate. In this paper, we study the problem of online non-preemptive scheduling of jobs with arbitrary release times and simple linear deteriorating rates on a single machine to minimize the total general completion time. We present an algorithm DSDR (Delayed Smallest Deteriorating Rate) and prove that it achieves the best-possible competitive ratio (1+bmax)α for all deterministic online algorithms, where α is the general index of completion time and α>0.

A graph coloring approach to scheduling of multiprocessor tasks on dedicated machines with availability constraints

We address a generalization of the classical 1- and 2-processor unit execution time scheduling problem on dedicated machines. In our chromatic model of scheduling machines have non-simultaneous availability times and tasks have arbitrary release times and due dates. Also, the versatility of our approach makes it possible to generalize all known classical criteria of optimality. Under these stipulations we show that the problem of optimal scheduling of sparse tree-like instances can be solved in polynomial time. However, if we admit dense instances then the problem becomes NP-hard, even if there are only two machines.