Non-preemptive Scheduling Problem Research Articles

A novel exact formulation for parallel machine scheduling problems

Machine scheduling is one of the most studied problems due to its technical challenges and prevalence in real life. In the literature, continuous- and discrete-time formulations are the two most known formulations for scheduling problems. However, continuous-time formulations often suffer from weak linear relaxations, while discrete-time formulations struggle with large numbers of variables. In contrast, the bucket-indexed formulation is an alternative that mitigates both issues by working with partial time discretization. We propose a mixed-integer linear programming model based on a bucket-indexed formulation to solve a nonpreemptive scheduling problem of identical parallel machines considering release dates, deadlines, precedence, eligibility, and machine availability constraints. We evaluate the proposed formulation against real-world instances comprising more than 400 jobs and 100 machines, comparing its performance against equivalent continuous- and discrete-time formulations. Remarkably, our formulation can be solved to optimality for all instances, outperforming both continuous- and discrete-time formulations.

EPTAS for parallel identical machine scheduling with time restrictions

We consider the non-preemptive scheduling problem on identical machines where there is a parameter B and each machine in every unit length time interval can process up to B different jobs. The goal function we consider is the makespan minimization and we develop an EPTAS for this problem. Prior to our work a PTAS was known only for the case of one machine and constant values of B, and even the case of non-constant values of B on one machine was not known to admit a PTAS.

A NOTE ON HARDNESS OF MULTIPROCESSOR SCHEDULING WITH SCHEDULING SOLUTION SPACE TREE

We study the computational complexity of the non-preemptive scheduling problem of a listof independent jobs on a set of identical parallel processors with a makespan minimizationobjective. We make a maiden attempt to explore the combinatorial structure showing theexhaustive solution space of the problem by defining the Scheduling Solution Space Tree(SSST) data structure. The properties of the SSST are formally defined and characterizedthrough our analytical results. We develop a unique technique to show the problemNP using the SSST and the Weighted Scheduling Solution Space Tree (WSSST) datastructures. We design the first non-deterministic polynomial-time algorithm named MagicScheduling (MS) for the problem based on the reduction framework. We also define anew variant of multiprocessor scheduling by including the user as an additional inputparameter. We formally establish the complexity class of the variant by the reductionprinciple. Finally, we conclude the article by exploring several interesting open problemsfor future research investigation.

Online Non-preemptive Scheduling on Unrelated Machines with Rejections

When a computer system schedules jobs there is typically a significant cost associated with preempting a job during execution. This cost can be incurred from the expensive task of saving the memory’s state or from loading data into and out of memory. Thus, it is desirable to schedule jobs non-preemptively to avoid the costs of preemption. There is a need for non-preemptive system schedulers for desktops, servers, and data centers. Despite this need, there is a gap between theory and practice. Indeed, few non-preemptive online schedulers are known to have strong theoretical guarantees. This gap is likely due to strong lower bounds on any online algorithm for popular objectives. Indeed, typical worst-case analysis approaches, and even resource-augmented approaches such as speed augmentation, result in all algorithms having poor performance guarantees. This article considers online non-preemptive scheduling problems in the worst-case rejection model where the algorithm is allowed to reject a small fraction of jobs. By rejecting only a few jobs, this article shows that the strong lower bounds can be circumvented. This approach can be used to discover algorithmic scheduling policies with desirable worst-case guarantees. Specifically, the article presents algorithms for the following three objectives: minimizing the total flow-time, minimizing the total weighted flow-time plus energy where energy is a convex function, and minimizing the total energy under the deadline constraints. The algorithms for the first two problems have a small constant competitive ratio while rejecting only a constant fraction of jobs. For the last problem, we present a constant competitive ratio without rejection. Beyond specific results, the article asserts that alternative models beyond speed augmentation should be explored to aid in the discovery of good schedulers in the face of the requirement of being online and non-preemptive.

Corrigendum to “A Bucket Indexed Formulation for Nonpreemptive Single Machine Scheduling Problems,” INFORMS Journal on Computing 28(1):14–30, 2016

Abstract. This note corrects an error in our paper “N. Boland, R. Clement, and H. Waterer. A bucket indexed formulation for nonpreemptive single machine scheduling problems. INFORMS Journal on Computing 28(1):14–30, 2016.”

An Energy-Aware Multiobjective Optimization Framework to Minimize Total Tardiness and Energy Cost on a Single-Machine Nonpreemptive Scheduling

Energy-aware scheduling in a manufacturing environment with real-time energy pricing is a challenging problem. The purpose of this paper is to study a nonpreemptive scheduling problem on a single-machine to minimize the total tardiness and total energy cost under time-of-use electricity tariffs, which is a mixed-integer multi-objective mathematical programming model. To achieve these objectives, we develop several new holistic genetic algorithms. The proposed model is solved via several methods including weighted sum method and multiobjective genetic algorithms based on dominance rank (GA-1), weighted sum aggregation (GA-2), dominance ranking procedure and crowding distance comparison (GA-3), and heuristic approach (GA-H). This paper illustrates that operations management, which is typically observed as a significant technique that allows manufacturing to operate in challenging data enabled environment in an industrial internet of things ecosystem, can also carefully optimize a production process to improve energy cost in order to manage environmental challenges. Thus, the findings provide information on when to start each job. We provide detailed experimental results evaluating the performance of the proposed algorithms. In a case study, we illustrate how the results of the multiobjective model could be utilized in decision making using the technique for order preference by similarity to ideal solution method.

Approximating total weighted completion time on identical parallel machines with precedence constraints and release dates

We present a (2+2ln2+ε)-approximation algorithm for the classical nonpreemptive scheduling problem to minimize the total weighted completion time of jobs on identical parallel machines subject to release dates and precedence constraints, improving upon the previously best known 4-approximation algorithm from 1998. The result carries over to the more general problem with precedence delays and generalizes a recent result by Li (2017) for the problem without release dates or delays.

Greed Works—Online Algorithms for Unrelated Machine Stochastic Scheduling

This paper establishes performance guarantees for online algorithms that schedule stochastic, nonpreemptive jobs on unrelated machines to minimize the expected total weighted completion time. Prior work on unrelated machine scheduling with stochastic jobs was restricted to the offline case and required linear or convex programming relaxations for the assignment of jobs to machines. The algorithms introduced in this paper are purely combinatorial. The performance bounds are of the same order of magnitude as those of earlier work and depend linearly on an upper bound on the squared coefficient of variation of the jobs’ processing times. Specifically for deterministic processing times, without and with release times, the competitive ratios are 4 and 6, respectively. As to the technical contribution, this paper shows how dual fitting techniques can be used for stochastic and nonpreemptive scheduling problems.

Approximate policy iteration for dynamic resource-constrained project scheduling

We study non-preemptive scheduling problems where heterogeneous projects stochastically arrive over time. The projects include precedence-constrained tasks that require multiple resources. Incomplete projects are held in queues. When a queue is full, an arriving project must be rejected. The goal is to choose which tasks to start in each time-slot to maximize the infinite-horizon discounted expected profit. We provide a weakly coupled Markov decision process (MDP) formulation and apply a simulation-based approximate policy iteration method. Extensive numerical results are presented.

An algorithm for solving a certain sequencing problem

The authors consider the problem of nonpreemptive scheduling of n tasks in a general job shop. The objective is to find a schedule of minimum length. The algorithm presented in the paper is based on the disjunctive graph approach. Its performance is not compared with other algorithms constructed for that problem.

A 2.542-approximation for precedence constrained single machine scheduling with release dates and total weighted completion time objective

We present a e/(e−1)-approximation algorithm for the nonpreemptive scheduling problem to minimize the total weighted completion time of jobs on a single machine subject to release dates and precedence constraints. The previously best known approximation algorithm dates back to 1997; its performance guarantee can be made arbitrarily close to the Euler constant e (Schulz and Skutella, 1997).

Efficient Scheduling for Video Transmissions in Maritime Wireless Communication Networks

This paper develops a framework for vessel surveillance video uploading via maritime wideband communication networks. A broadband wireless network utilizing a time-division-multiple-access (TDMA)-based media access control protocol is employed to establish a shore-side network infrastructure, and a packet store–carry–forward routing mechanism is adopted to achieve intermittent network connectivity in maritime communications. To provide high-quality videos to the administrative authority, a resource allocation problem is formulated to maximize the throughput priority-based video transmission problem, subject to the intermittent network connections and the time indexes such as the release time and deadline of each video packet. To reduce computational complexity, time-capacity mapping is applied to transform the original resource allocation problem into a two-machine nonpreemptive scheduling problem. Three offline scheduling algorithms are proposed, namely, a time-capacity-mapping-based two-phase (TMTP) algorithm for a single machine, a TMTP algorithm for two machines, and an interval graph-theory-based job relay selection (IGTJRS) algorithm. It is mathematically proved that the IGTJRS algorithm has an approximation ratio (i.e., the ratio of the throughput of an optimal schedule to that of the IGTJRS algorithm) of 2 and time complexity of ${\cal O}(n^{2})$ . Simulations results validate the performance of the proposed algorithms, based on real ship route traces obtained from navigation software BLM-Shipping.

A fast heuristic to minimize number of tardy jobs in preemptive open shops

This article considers the problem of scheduling preemptive open shops to minimize the number of tardy jobs. A mixed integer program is presented for solving small-sized problems. An efficient heuristic is constructed for solving large-sized problems. This heuristic can be viewed as a generalization of the well-known Moore’s algorithm for the single machine non-preemptive scheduling problem to the preemptive open shop scheduling problem. A lower bound based on assignment problem is proposed for performance evaluation of the heuristic for large-sized problems. Computational results for randomly generated problems are reported. For small-sized problems, the solution obtained by the heuristic has an average deviation of about 4.02% from the optimal value. The lower bound has an average deviation of about 21.03% from the optimal value. For large-sized problems, the solution obtained by the heuristic has an average deviation of less than 54% from the lower bound.

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.

Simulated annealing and imperialist competitive algorithm for minimising makespan in an open shop

This paper presents an imperialist competitive algorithm (ICA) and a simulated annealing (SA) algorithm in a non-preemptive open shop scheduling problem with job dependent setup times and sequence dependent transportation times to minimise the makespan (total completion time). The parameters of the algorithms are tuned by the response surface methodology (RSM). Based on classic approach, the scheduling problems are classified into small, medium and large sized problems. To evaluate the performance of the proposed ICA, its results are compared with the optimum ones obtained by GAMS for the small sized instances. Moreover, for the medium to large sized instances, the obtained solutions by the ICA are compared with the solutions of the effective method – SA algorithm – and the results are analysed.

Online scheduling with one rearrangement at the end: Revisited

In this paper, we consider an online non-preemptive scheduling problem on two related machines, with only one rearrangement at the end, called Online scheduling with one rearrangement at the end (OSORE). We proposed an improved algorithm for 1⩽s⩽2, where s is the speed ratio between the fast machine and slow machine. The upper bounds are 2(s+1)s+2 for 1⩽s⩽2 and s+2s+1 for 2<s⩽2, which are better than previous results, i.e. (s+1)2s+2 for 1⩽s⩽2 and s+1s for 2<s⩽2 (Liu et al., 2009 [7]).

On Preemptive Multi-wavelength Scheduling in Hybrid WDM/TDM Passive Optical Networks

In this paper, we investigate the wavelength scheduling problem in hybrid wavelength division multiplexing/time division multiplexing passive optical networks (WDM/TDM PONs), which can be mapped into multiprocessor scheduling problems with wavelengths and optical network unit (ONU) requests being considered as machines and jobs, respectively. To achieve high bandwidth utilization, guarantee low delay, and ensure short-term fairness, we try to construct a schedule with the minimum latest job completion time. First, we investigate the non-preemptive scheduling problem, which was shown to be NP-hard, and hence requires heuristic algorithms to approximate the optimal solution. The approximation ratio of the best heuristic algorithm is as large as 2-1/m, where m is the number of wavelengths. Motivated to achieve a smaller latest job completion time, we then investigate the preemptive scheduling problem. Preemption allows jobs to be scheduled more flexibly, and thus may yield a smaller makespan. However, with preemption, jobs may be split into subjobs and scheduled in discontinuous time durations at the expense of more guard time. We show that, with the consideration of guard time, the preemptive scheduling with the objective of minimizing the latest job completion time is NP-hard. To address the problem, we propose an approach by using linear programming with guard time supplement. It is shown that the proposed algorithm can ensure that the latest job completion time is no greater than the optimal value plus (m-1)g/m, where g is the guard time between the scheduling of two ONUs. When the network is highly loaded, the approximation ratio is around 1.00061 and 1.002056 for hybrid WDM/TDM Ethernet PON (EPON) and Gigabit-capable PON (GPON), respectively.

Algorithm for Cost Non-preemptive Scheduling of Partial k-Trees

Let G be a graph, in which each vertex (job) v has a positive integer weight (processing time) p(v) and eachedge (u,v) represented that the pair of jobs u and v cannot be processed in the same slot. In this paper we assume that every job is non-preemptive. Let C={1,2,...} be a color set. A multicoloring (scheduling) F of G is to assign each job v a set of p(v) consecutive positive integers (processing consecutive time slots) in C so that any pair of adjacent vertices receive disjoint sets. Such a multicoloring is called a non-preemptive scheduling. The cost non-preemptive scheduling problem is to find an optimal multicoloring of G.

Single-facility scheduling by logic-based Benders decomposition

Logic-based Benders decomposition can combine mixed integer programming and constraint programming to solve planning and scheduling problems much faster than either method alone. We find that a similar technique can be beneficial for solving pure scheduling problems as the problem size scales up. We solve single-facility non-preemptive scheduling problems with time windows and long time horizons. The Benders master problem assigns jobs to predefined segments of the time horizon, where the subproblem schedules them. In one version of the problem, jobs may not overlap the segment boundaries (which represent shutdown times, such as weekends), and in another version, there is no such restriction. The objective is to find feasible solutions, minimize makespan, or minimize total tardiness.

A Note on “A Genetic Algorithm for the Preemptive and Non-Preemptive Multi-Mode Resource-Constrained Project Scheduling Problem

Peteghem et al. [1] considered resource-constrained project scheduling problem (RCPSP) with preemptive activities. However, some points should be made clear. How and when an activity is divided? How many parts an activity should be splitted? Whether the preemptive-based scenario is correctly performed to further improve the total makespan of a project? The first two questions are not very clearly presented. As for the last question, the answer is “no exactly” after careful examination..