Online Scheduling Problem Research Articles

Optimal algorithms for solving green online reheat furnace scheduling problems with deterioration effect

Optimizing reheating furnace scheduling in terms of energy saving and reheating time reduction is a vital component in improving competitive advantage of the steel enterprises. However, current reheating furnace scheduling models are still limited since (1) most of the scheduling problems involving reheating furnace suppose that the steel orders and their information are known in advance and (2) the reheating time of a slab in reheating operation is a constant in the majority of current reheating furnace scheduling models. To address these issues, three online reheat furnace scheduling models with deterioration effect are proposed in order to minimize the maximum residence time, the maximum energy consumption as well as total energy consumption of all slabs in reheating operation, respectively. Furthermore, for these online scheduling problems, deterministic online algorithms are presented and shown to be optimal, respectively. In addition, the computational experiments confirm that the three online algorithms developed in this paper are particularly efficient and effective in practice.

Online scheduling problem of incompatible batch processing with deterioration effect and delivery time in the steel rolling process

As market competition intensifies, modern enterprises prioritize customer demands, leading to an increased emphasis on multi-variety and small-batch production. In this article, we study the online scheduling problem for incompatible batch processing with the deterioration effect to minimize the maximum delivery completion time in the billet rolling process, where the batch capacity and delivery capacity are unbounded. We assume that the processing time of job Jj is expressed as p j = a j ( A + Bt ) , where A > 0, B > 0, t denotes the start time of job and aj > 0 represents the job’s processing deterioration rate. For such an online problem, we first prove that the lower bound of the problem is ( 1 + B a max ) k , where k denotes the number of job families and a max represents the maximum deterioration ratio in job instance. Then we design an online algorithm Largest Delivery Time With Batch Processing and demonstrate that the competitive ratio of the algorithm is no more than 1 + ( 1 + B a max ) k . Finally, experiments on randomly generated instances prove that our algorithm is reasonable and effective.

Improved Online Scheduling of Moldable Task Graphs under Common Speedup Models

We consider the online scheduling problem of moldable task graphs on multiprocessor systems for minimizing the overall completion time (or makespan). Moldable job scheduling has been widely studied in the literature, in particular when tasks have dependencies (i.e., task graphs) or when tasks are released on-the-fly (i.e., online). However, few studies have focused on both (i.e., online scheduling of moldable task graphs). In this article, we design a new online scheduling algorithm for this problem and derive constant competitive ratios under several common yet realistic speedup models (i.e., roofline, communication, Amdahl, and a general combination). These results improve the ones we have shown in the preliminary version of the article. We also prove, for each speedup model, a lower bound on the competitiveness of any online list scheduling algorithm that allocates processors to a task based only on the task’s parameters and not on its position in the graph. This lower bound matches exactly the competitive ratio of our algorithm for the roofline, communication, and Amdahl’s model, and is close to the ratio for the general model. Finally, we provide a lower bound on the competitive ratio of any deterministic online algorithm for the arbitrary speedup model, which is not constant but depends on the number of tasks in the longest path of the graph.

A good balance for an online scheduling problem considering both learning and deteriorating effects in the handicraft process

The paper considers an online scheduling problem with the effects of both learning and deterioration to minimize the total completion time. More specifically, we assume that the actual processing length of job Jj is p jr = p j r b + at , where pj is the initial processing time of Jj , t is the starting time of Jj , r is the seating arrangement position of Jj , b is the learning factor and a is the deterioration factor, respectively. For this problem, we show that the performance ratio of any deterministic online algorithm is not <2 and provide a best possible online algorithm DSBPT with a competitive ratio of 2. Furthermore, we also present a concise computational simulation study to verify the effectiveness and efficiency of the proposed algorithm DSBPT, as well as the management implications provided for decision-makers to production optimization.

Risk aware decomposition of online scheduling for large flexible consumers considering the age of information

The stability and security of the power system is significantly influenced by large electricity consumers, especially those with flexible demand, whose electricity purchase scheduling has been extensively studied. However, the high penetration of renewable energy and various widespread distributed storage systems have increased uncertainty of the power system, making it difficult to plan effective day-ahead electricity purchase for major electrical consumers. Online scheduling is therefore required so that the surplus can be sold to and the insufficient can be purchased from the real-time market at the lowest electricity cost. To this end, we formulate a multi-stage online scheduling model for large power consumers with flexible demand. To improve the efficiency of online scheduling, we decompose the problem into multiple single-stage sub-problems. Aimed at each single-stage scheduling, an online algorithm is designed to ensure the performance of optimal scheduling strategies maintains at a level comparable to the offline fixed strategies obtained from an oracle who has complete knowledge of the problem’s settings. We prove that our proposed online energy schedule algorithm is able to achieve O(T) regret bound for the single-stage online scheduling problem. To further highlight the significance of data and improve the multi-stage performance of our online scheduling algorithm, we also involve the notion of age of information combined with regret bound to help determine the optimal interval length.

Online Single-Processor Scheduling with an Unexpected Breakdown

In this paper, we consider two single-processor online scheduling problems with an unexpected breakdown. Speaking specifically, there is a group of nonresumable jobs being processed on the single processor. Note that the breakdown will emerge on the processor suddenly, which signifies that its beginning time and its length are unknown in advance. In this study, we are interested in scheduling the jobs so as to minimize the maximum weighted completion time. Most noticeably, when all jobs respect an agreeable condition, i.e., for each two jobs [Formula: see text] and [Formula: see text], [Formula: see text] means that [Formula: see text], we design an optimal online algorithm. In addition, for the general version, we propose an online algorithm with a competitive ratio of at most 2.

Online Throughput Maximization on Unrelated Machines: Commitment is No Burden

We consider a fundamental online scheduling problem in which jobs with processing times and deadlines arrive online over time at their release dates. The task is to determine a feasible preemptive schedule on a single or multiple possibly unrelated machines that maximizes the number of jobs that complete before their deadline. Due to strong impossibility results for competitive analysis on a single machine, we require that jobs contain some slack ɛ &gt; 0, which means that the feasible time window for scheduling a job is at least 1+ɛ times its processing time on each eligible machine. Our contribution is two-fold: (i) We give the first non-trivial online algorithms for throughput maximization on unrelated machines, and (ii), this is the main focus of our paper, we answer the question on how to handle commitment requirements which enforce that a scheduler has to guarantee at a certain point in time the completion of admitted jobs. This is very relevant, e.g., in providing cloud-computing services, and disallows last-minute rejections of critical tasks. We present an algorithm for unrelated machines that is \(\Theta (\frac{1}{\varepsilon })\) -competitive when the scheduler must commit upon starting a job. Somewhat surprisingly, this is the same optimal performance bound (up to constants) as for scheduling without commitment on a single machine. If commitment decisions must be made before a job’s slack becomes less than a δ-fraction of its size, we prove a competitive ratio of \(\mathcal {O}(\frac{1}{\varepsilon - \delta })\) for 0 &lt; δ &lt; ɛ. This result nicely interpolates between commitment upon starting a job and commitment upon arrival. For the latter commitment model, it is known that no (randomized) online algorithm admits any bounded competitive ratio. While we mainly focus on scheduling without migration, our results also hold when comparing against a migratory optimal solution in case of identical machines.

Best possible algorithms for online scheduling on identical batch machines with periodic pulse interruptions

We consider an online scheduling problem on identical batch machines to minimize the makespan with periodic pulse interruptions. Periodic pulse interruptions are machine unavailable intervals with negligible length and divide the scheduling horizon into available intervals. Jobs are released online over time and processed simultaneously as batches with the same processing times on identical batch machines. Every batch must be entirely processed in an available interval without any preemption. For unbounded machine capacity, we design best possible online algorithms with the competitive ratios of 1+η and 2m for a single machine (m=1) and m identical parallel machines (m≥2), respectively, where η≈0.8019 is the positive root of η3+2η2−η=1. For bounded machine capacity, we derive a best possible online algorithm with a competitive ratio of 1+η.

Online scheduling on a single machine with one restart for all jobs to minimize the weighted makespan

&lt;abstract&gt;&lt;p&gt;In this paper, we consider the online scheduling problem on a single machine to minimize the weighted makespan. In this problem, all jobs arrive over time and they are allowed to be restarted only once. For the general case when the processing times of all jobs are arbitrary, we show that there is no online algorithm with a competitive ratio of less than 2, which matches the lower bound of the problem without restart. That is, only one restart for all jobs is invalid for improving the competitive ratio in the general case. For the special case when all jobs have the same processing time, we present the best possible online algorithm with a competitive ratio of 1.4656, which improves the competitive ratio of $ \frac{1+\sqrt{5}}{2}\approx1.618 $ for the problem without restart.&lt;/p&gt;&lt;/abstract&gt;

A best possible algorithm for an online scheduling problem with deteriorating effect in steel box girder section production

&lt;p style='text-indent:20px;'&gt;The paper focuses on an online scheduling problem with the effect of deterioration to minimize the maximum delivery time in steel box girder sections. This deterioration is considered in terms of job processing and delivery. Specifically, the processing time of job &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ J_j $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; is defined by an increasing function of its starting time &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ t $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, i.e., &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$ p_j = \alpha_j(A+Bt) $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, where &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$ \alpha_j&amp;gt;0 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; is the processing deterioration rate of job &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$ J_j $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;. Moreover, the delivery time of job &lt;inline-formula&gt;&lt;tex-math id="M6"&gt;\begin{document}$ J_j $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; is determined with an increasing function of its completion time, i.e., &lt;inline-formula&gt;&lt;tex-math id="M7"&gt;\begin{document}$ q_j = b_jC_j $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, where &lt;inline-formula&gt;&lt;tex-math id="M8"&gt;\begin{document}$ b_j&amp;gt;0 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; is the delivery deterioration rate of job &lt;inline-formula&gt;&lt;tex-math id="M9"&gt;\begin{document}$ J_j $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;. For this problem, we prove the property of optimal scheduling and show that the performance ratio of any deterministic online algorithm is not less than &lt;inline-formula&gt;&lt;tex-math id="M10"&gt;\begin{document}$ 2+B\alpha_{\max} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;. Furthermore, we provide a best possible online algorithm &lt;i&gt;LDDR&lt;/i&gt; with a competitive ratio of &lt;inline-formula&gt;&lt;tex-math id="M11"&gt;\begin{document}$ 2+B\alpha_{\max} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;. And then a concise computational simulation study is presented to show that our algorithm performs very well in practice.&lt;/p&gt;

Online scheduling on parallel-batch machines with periodic availability constraints and job delivery

We address an online scheduling problem on identical parallel-batch machines with periodic availability constraints and job delivery. A parallel-batch machine can process several jobs simultaneously in a batch without any preemption. The processing time of a batch is equal to the maximum processing time of the jobs in this batch, and the job processing times we consider are identical on all machines. Available and unavailable time intervals occur alternately on machines. The unavailable time intervals have the same start and end time on different machines. Jobs are released over time, which means that no information of the job is known in advance before its release date. After completion, job is delivered to customer. Three objective functions, namely, maximum flow time, maximum delivery time and total flow time are considered separately. For these objectives, we derive lower bounds on competitive ratios, provide online algorithms and analyze their competitive ratios.

A decomposition-based two-stage online scheduling approach and its integrated system in the hybrid flow shop of steel industry

Steelmaking-continuous casting (SCC) is one of the most critical building blocks in the modern steel industry. Many random events occur in the real-world SCC production system. In this paper, we propose a two-stage online scheduling policy that protects the baseline schedule by the slacks provided by intra-flow times and casting speeds. The main task of the two-stage online scheduling model is: (1) to make “here-and-now” decisions for minimizing economic costs and penalties caused by constraint violations; (2) make “wait-and-see” decisions for online scheduling. Afterward, we propose a decomposition-based optimization algorithm that divides the online scheduling problem into a master problem (MP) to seek partial solutions at the last processing stage and a slave problem (SP) to check optimal solutions for upstream processing stages. Then, we employ the IBM ILOG CPLEX to solve MP and use the constraint programming (CP) optimizer to solve SP. Sensitivity analyses and algorithm comparisons are conducted on a set of well-synthetic and realistic instances to validate the proposed model and algorithm. The results show that the proposed online scheduling model and algorithm can solve realistic industrial case studies. Finally, we also develop a scheduling system integrating the proposed model and algorithm.

Independent double DQN-based multi-agent reinforcement learning approach for online two-stage hybrid flow shop scheduling with batch machines

Two-stage hybrid flow shop scheduling with batch machines and jobs arriving over time is complex and challenging in various real-world production scenarios. For the online scheduling problem, traditional heuristic rules can quickly respond to dynamically arrived jobs, while with poor and unstable performance. To close the research gap in the problem, this paper proposes an independent double deep-q-network-based multi-agent reinforcement learning (MA-IDDQN) approach to produce an adaptive rule for batch forming and scheduling. Specifically, the online scheduling problem is transformed into a cooperative Markov decision process by defining state space, action space, and reward function for different agents. Then, two agents are constructed and trained via double DQN to address the batch forming task and scheduling task respectively. Meanwhile, multi-agent cooperates through the behavior analysis mechanism among agents. Moreover, we designed a ε-greedy policy considering waiting in batch forming to make a reasonable decision through historical data. To validate the proposed approach, 27 instances with different scales are settled and contrasted. By comparing with frequently-used heuristic rules and other deep reinforcement learning methods, the experimental results demonstrate that the MA-IDDQN can integrate online batch forming and scheduling to minimize the total tardiness time effectively.

An optimal online algorithm for single-processor scheduling problem with learning effect

This paper deals with the canonical single-processor online scheduling problem with the position-based learning effect. Specially speaking, a round of jobs arriving online over time will be processed on a single processor. Noticeably, in this model, for each job Jk, the actual processing time pkl is defined as a power function of its position l, i.e., pkl=pklβ, where pk indicates its normal processing time and β≤0 is the learning index. Our goal is to make the sum of completion times as small as possible. For this problem, we testify that there is no online algorithm with a competitive ratio of less than 2. Most notably, we design an online algorithm entitled as Delayed Shortest Normal Processing Time (DSNPT), matching the lower bound proposed by us, and hence DSNPT is optimal.

Downlink Transmission Scheduling With Data Sharing

We formulate and analyze a fundamental downlink transmission scheduling problem in a wireless communication system, composed of a base station and a set of users, each requesting a packet to be served within a time window. Some packets are requested by several users and can be served simultaneously due to the broadcast nature of the wireless medium. The base station can choose from a set of transmission strategies, e.g., in terms of combination of data rate and coding scheme, to serve the users. Each request can be served by a subset of transmission strategies. We seek a downlink transmission scheduling algorithm generating maximum aggregated system-wide utility. In this paper, we develop approximation algorithms for the formulated downlink transmission scheduling problem in both offline and online settings. We first establish the NP-hardness of the offline scheduling problem and the approximation hardness and bound of the online scheduling problem in non-preemptive and preemptive-restart models, respectively. We then design approximation algorithms and derive the approximation and competitive ratios of our online and offline scheduling algorithms. Numerical simulations are performed to further evaluate our algorithms in a wide range of network settings.

Car-sharing between two locations: Online scheduling with flexible advance bookings

We study an online scheduling problem that is motivated by applications such as car-sharing. Users submit ride requests, and the scheduler aims to accept requests of maximum total profit using a single server (car). Each ride request specifies the pick-up time and the pick-up location (among two locations, with the other location being the destination). The scheduler has to decide whether or not to accept a request immediately at the time when the request is submitted (booking time). We consider two variants of the problem with respect to constraints on the booking time: In the fixed booking time variant, a request must be submitted a fixed amount of time before the pick-up time. In the variable booking time variant, a request can be submitted at any time during a certain time interval that precedes the pick-up time. We present lower bounds on the competitive ratio of deterministic and randomized algorithms for both variants and propose a greedy algorithm that achieves the best possible competitive ratio among deterministic algorithms.

Online order scheduling of multi 3D printing tasks based on the additive manufacturing cloud platform

Cloud-based additive manufacturing is one of the important forms of cloud manufacturing service platform, which can match manufacturing resources for multi-task requirements to further improve the utilization of idle resources and achieve cost reductions. This paper proposes a more realistic scenario of online scheduling rather than offline scheduling, in which tasks arrive randomly. According to the scenario, a mixed integer linear programming model of multi 3D printing tasks based on the additive manufacturing cloud platform is constructed, with the goal of minimizing the average cost per volume of material. A heuristic strategy is proposed to solve the problem, and different scale instances are tested to compare the performance. Simulation shows that the proposed algorithm can effectively solve the 3D printing online scheduling problem.

Online scheduling of time-critical tasks to minimize the number of calibrations

We study the online scheduling problem where the machines need to be calibrated before processing any jobs. To calibrate a machine, it will take λ time steps as the activation time, and then the machine will remain calibrated status for T time steps. The job can only be processed by the machine that is in calibrated status. Given a set of jobs arriving online, each of the jobs is characterized by a release time, a processing time, and a deadline. We assume that there is an infinite number of machines for usage. The objective is to minimize the total number of calibrations while feasibly scheduling all jobs.For the case that all jobs have unit processing times, we propose an O(λ)-competitive algorithm, which is asymptotically optimal. When λ=0, the problem is degraded to rent minimization, where our algorithm achieves a competitive ratio of 3e+7(≈15.16) which improves upon the previous results for such problems.

SAAS parallel task scheduling based on cloud service flow load algorithm

In cloud platform applications, the user’s goal is to obtain high-quality application services, while the service provider’s goal is to obtain revenue by performing the tasks submitted by the user. The platform built by the service provider’s application resources needs to improve the mapping between service requests and resources to achieve higher value. Through the current situation of resource management in the cloud environment, it is found that many task scheduling and resource allocation algorithms are still affected by factors such as the diversity, dynamics, and multiple constraints of resources and tasks. This paper focuses on Software as a Service (SaaS) applications’ task scheduling and resource configuration in a dynamic and uncertain cloud environment. It is a challenging online scheduling problem to automatically and intelligently allocate user task requests that continually reach SaaS applications to appropriate resources for execution. To this end, a real-time task scheduling method based on deep reinforcement learning is proposed, which automatically and intelligently allocates user task requests that continually reach SaaS applications to appropriate resources for execution. In this way, the limited virtual machine resources rented by SaaS providers can be used in a balanced and efficient manner. In the experiment, by comparing with other five task scheduling algorithms, it is proved that the algorithm proposed in this paper not only improves the execution efficiency of better deploying workflow in IaaS public cloud, but also makes the resources provided by SaaS are used in a balanced and efficient manner.

An Optimal Online Algorithm for Scheduling with Learning Consideration

This paper investigates a classic online scheduling problem with learning effect on a single machine. Specifically, a number of independent jobs that arrive online over time will be processed on a single machine and learning effect implies that the real processing time of job [Formula: see text] is a non-increasing function of its position [Formula: see text], i.e., [Formula: see text], where [Formula: see text] is the basic processing time of job [Formula: see text] and [Formula: see text] is the learning index. Our goal is to minimize the total completion time of all jobs. For the problem, we develop a deterministic polynomial time online algorithm called Delayed Shortest Basic Processing Time (DSBPT) and state that it is an online algorithm with a competitive ratio of 2, which matches the lower bound of the online scheduling problem we focus on.