Makespan Of Schedule Research Articles

A Service Revenue-oriented Task Scheduling Model of Cloud Computing

Task scheduling strategy aims at finding an effective matching method between computing resources and submitted tasks, so as to achieve the reasonable allocation and effective execution of a large number of submitted tasks among computing resources. As a commercial service, cloud computing should gain as much service revenue as possible on condition that the QoS requirements of submitted tasks are satisfied. However, the majority of the existing cloud task scheduling methods aim at meeting the resource requests and QoS constraints of submitted tasks rather than earning more service revenue. Focusing on this point, a service revenue-oriented task scheduling model of cloud computing is proposed in this paper, which tries to improve the service revenue of cloud providers under the same condition. The final experimental results demonstrate that the service revenue-oriented cloud task scheduling strategy is superior to the classic Min-min algorithm and the improved Min-min algorithm based on QoS constraints in terms of the scheduling makespan of all submitted tasks and the service revenue per unit computing cost of the whole cloud system.

Improved semi-online makespan scheduling with a reordering buffer

We study semi-online scheduling with a reordering buffer for identical parallel machines. In this problem, jobs arrive one by one and the online algorithm is equipped with a buffer of limited size, which can be used to reorder the jobs when making scheduling decisions. When the buffer is full, one of the jobs in the buffer must be irrevocably assigned to a machine before the next job can be revealed. No preemption is allowed and the objective is to minimize the makespan. We propose an optimal online algorithm using a buffer size of 2.068m for large m and a 1.5-competitive algorithm using a buffer size of 1.477m, where m is the number of machines. Both results improve upon the best existing buffer sizes for the corresponding competitive ratios by a constant fraction of m.

PASTA: a power-aware solution to scheduling of precedence-constrained tasks on heterogeneous computing resources

Power efficiency is one of the main challenges in large-scale distributed systems such as datacenters, Grids, and Clouds. One can study the scheduling of applications in such large-scale distributed systems by representing applications as a set of precedence-constrained tasks and modeling them by a Directed Acyclic Graph. In this paper we address the problem of scheduling a set of tasks with precedence constraints on a heterogeneous set of Computing Resources (CRs) with the dual objective of minimizing the overall makespan and reducing the aggregate power consumption of CRs. Most of the related works in this area use Dynamic Voltage and Frequency Scaling (DVFS) approach to achieve these objectives. However, DVFS requires special hardware support that may not be available on all processors in large-scale distributed systems. In contrast, we propose a novel two-phase solution called PASTA that does not require any special hardware support. In its first phase, it uses a novel algorithm to select a subset of available CRs for running an application that can balance between lower overall power consumption of CRs and shorter makespan of application task schedules. In its second phase, it uses a low-complexity power-aware algorithm that creates a schedule for running application tasks on the selected CRs. We show that the overall time complexity of PASTA is $$O(p.v^{2})$$ where $$p$$ is the number of CRs and $$v$$ is the number of tasks. By using simulative experiments on real-world task graphs, we show that the makespan of schedules produced by PASTA are approximately 20 % longer than the ones produced by the well-known HEFT algorithm. However, the schedules produced by PASTA consume nearly 60 % less energy than those produced by HEFT. Empirical experiments on a physical test-bed confirm the power efficiency of PASTA in comparison with HEFT too.

Assignment problem in content distribution networks

In a Content Distribution Network (CDN) , there are m servers storing the data; each of them has a specific bandwidth. All the requests from a particular client should be assigned to one server because of the routing protocol used. The goal is to minimize the total cost of these assignments—cost of each is proportional to the distance between the client and the server as well as the request size—while the load on each server is kept below its bandwidth limit. When each server also has a setup cost, this is an unsplittable hard-capacitated facility location problem . As much attention as facility location problems have received, there has been no nontrivial approximation algorithm when we have hard capacities (i.e., there can only be one copy of each facility whose capacity cannot be violated) and demands are unsplittable (i.e., all the demand from a client has to be assigned to a single facility). We observe it is NP-hard to approximate the cost to within any bounded factor in this case. Thus, for an arbitrary constant ϵ>0, we relax the capacities to a 1+ϵ factor. For the case where capacities are almost uniform , we give a bicriteria O (log n , 1+ϵ)-approximation algorithm for general metrics and a (1+ϵ, 1+ϵ)-approximation algorithm for tree metrics. A bicriteria (α,β)-approximation algorithm produces a solution of cost at most α times the optimum, while violating the capacities by no more than a β factor. We can get the same guarantees for nonuniform capacities if we allow quasipolynomial running time. In our algorithm, some clients guess the facility they are assigned to, and facilities decide the size of the clients they serve. A straightforward approach results in exponential running time. When costs do not satisfy metricity, we show that a 1.5 violation of capacities is necessary to obtain any approximation. It is worth noting that our results generalize bin packing (zero connection costs and facility costs equal to one), knapsack (single facility with all costs being zero), minimum makespan scheduling for related machines (all connection costs being zero), and some facility location problems.

A two-stage Ant Colony optimization algorithm to minimize the makespan on unrelated parallel machines—part II: enhancements and experimentations

In a previous paper (Arnaout et al in J Intell Manuf 21:693---701, 2010), an Ant Colony optimization (ACO I) algorithm was introduced for minimizing the schedule's makespan on unrelated parallel machines with sequence-dependent setup times. Optimal solutions for small instances of this problem were obtained by solving a mixed integer program. However, for larger instances (up to 10 machines and 120 jobs), heuristic and approximate algorithms were necessary to reach solutions in reasonable computational times. ACO I's performance was evaluated by comparing its solutions to solutions obtained using Tabu Search and MetaRaPS (metaheuristic for Randomized Priority Search). While the results indicated that ACO I outperformed the other heuristics, it also showed that MetaRaPS had a better performance when all ratios of N/M (jobs to machines ratio) were considered. In this paper, we introduce an enhanced ACO which will be referred to as ACO II and compare its performance to other existing and new algorithms including ACO I, MetaRaPS, and SA. The extensive and expanded experiments conducted prove the superiority of the enhanced ACO II.

Semi-online scheduling on two identical machines with rejection

In this paper we consider two semi-online scheduling problems with rejection on two identical machines. A sequence of independent jobs are given and each job is characterized by its size (processing time) and its penalty, in the sense that, jobs arrive one by one and can be either rejected by paying a certain penalty or assigned to some machine. No preemption is allowed. The objective is to minimize the sum of the makespan of schedule, which is yielded by all accepted jobs and the total penalties of all rejected ones. In the first problem one can reassign several scheduled jobs in rejection tache, in the second a buffer with length k is available in rejection tache. Two optimal algorithms both with competitive ratio $\frac{3}{2}$ are presented.

New algorithms and complexity status of the reducibility problem of sequences in open shop scheduling minimizing the makespan

We consider the problem of minimizing the makespan in open shop scheduling. The decision problem whether a given sequence in open shop scheduling is irreducible has already been considered, however, has not been solved yet. A sequence is an acyclic orientation of the Hamming graph K n ×K m . Irreducible sequences in open shop are the local optimal elements. We present two variants of algorithms based on the specific properties of the H-comparability graph. The first is polynomial whereas the second is exponential. The irreducibility is co-NP. The stated properties argue whether it belongs to P. The complexity status of the considered decision problem is updated.

A Flow Shop Scheduling Problem with Transportation Time and Separated Setup Time of Jobs

A flowshop scheduling problem has been one of the classical problems in production scheduling since Johnson proposed the well-known Johnson's rule in the two-stage flow-shop make-span scheduling problem. Mitten and Johnson (1959) separately gave solution algorithm of obtaining an optimal sequence for an ′n-job, 2-machine′ flow shop scheduling problem in which each job involves arbitrary time lags (start-lag, stop-lag). Also Maggu and Das (1980) gives solution algorithm of obtaining optimal sequence for a ′ n-job, 2-machine′ flow shop scheduling problem where in each job involves transportation time. Johnson (1959) presented a solution to the n-job, 2-machine flow-shop problem with an algorithm that produces an ordered sequence with minimum total elapsed time. Kim and Bobrowski (1994) present a computer simulation model for a limited machine job shop scheduling problem with sequence-dependent setup times. They study the influence of setup times and due date's information in priority rules performance for job-shop problem with setup times. S. M. Johnson (1954) presents optimal two and three stage production schedules with setup time included. Wlodzimierz Szwarc (1986) discussed the flow shop problem with time lags and separated setup times. C.T. Ng et al. (2007) presents the three-machine flow-shop scheduling problem to minimize maximum lateness with separate setup times. W. H. Yang et al. (1999) addressed a survey of scheduling research involving setup times. An overall view on set up times in sequencing problems is presented. In this paper, we addressed the three machine flow shop scheduling problem to minimize total completion time where setup times are treated as separate from processing times. Two cases are studied, taking into consideration these factors and the set up times separated from the processing times. This new algorithm provides an optimal scheduling sequence for flow-shop scheduling problems of 5-jobs on 3-machines and is proposed by using separated setup times of a job.The present paper is a modest attempt to investigate how the setup time is helpful for the production.

Simultaneous scheduling of machines and automated guided vehicles in flexible manufacturing systems using genetic algorithms

The problem of simultaneous scheduling of machines and vehicles in flexible manufacturing system (FMS) was addressed. A spreadsheet based genetic algorithm (GA) approach was presented to solve the problem. A domain independent general purpose GA was used, which was an add-in to the spreadsheet software. An adaptation of the propritary GA software was demonstrated to the problem of minimizing the total completion time or makespan for simultaneous scheduling of machines and vehicles in flexible manufacturing systems. Computational results are presented for a benchmark with 82 test problems, which have been constructed by other researchers. The achieved results are comparable to the previous approaches. The proposed approach can be also applied to other problems or objective functions without changing the GA routine or the spreadsheet model.

A three-fold approach for job shop problems: A divide-and-integrate strategy with immune algorithm

This paper presents a novel divide-and-integrate strategy based approach for solving large scale job-shop scheduling problems. The proposed approach works in three phases. First, in contrast to traditional job-shop scheduling approaches where optimization algorithms are used directly regardless of problem size, priority rules are deployed to decrease problem scale. These priority rules are developed with slack due dates and mean processing time of jobs. Thereafter, immune algorithm is applied to solve each small individual scheduling module. In last phase, integration scheme is employed to amalgamate the small modules to get gross schedule with minimum makespan. This integration is carried out in dynamic fashion by continuously checking the preceding module's machine ideal time and feasible slots (satisfying all the constraint). In this way, the proposed approach will increase the machine utilization and decrease the makespan of gross schedule. Efficacy of the proposed approach has been tested with extremely hard standard test instances of job-shop scheduling problems. Implementation results clearly show effectiveness of the proposed approach.

Optimizing fuzzy makespan and tardiness for unrelated parallel machine scheduling with archived metaheuristics

This research presents two simulated annealing (SA) and a greedy randomized adaptive search procedure (GRASP) to solve unrelated parallel machine scheduling problems (UPMSPs) with two fuzzy optimization objectives—makespan and average tardiness. Few studies have employed fuzzy approach to solve multi-objective UPMSPs. In the research, several schemes are incorporated into the algorithm, including (1) matching-based decoding; (2) acceptance rule based on Pareto dominance, objective fitness, or Pareto reference point distance; (3) random or fixed weighted direction search. The matching-based decoding scheme has two phases: first max–min matching and then Hungarian method. Experiments were conducted to evaluate the algorithms’ performance for moderate to large problem size instances. The results indicate that matching-based decoding scheme significantly improves solution quality, but will require more computation time. GRASP with path relinking performs slightly worse than objective fitness-based multi-objective simulated annealing algorithms (MOSA), but better than Pareto dominance-based MOSA in terms of several Pareto performance measures.

A job grouping approach for planning container transfers at automated seaport container terminals

This paper proposes a practical job grouping approach, which aims to enhance the time related performance metrics of container transfers in the Patrick AutoStrad container terminal, located in Brisbane, Australia. It first formulates a mathematical model of the automated container transfers in a relatively complex environment. Apart from the consideration on collision avoidance of a fleet of large vehicles in a confined area, it also deals with many other difficult practical challenges such as the presence of multiple levels of container stacking and sequencing, variable container orientations, and vehicular dynamics that require finite acceleration and deceleration times. The proposed job grouping approach aims to improve the makespan of the schedule for yard jobs, while reducing straddle carrier waiting time by grouping jobs using a guiding function. The performance of the current sequential job allocation method and the proposed job grouping approach are evaluated and compared statistically using a pooled t-test for 30 randomly generated yard configurations. The experimental results show that the job grouping approach can effectively improve the schedule makespan and reduce the total straddle carrier waiting time.

A Three-Fold Approach to Solve Dynamic Job Shop Scheduling Problems by Artificial Immune Algorithm

This paper aims to propose a novel three-fold approach to solve dynamic job-shop scheduling problems by artificial immune algorithm. The proposed approach works in three phases. Firstly, priority rules are deployed to decrease problem scale instead of using scheduling algorithms directly. Secondly, immune algorithm is applied to optimize the individual scheduling modules. Finally, integration schema is employed to reschedule operations and minimize makespan of gross schedule. The integration schema is carried out in a dynamic manner that the previous modules’ machine idle time is searched continuously. In this way, the machine utilization is increased while the objective of makespan minimization is maintained. Efficacy of the proposed approach has been tested with test instances of job-shop scheduling problems. The experimentation results clearly show effectiveness of the proposed approach.

Profinet IO IRT Message Scheduling With Temporal Constraints

This paper presents an algorithm that allows one to create a static schedule of the Profinet IO IRT (Isochronous Real Time) communication, which is an industrial Ethernet protocol standardized in IEC 61158. This algorithm offers an alternative to the available commercial tool, providing comparable results with respect to the resulting schedule makespan. Furthermore, the problem is extended by useful temporal constraints (i.e., release dates, deadlines and end-to-end deadlines of the messages) providing a greater flexibility with respect to the individual messages. Due to this flexibility, it is possible to place the selected messages in various parts of the communication cycle (in order to increase the computational time available for the main-controller application, or to retransmit the synchronization message without holdup in the switch, or to add new messages into the original schedule). The solution is based on a formulation of the Profinet IO IRT scheduling problem in terms of the Resource Constrained Project Scheduling with Temporal Constraints.

Optimal semi-online algorithm for scheduling with rejection on two uniform machines

In this paper we consider a semi-online scheduling problem with rejection on two uniform machines with speed 1 and s?1, respectively. A sequence of independent jobs are given and each job is characterized by its size (processing time) and its penalty, in the sense that, jobs arrive one by one and can be either rejected by paying a certain penalty or assigned to some machine. No preemption is allowed. The objective is to minimize the sum of the makespan of schedule, which is yielded by all accepted jobs and the total penalties of all rejected ones. Further, two rejection strategies are permitted thus an algorithm can propose two different schemes, from which the better solution is chosen. For the above version, we present an optimal semi-online algorithm H that achieves a competitive ratio ? H (s) as a piecewise function in terms of the speed ratio s.

Sequencing and scheduling of job and tool in a flexible manufacturing system using ant colony optimization algorithm

Many optimization problems from the manufacturing systems are very complex in nature and quite hard to solve by conventional optimization techniques. The theme of this paper is to generate an active schedules and optimal sequence of job and tool that can meet minimum makespan schedule for the flexible manufacturing system. It consists of similar work center which is capable of doing many operations. The tools are stored in a common tool magazine that shares with and serves for several work centers to reduce the cost of duplicating tools in each and every work center. This type of manufacturing system is used for a manufacturing environment in which tools are expensive. To achieve the objective, the jobs and tools are sequenced and scheduled. In this work, non-traditional optimization technique such as ant colony optimization (ACO) algorithm are proposed to derive near-optimal solutions which adopt the Extended Giffler and Thompson algorithm for active feasible schedule generation. In this paper, the proposed algorithm is used for solving number of problems taken from the literature. The results available for the various existing algorithms are compared with results obtained by the ACO algorithm. The analysis reveals that ACO algorithm provides better solution with reasonable computational time.

Randomized priority algorithms

Borodin, Nielsen and Rackoff [13] introduced the class of priority algorithms as a framework for modeling deterministic greedy-like algorithms. In this paper we address the effect of randomization in greedy-like algorithms. More specifically, we consider approximation ratios within the context of randomized priority algorithms. As case studies, we prove inapproximation results for two well-studied optimization problems, namely facility location and makespan scheduling.

Design and Comparison of Simulated Annealing Algorithm and GRASP to Minimize Makespan in Single Machine Scheduling with Unrelated Parallel Machines

This paper discusses design and comparison of Simulated Annealing Algorithm and Greedy Randomized Adaptive Search Procedure (GRASP) to minimize the makespan in scheduling n single operation independent jobs on m unrelated parallel machines. This problem of minimizing the makespan in single machine scheduling problem with uniform parallel machines is NP hard. Hence, heuristic development for such problem is highly inevitable. In this paper, two different Meta-heuristics to minimize the makespan of the assumed problem are designed and they are compared in terms of their solutions. In the first phase, the simulated annealing algorithm is presented and then GRASP (Greedy Randomized Adaptive Search procedure) is presented to minimize the makespan in the single machine scheduling problem with unrelated parallel machines. It is found that the simulated annealing algorithm performs better than GRASP.

A hybrid decomposition procedure for scheduling projects under multiple resource constraints

This paper presents a hybrid decomposition procedure for solving the resource-constrained project scheduling problem. The procedure finds an initial schedule for the project, and refines it through a decomposition process. This is performed through a refinement process which consists of (i) analyzing the initial schedule to find appropriate decomposition point(s), (ii) decomposing the associated project into appropriate subprojects, (iii) optimizing the subprojects by an efficient implicit enumeration technique, and subsequently (iv) integrating optimal sub-schedules to create a feasible schedule. This refinement process is aimed at reducing the makespan of the initial schedule. To achieve further reduction, the refined schedule is overrefined by a genetic algorithm. The results of computational experiments performed on 2,040 benchmark instances indicate that in a reasonable time the procedure can obtain solutions whose average percentage deviation from their associated best solutions in the litrature is 0.41.

Makespan minimization of multi-slot just-in-time scheduling on single and parallel machines

The paper addresses the problem of multi-slot just-in-time scheduling. Unlike the existing literature on this subject, it studies a more general criterion--the minimization of the schedule makespan rather than the minimization of the number of slots used by schedule. It gives an O(nlog?2 n)-time optimization algorithm for the single machine problem. For arbitrary number of m>1 identical parallel machines it presents an O(nlog?n)-time optimization algorithm for the case when the processing time of each job does not exceed its due date. For the general case on m>1 machines, it proposes a polynomial time constant factor approximation algorithm.