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In this paper, we consider the rescheduling problem for jobs on a single machine with release dates to minimize total sequence disruption under a limit on the makespan. We show that the considered problem can be solved in polynomial time. Consequently, the rescheduling problem for jobs on a single machine with release dates to minimize makespan under a limit on the total sequence disruption can also be solved in polynomial time.

This paper is a contribution to the research which aims to provide an efficient optimization algorithm for job-shop scheduling problems with multi-purpose machines or MPMJSP. To meet its objective, this paper proposes a new variant of particle swarm optimization algorithm, called GLN-PSO_c, which is an extension of the standard particle swarm optimization algorithm that uses multiple social learning topologies in its evolutionary process. GLN-PSO_c is a metaheuristic that can be applied to many types of optimization problems, where MPMJSP is one of these types. To apply GLN-PSO_c in MPMJSP, a procedure to map the position of particle into the solution of MPMJSP is proposed. Throughout this paper, GLN-PSO_c combined with this procedure is named MPMJSP-PSO. The performance of MPMJSP-PSO is evaluated on well-known benchmark instances, and the numerical results show that MPMJSP-PSO performs well in terms of solution quality and that new best known solutions were found in some instances of the test problems.

The flow-shop minimum-length scheduling problem with n jobs processed on two machines is addressed where processing times are uncertain: only lower and upper bounds of the random processing times are given before scheduling, but their probability distributions are unknown. For such a problem, there may not exist a dominant schedule that remains optimal for all possible realizations of the processing times and so we look for a minimal set of schedules that are dominant. We obtain necessary and sufficient conditions for the case when it is possible to fix the order of two jobs in a minimal set of dominant schedules. The necessary and sufficient conditions are proven for the case when one schedule dominates all the others. We characterize also the case where there does not exist non-trivial schedule domination. All the conditions proven may be tested in polynomial time of n.

In this paper, we address the scheduling model with discretely compressible release dates, where processing any job with a compressed release date incurs a corresponding compression cost. We consider the following problem for the first time: scheduling with discretely compressible release dates to minimize the sum of makespan plus total compression cost. We show its NP-hardness, and design an approximation algorithm with worst-case performance ratio 2, which is the best possible if the processing order of the jobs is pre-specified.

We consider the offline scheduling problem to minimize the makespan on m parallel and identical machines with certain features. Each job and machine are labeled with the grade of service (GoS) levels, and each job can only be executed on the machine whose GoS level is no more than that of the job. In this paper, we present an efficient polynomial-time approximation scheme (EPTAS) with running time O(n log n) for the special case where the GoS level is either 1 or 2. This partially solves an open problem posed in (Ou et al., 2008). We also present a simpler full polynomial-time approximation scheme (FPTAS) with running time O(n) for the case where the number of machines is fixed.

In this study, we consider a permutation flow shop scheduling problem on a three-machine with deteriorating jobs (a deteriorating job means that the job's processing time is an increasing function of its starting time) so as to minimize the makespan. We model job deterioration as a function that is proportional to a linear function of time. For some special cases, we prove that the problem can be solved in polynomial time. We develop branch-and-bound and heuristic procedures for the general case. Computational experiments for the branch-and-bound algorithm and heuristic algorithm are presented.

We study a preemptive scheduling problem on two identical parallel machines that share a common server. Each job has to be loaded by the server before being processed on one of the machines and unloaded by the server after its processing. The loading and unloading times are both equal to one time unit. The goal is to minimize the makespan. We propose a O(n log n) solution algorithm for the preemptive variant of the problem.

In this paper, we consider the online-list scheduling on a single bounded parallel-batch machine to minimize makespan. In the problem, the jobs arrive online over list. The first unassigned job in the list should be assigned to a batch before the next job is released. Each batch can accommodate up to b jobs. For b = 2, we establish a lower bound 1 + γ of competitive ratio and provide an online algorithm with a competitive ratio of , where γ is the positive root of γ(γ + 1)² = 1. For b = 3, we establish a lower bound 1 + α of competitive ratio and provide an online algorithm with a competitive ratio of 2, where α is the positive root of the equation (1 + α)(1 + α²) = 2.

This paper addresses online scheduling of malleable parallel jobs to minimize the maximum completion time, i.e., makespan. It is assumed that the execution time of a job J_j with processing time p_j is p_j/k + (k-1)c if the job is assigned to k machines, where c > 0 is a constant setup time. We consider online algorithms for the scheduling problem on two identical machines. Namely, the job J_j can be processed on one machine with execution time p_j or alternatively two machines in parallel with execution time p_j/2+c. For the asymptotical competitive ratio, we provide an improved online algorithm with makespan no more than (3/2)C* +c/2, where C* is the optimal makespan. For the strict competitive ratio, we propose an online algorithm with competitive ratio of 1.54, which is close to the lower bound of 1.5.

The $n$-job and $m$-machine permutation flow shop scheduling problem with a proportional deterioration is considered in which all machines process the jobs in the same order, i.e., a permutation schedule. A proportional deterioration means that the job deterioration as an increasing function that is proportional to a linear function of time. The objective is to minimize the makespan, i.e., the maximum completion time. When some dominant relationships between $m-1$ machines can be satisfied, we show that some special cases of the problem can be polynomial solvable. For the general case, we also propose a heuristic algorithm and give the computational experiments.

In this paper, we consider a three-machine makespan minimization permutation flow shop scheduling problem with shortening job processing times. Shortening job processing times means that its processing time is a nonincreasing function of its execution start time. Optimal solutions are obtained for some special cases. For the general case, several dominance properties and two lower bounds are developed to construct a branch-and-bound (B&B) algorithm. Furthermore, we propose a heuristic algorithm to overcome the inefficiency of the branch-and-bound algorithm.

In this paper, we consider the scheduling problem in which the processing time of a job is a linear increasing function of its starting time and machine with availability constraints. The objective is to minimize the makespan. We first present a fully polynomial-time approximation scheme (FPTAS) for the case with a single machine. We then show that there exists no polynomial time approximation algorithm with a constant worst-case bound for the case with two identical machines unless $\mathrm{\text{P}}=\mathrm{\text{NP}}$.

In this paper, we study an online scheduling on two parallel machines in MapReduce-like system where each job contains two kinds of tasks: map tasks and reduce tasks. A job’s reduce tasks can only be processed after all its map tasks are finished. We assume that the map tasks are fractional and the reduce tasks are preemptive. Our objective is to minimize makespan. We show that the lower bound for this MapReduce scheduling problem is $\sqrt{2}$. We then present an online algorithm with competitive ratio of $\sqrt{2}$ and thus it is optimal.

In this paper, we consider the scheduling of high multiplicity jobs on parallel multi-purpose machines with setup times and machine available times, with the objective of minimizing makespan. High multiplicity means that jobs are partitioned into several groups and in each group all jobs are identical. Whenever there is a switch from processing a job of one group to a job of another group, a setup time is needed. Multi-purpose machine implies that each job can only be processed by a specific subset of all the machines, called processing set. A mixed integer programming is formulated for this NP-hard problem. A heuristic is proposed to solve the problem. Lower bounds are developed to evaluate the heuristic algorithm. Extensive numerical computations are performed and the results show that the heuristic generates solutions with makespan within 2% above the lower bounds in average, and outperforms CPLEX 12.6 for large scale and complex problems.

Scheduling is considered to be a major task to improve the shop-floor productivity. The job shop problem is under this category and is combinatorial in nature. Research on optimization of job shop problem is one of the most significant and promising areas of optimization. This paper presents an application of the Ant Colony Optimization meta heuristic to job shop problem. The main characteristics of this model are positive feedback and distributed computation. The settings of parameter values have more influence in solving instances of job shop problem. An algorithm is introduced to improve the basic ant colony system by using a pheromone updating strategy and also to analyze the quality of the solution for different values of the parameters. In this paper, we present statistical analysis for parameter tuning and we compare the quality of obtained solutions by the proposed method with the competing algorithms given in the literature for well known benchmark problems in job shop scheduling.

This paper discusses about the flow shop scheduling problems using shortest processing time, earliest due date (EDD), Nawaz, Enscore, and Ham (NEH), NEH-EDD, and modified-NEH methods. The objective of this research is to determine the performance of these methods in minimizing makespan and total tardiness. Processing times and due dates were randomly generated, and computational studies were performed in Microsoft Visual Basic 6.0. The experiments are performed for small and medium data sets. Efficiency index, relative error, and run time measure the performance of each method. Experimental results showed that NEH has the best performance in minimizing the makespan in both data sets; these are 53.35 time unit for small data sets and 83.803 time unit for medium data sets. NEH-EDD has the best performance in minimizing total tardiness with 9.37 time unit for small data sets and 231.02 time unit for medium data sets. Modified-NEH, as the proposed method for minimizing makespan and total tardiness at the same time, has good enough result. For minimizing the makespan, modified-NEH results in 57.15 time unit for small data sets and 88.107 time unit for medium data sets. For minimizing total tardiness, the modified-NEH results in 14.21 time unit for small data sets and 246.57 time unit for medium sets.

We address a generalization of the classical job-shop problem which is called a hybrid job-shop problem. The criteria under consideration are the minimization of the makespan and mean flow time. In the hybrid job-shop, machines of type $k$ are available for processing the specific subset ${{𝒪}}^k$ of the given operations. Each set ${{𝒪}}^k$ may be partitioned into subsets for their processing on the machines of type $k$. Solving the hybrid job-shop problem implies the solution of two subproblems: an assignment of all operations from the set ${{𝒪}}^k$ to the machines of type $k$ and finding optimal sequences of the operations for their processing on each machine. In this paper, a genetic algorithm is developed to solve these two subproblems simultaneously. For solving the subproblems, a special chromosome is used in the genetic algorithm based on a mixed graph model. We compare our genetic algorithms with a branch-and-bound algorithm and three other recent heuristic algorithms from the literature. Computational results for benchmark instances with 10 jobs and up to 50 machines show that the proposed genetic algorithm is rather efficient for both criteria. Compared with the other heuristics, the new algorithm gives most often an optimal solution and the average percentage deviation from the optimal function value is about 4%.

This paper develops a new harmony search (HS) algorithm for the hybrid flow shop scheduling problem with multiprocessor tasks, which is known to be NP-hard in the strong sense. The goal is to minimize the makespan. Thus, the proposed HS starts with the application of an opposition based learning (OBL) method to increase the diversity level of the initial harmony memory (HM). Furthermore, we use novel improvisation rules of producing new harmonies based on crossover and mutation operators. Also, neighborhood techniques are employed to enhance the searching and improve the solution quality. The proposed HS is compared with three algorithms from the literature. The computational experiments demonstrate the effectiveness of the proposed HS algorithm in terms of makespan.

Scheduling jobs and tools is a significant problem for manufacturing systems. Inefficient job scheduling and tool loading planning may result in under utilization of capital intensive machines and a high level of machine idle time. Therefore, efficient scheduling of jobs and tools enables a manufacturing system to increase machines’ utilization and decrease their idle times. This paper addresses machines’ and tools’ joint scheduling with alternate machines in a multimachine flexible manufacturing system (FMS) to minimize makespan (MSN). Only one copy of each type of tool is made available in FMS where tools are expensive. The tools are stored in the central tool magazine (CTM), which shares and serves them to several machines in order to reduce the cost of duplicating the tools in every machine. The problem is to select machines from alternate machines for job-operations, allocation of tools to the job-operations and job-operations’ sequencing on machines for MSN minimization. This paper presents nonlinear mixed integer programming (MIP) formulation to model this simultaneous scheduling problem and crow search algorithm (CSA) built on the crows’ intelligent behavior for solving this problem. The results show that CSA is providing better solutions than Jaya algorithm and the usage of alternate machines for the operations can reduce MSN.

Scheduling jobs and tools is a significant problem for manufacturing systems. Inefficient job scheduling and tool loading planning may result in the underutilization of capital-intensive machines and a high machine idle time. Tools are transferred by a tool transporter (TT) between machines. Therefore, efficient scheduling of jobs, TT, and the tools with alternate machines enables a manufacturing system to increase machines’ utilization and decrease their idle times. This paper addresses machines, TT, and tools concurrent scheduling with alternate machines and only one copy of every tool variety is made available where the tools are costly, in a multi-machine flexible manufacturing system, taking into account tool transfer times for makespan (MS) minimization. The tools are placed in a central tool magazine, which shares and serves them to many machines to cut down the price of duplicating the tools in each machine. The problem is to assign machines from alternate machines, tools, and corresponding TT trips, including the deadheading trip and loaded trip, to job operations for MS minimization. This paper uses a nonlinear mixed-integer programming framework to present the problem, and a flower pollination algorithm (FPA) is employed to solve it. The results show that FPA outperforms the Jaya algorithm, and the usage of alternate machines for the operations reduces the MS. Reduction in MS indicates an improvement in utilization of resources.