A PSO and a Tabu search heuristics for the assembly scheduling problem of the two-stage distributed database application

The assembly flowshop scheduling problem has been addressed recently in the literature. There are many problems that can be modeled as assembly flowshop scheduling problems including queries scheduling on distributed database systems and computer manufacturing. The problem has been addressed with respect to either makespan or total completion time criterion in the literature. In this paper, we address the problem with respect to a due date-based performance measure, i.e., maximum lateness. We formulate the problem and obtain a dominance relation. Moreover, we propose three heuristics for the problem: particle swarm optimization (PSO), Tabu search, and EDD. PSO has been used in the areas of function optimization, artificial neural network training, and fuzzy system control in the literature. In this paper, we show how it can be used for scheduling problems. We have conducted extensive computational experiments to compare the three heuristics along with a random solution. The computational analysis indicates that Tabu outperforms the others for the case when the due dates range is relatively wide. It also indicates that the PSO significantly outperforms the others for difficult problems, i.e., tight due dates. Moreover, for difficult problems, the developed dominance relation helps reduce error by 65%.     

Using two-machine flowshop with maximum lateness objective to model multimedia data objects scheduling problem for WWW applications

The multimedia data objects scheduling problem for WWW applications is modeled using the two-machine flowshop problem of minimizing maximum lateness with separate setup times. We establish three dominance relations, and propose four heuristics. Also, we conduct computational experiments to compare the performance of the proposed heuristics and that of existing ones in the literature. The results of the computational experiments show that the proposed heuristics are quite efficient.Scope and purposeA two-machine flowshop scheduling problem involves scheduling a number of jobs on the machines in order to optimize a given criterion. The majority of research assumes that setup times are negligible or can be combined with the processing times. However, the latter assumption is invalid since it may lead to more idle time on the second machine. In the literature, the separate setup times problem has been mainly addressed with the completion-time-related objective functions such as makespan. However, there are many real-life situations in which a due-date-related objective function such as maximum lateness is more appropriate. The problem with maximum lateness objective has received limited attention from researchers as indicated by a recent survey paper. In this paper, we show a real-life situation in the Internet where the two-machine flowshop problem of minimizing maximum lateness with separate setup times can be used to model the multimedia object scheduling problem. We propose new improved heuristics for this problem and compare with existing ones in the literature.     

Makespan minimization subject to flowtime optimality on identical parallel machines

We consider the identical parallel machine problem with makespan minimization subject to minimum total flowtime. First, we develop an optimal algorithm to the identical parallel machine problem with the objective of minimizing makespan. To improve the computational efficiency, two implementation techniques, the lower bound calculation and the job replacement rule, are applied. Based on the algorithm, an optimal algorithm, using new lower bounds, to the considered problem is developed. The result of this study can also be used to solve the bicriteria problem of minimizing the weighted sum of makespan and mean flowtime. Computational experiments are conducted up to six machines and 1000 jobs. Although the proposed algorithm has an exponential time complexity, the computational results show that it is efficient to find the optimal solution.     

A branch-and-bound algorithm for the three-machine flowshop scheduling problem with bicriteria of makespan andtotal flowtime

This paper addresses the three‐machine flowshop scheduling problem with a bicriteria of minimizing a weighted sum of makespan and total flowtime. Three lower bounds, an upper bound, and several dominance relations are developed. The upper bound is developed using a two‐phase hybrid heuristic method. A branch‐and‐bound algorithm, incorporating the developed bounds and dominance relations, is presented. An extensive computational analysis on randomly generated problems is conducted. The analysis indicates that the proposed bounds, dominance relations, and branch‐and‐bound algorithm are efficient.     

Scalable,low complexity,and fast greedy scheduling heuristics for highly heterogeneous distributed computing systems

For heterogeneous distributed computing systems, important design issues are scalability and system optimization. Given such systems, it is crucial to develop low computational complexity algorithms to schedule tasks in a manner that exploits the heterogeneity of the resources and applications. In this paper, we report and evaluate three scalable, and fast scheduling heuristics for highly heterogeneous distributed computing systems. We conduct a comprehensive performance evaluation study using simulation. The benchmarking outlines the performance of the schedulers, representing scalability, makespan, flowtime, computational complexity, and memory utilization. The set of experimental results shows that our heuristics perform as good as the traditional approaches, for makespan and flowtime, while featuring lower complexity, lower running time, and lower used memory. The experimental results also detail the various scenarios under which certain algorithms excel and fail.     

Worst-case and numerical analysis of heuristic algorithms for flowshop scheduling problems with a time-dependent learning effect

In this paper, we investigate a time-dependent learning effect in a flowshop scheduling problem. We assume that the time-dependent learning effect of a job was a function of the total normal processing time of jobs scheduled before the job. The following objective functions are explored: the makespan, the total flowtime, the sum of weighted completion times, the sum of the kth power of completion times, and the maximum lateness. Some heuristic algorithms with worst-case analysis for the objective functions are given. Moreover, a polynomial algorithm is proposed for the special case with identical processing time on each machine and that with an increasing series of dominating machines, respectively. Finally, the computational results to evaluate the performance of the heuristics are provided.     

Minimizing mean flowtime and makespan on master–slave systems

The master–slave scheduling model is a new model recently introduced by Sahni. It has many important applications in parallel computer scheduling and industrial settings such as semiconductor testing, machine scheduling, etc. In this model each job is associated with a preprocessing task, a slave task and a postprocessing task that must be executed in this order. While the preprocessing and postprocessing tasks are scheduled on the master machine, the slave tasks are scheduled on the slave machines. In this paper, we consider scheduling problems on single-master master–slave systems. We first strengthen some previously known complexity results for makespan problems, by showing them to be strongly NP-hard. We then show that the problem of minimizing the mean flowtime is strongly NP-hard even under severe constraints. Finally, we propose some heuristics for the mean flowtime and makespan problems subject to some constraints, and we analyze the worst-case performance of these heuristics.     

Heuristics for a two-stage assembly flowshop with bicriteria of maximum lateness and makespan

We consider a two-stage assembly flowshop scheduling problem with the objective of minimizing a weighted sum of makespan and maximum lateness. The problem is known to be NP-hard, and therefore, we propose heuristics to solve the problem. The proposed heuristics are Tabu search (Tabu), particle swarm optimization (PSO), and self-adaptive differential evolution (SDE). An extensive computational experiment is conducted to compare performances of the proposed heuristics. The computational experiment reveals that both PSO and SDE are much superior to Tabu. Moreover, it is statistically shown that PSO performs better than SDE. The computation times of both PSO and SDE are close to each other and they are less than 40 and 45 s, respectively, for the largest size problem considered.     

Single machine scheduling problems with exponentially time-dependent learning effects

In this paper, we introduce a single-machine scheduling problem with an exponentially time-dependent learning effect. The processing time of a job is assumed to be an exponential function of the total normal processing time of jobs already processed before it. For such a scheduling problem, we first provide the upper bound for the maximum lateness and for the total weighted completion time. Next, we show that problems with the following criteria: makespan, the total completion time, the total weighted completion time, the total earliness/tardiness penalties and the maximum lateness under some agreeable conditions, are polynomially solvable.     

Minimizing total tardiness in a two-machine re-entrant flowshop with sequence-dependent setup times

We consider a two-machine re-entrant flowshop scheduling problem in which all jobs must be processed twice on each machine and there are sequence-dependent setup times on the second machine. For the problem with the objective of minimizing total tardiness, we develop dominance properties and a lower bound by extending those for a two-machine re-entrant flowshop problem (without sequence-dependent setup times) as well as heuristic algorithms, and present a branch and bound algorithm in which these dominance properties, lower bound, and heuristics are used. For evaluation of the performance of the branch and bound algorithm and heuristics, computational experiments are performed on randomly generated instances, and results are reported.     

Hierarchical minimization of completion time variance and makespan in jobshops

This paper addresses the problem of minimizing makespan for a given set of n jobs to be processed on each of m machines in a static jobshop, subject to the minimum completion time variance (CTV). A lower bound on CTV is developed for the static jobshop problem. A backward scheduling approach is proposed using the observations on the development of lower bound for hierarchical minimization of CTV and makespan. A lower bound on makespan subject to minimum CTV is also presented for this problem. Finally, we present two simulated annealing heuristic approaches using the concepts of forward and backward scheduling. Their performances are compared against each other through the use of the lower bounds established in this work. The simulated annealing heuristic based on backward scheduling is shown to perform well by evaluating the developed heuristics on 82 jobshop problems taken from literature.     

A new heuristic and dominance relations for no-wait flowshops with setups

The two-machine no-wait flowshop problem, where setup times are considered separate from processing times and sequence independent, is addressed with respect to minimizing total flowtime. A local and a global dominance relation are developed and a new heuristic is provided. Furthermore, a lower bound is obtained and used along with the dominance relations in a branch-and-bound algorithm in order to evaluate the efficiency of the heuristic. Computational experience demonstrates the superiority of the local dominance relation and the new heuristic.Scope and purposeNo-wait flowshop problems, where jobs have to be processed without interruption between consecutive machines, represent an important area in scheduling. There are several industries where the no-wait flowshop problem applies including the metal, plastic, and chemical industries. For instance, in the case of steel production, the heated metal must continuously go through a sequence of operations before it is cooled in order to prevent defects in the composition of the material. Another important area arises when setup time is considered separate from processing time. Such a consideration is particularly justified when the ratio of setup to processing time is non-negligible. Many applications warrant separate consideration of setup; examples include the re-tooling of multi-tool equipment. Other applications can be found in textile, plastic, chemical, and semi-conductor industries. This paper develops a new heuristic and dominance relations for the two-machine no-wait separate setup flowshop problem, where the performance criterion is total flowtime.     

Worst-case performance of critical path type algorithms

The critical path method remains one of the most popular approaches in practical scheduling. Being developed for the makespan problem this method can also be generalized to the maximum lateness problem. For the unit execution time task system and parallel processors this generalization is known as the Brucker–Garey–Johnson algorithm. We characterize this algorithm by introducing an upper bound on the deviation of the criterion from its optimal value. The bound is stated in terms of parameters characterizing the problem, namely number of processors, the length of the longest path, and the total required processing time. We also derive a similar bound for the preemptive version of the Brucker– Garey–Johnson algorithm.     

Scheduling unrelated parallel batch processing machines with non-identical job sizes

Scheduling unrelated parallel batch processing machines to minimize makespan is studied in this paper. Jobs with non-identical sizes are scheduled on batch processing machines that can process several jobs as a batch as long as the machine capacity is not violated. Several heuristics based on best fit longest processing time (BFLPT) in two groups are proposed to solve the problem. A lower bound is also proved to evaluate the quality of the heuristics. Computational experiments were undertaken. These showed that J_SC-BFLPT, considering both load balance of machines and job processing times, was robust and outperformed other heuristics for most of the problem categories.     

具有线性恶化加工时间的调度问题

讨论了工件具有线性恶化加工时间的调度问题.在这类问题中,工件的恶化函数为线性函数.对单机调度问题中目标函数为极小化最大完工时间加权完工时间和,最大延误以及最大费用等问题分别给出了最优算法.对两台机器极小化最大完工时间的Flowshop问题,证明了利用Johnson规则可以得到最优调度.对于一般情况,如果同一工件的工序的加工时间均相等,则Flowshop问题可以转化为单机问题.     

Several flow shop scheduling problems with truncated position-based learning effect

The concept of truncated position-based learning process plays a key role in production environments. However, it is relatively unexplored in the flow shop setting. In this paper, we consider the flow shop scheduling with truncated position-based learning effect, i.e., the actual processing time of a job is a function of its position and a control parameter in a processing permutation. The objective is to minimize one of the six regular performance criteria, namely, the total completion time, the makespan, the total weighted completion time, the discounted total weighted completion time, the sum of the quadratic job completion times, and the maximum lateness. We present heuristic algorithms and analyze the worst-case bound of these heuristic algorithms. We also provide the computational results to evaluate the performance of the heuristics.     

Solving a two-agent single-machine scheduling problem considering learning effect

Scheduling with multiple agents and learning effect has drawn much attention. In this paper, we investigate the job scheduling problem of two agents competing for the usage of a common single machine with learning effect. The objective is to minimize the total weighted completion time of both agents with the restriction that the makespan of either agent cannot exceed an upper bound. In order to solve this problem we develop several dominance properties and a lower bound based on a branch-and-bound to find the optimal algorithm, and derive genetic algorithm based procedures for finding near-optimal solutions. The performances of the proposed algorithms are evaluated and compared via computational experiments.     

Single machine scheduling to minimize maximum lateness subject to release dates and precedence constraints

This paper considers the problem of finding a nonpreemptive schedule for a single machine to minimize the maximum lateness with release dates and precedence constraints. A branch and bound algorithm is developed. The algorithm uses four different heuristics to find upper bounds at the initial branch node: early release date heuristic, modified Schrage's heuristic, heuristic BLOCK, and a variable neighborhood descent procedure. At each branch node, two branches evolve from a schedule found by heuristic BLOCK using a binary branching rule based on bottleneck and critical jobs, and a lower bound is obtained by optimally solving the relaxed problem with preemption. The algorithm solves 14,984 out of the 15,000 systematically generated instances with up to 1,000 jobs within 1 minute of CPU time.     

The three-stage assembly flowshop scheduling problem

We consider the three-stage assembly flowshop scheduling problem with the objective of minimizing the makespan. The three-stage assembly problem generalizes both the serial three machine flowshop problem and the two-stage assembly flowshop scheduling problem and is therefore strongly NP-hard. We analyze the worst-case ratio bound for several heuristics for this problem. We also analyze the worst-case absolute bound for a heuristic based on compact vector summation techniques and we point out that, for a large number of jobs, this heuristic becomes asymptotically optimal.Scope and purposeThe three-stage assembly flowshop scheduling problem models situations which arise frequently in manufacturing when various fabrication operations are performed concurrently and then collected and transported into an assembly area for a final assembly operation. The main criterion for this problem is the minimization of the maximum job completion time (makespan). The objective of this paper is to derive algorithms for minimizing the makespan. In doing so, we also demonstrate the reduction of assembly flowshop problems to their embedded serial flowshop problems.     

Scheduling rules for dynamic shops that manufacture multi-level jobs

The problem of scheduling in dynamic conventional jobshops has been extensively investigated over many years. However, the problem of scheduling in assembly jobshops (i.e. shops that manufacture multi-level jobs with components and subassemblies) has been relatively less investigated in spite of the fact that assembly jobshops are frequently encountered in real life. A survey of literature on dynamic assembly jobshop scheduling has revealed that the TWKR-RRP rule is the best one for minimizing the mean flowtime and staging delay, and the job due-date (JDD) rule is the best for minimizing the mean tardiness of jobs. However, the objectives of minimizing the maximum flowtime (and maximum staging delay) and standard deviation of flowtime (and standard deviation of staging delay) are as important as the minimization of mean flowtime and mean staging delay. Likewise, the objectives of minimizing the maximum tardiness and standard deviation of tardiness are also as important as the minimization of mean tardiness. The reason is that the maximum and standard deviation values of a performance measure indicate the worst-case performance of a dispatching rule. The present study seeks to develop efficient dispatching rules to minimize the maximum and standard deviation of flowtime and staging delay, and the maximum and the standard deviation of conditional tardiness of jobs. The dispatching rules are based on the computation of the earliest completion time of a job and consequently determining the latest finish time of operations on components/subassemblies of a job. An extensive simulation-based investigation of the performance evaluation of the existing dispatching rules and the proposed dispatching rules has been carried out by randomly generating jobs with different structures and different shop utilization levels. It has been found from the simulation study that the proposed rules are quite effective in minimizing the maximum and standard deviation of flowtime and staging delay, and the maximum conditional tardiness and standard deviation of conditional tardiness.