A branch-and-bound algorithm for three-machine flowshop scheduling problem to minimize total completion time with separate setup times

In this paper, we address the three-machine flowshop scheduling problem. Setup times are considered separate from processing times, and the objective is to minimize total completion time. We show that the three-site distributed database scheduling problem can be modeled as a three-machine flowshop scheduling problem. A lower bound is developed and a dominance relation is established. Moreover, an upper bound is developed by using a three-phase hybrid heuristic algorithm. Furthermore, a branch-and-bound algorithm, incorporating the developed lower bound, dominance relation, and the upper bound is presented. Computational analysis on randomly generated problems is conducted to evaluate the lower and upper bounds, the dominance relation, and the branch-and-bound algorithm. The analysis shows the efficiency of the upper bound, and, hence, it can be used for larger size problems as a heuristic algorithm.     

A two-machine flowshop scheduling problem with a truncated sum of processing-times-based learning function

Scheduling with learning effects has received continuing attention in the recent days. However, it can be found that the actual processing time of a given job drops to zero precipitously as the job has a big processing time or the number of jobs increases. Moreover, most researchers paid more attention to single-machine settings, and the flowshop settings then are relatively unexplored. Motivated by these observations, we consider a two-machine total completion time flowshop problem in which the actual job processing time is a function depending on the jobs that have already been processed and a control parameter. In this paper, we develop a branch-and-bound and a genetic heuristic-based algorithm for the problem. In addition, the experimental results of all proposed algorithms are also provided.     

Two-Stage Flowshop Scheduling Problem with Bicriteria

The two-stage flowshop scheduling problem with the objective of minimizing total flowtime subject to obtaining the optimal makespan is discussed. A branch-and-bound algorithm and two heuristic algorithms have been developed. The results of the experimental investigation of the effectiveness of the algorithms are also presented.     

No-wait flowshops with bicriteria of makespan and total completion time

We consider the m-machine no-wait flowshop scheduling problem with the objective of minimizing a weighted sum of makespan and total completion time. For the two-machine problem, we develop a dominance relation and embed it within a proposed branch-and-bound algorithm. For the m-machine problem, we propose a heuristic. Computational experiments show that the proposed heuristic outperforms the best existing multi-criteria heuristics and the best single criterion heuristics for makespan and total completion time. The efficiency of the dominance relation and branch-and-bound algorithm is also investigated and shown to be effective.     

含不相关机的动态可重入柔性流水车间问题的混合DABC-GA算法

为了改善生产线的物流平衡和加强阶段间的时间衔接,扩展一般可重入柔性流水车间调度理论,以最小化总加权完工时间为目标,研究了每阶段含不相关并行机的动态可重入柔性流水车间问题,工件在各阶段的加工时间取决于加工它的机器。鉴于所研究问题为NP-hard问题,首先,建立整数规划模型;其次,设计元胞矩阵编码方案,提出融合离散人工蜂群算法和遗传算法的一种混合算法以获得问题的近优解;最后,为了评估混合算法的性能,将所提出算法和一些元启发式算法进行了不同规模问题的对比测试,实验结果说明了所提算法的有效性。     

带准备时间的单机指数时间学习效应排序问题

研究带有准备时间的单机学习效应模型,其中工件加工时间具有指数时间学习效应,即工件的实际加工时间是已经排好的工件加工时间的指数函数。学习效应模型考虑工件的实际加工时间同时依赖于工件本身的加工时间和已加工工件的累计加工时间,目标函数为最小化总完工时间。这个问题是NP-难的,提出了一个数学规划模型来求解该问题的最优解。通过分析几个优势性质和下界,提出分支定界算法来求解此问题,并设计启发式算法改进分支定界算法的上界值。通过仿真实验验证了分支定界算法在求解质量和时间方面的有效性。     

Group scheduling in a two-stage flowshop

This paper investigates a two-stage flowshop group scheduling problem with the objective of minimising makespan (the completion time of the last job). In the multiple-stage group scheduling, each job is generally classified into one family by considering its characteristics at all stages as a whole. However, in this study, each job is classified into multiple families, one family per stage. For this problem, two heuristics based on the branch-and-bound algorithm are constructed and their efficiencies are investigated.     

A hybrid single and dual population search procedure for the job shop scheduling problem

This paper presents a genetic algorithm and a scatter search procedure to solve the well-known job shop scheduling problem. In contrast to the single population search performed by the genetic algorithm, the scatter search algorithm splits the population of solutions in a diverse and high-quality set to exchange information between individuals in a controlled way. The extension from a single to a dual population, by taking problem specific characteristics into account, can be seen as a stimulator to add diversity in the search process. This has a positive influence on the important balance between intensification and diversification. Computational experiments verify the benefit of this diversity on the effectiveness of the meta-heuristic search process. Various algorithmic parameters from literature are embedded in both procedures and a detailed comparison is made. A set of standard instances is used to compare the different approaches and the best obtained results are benchmarked against heuristic solutions found in literature.     

A Branch-and-Bound Approach for a Two-machine Flowshop Scheduling Problem

In this paper, we present a branch-and-bound approach for solving a two-machine flow shop scheduling problem, in which the objective is to minimize a weighted combination of job flowtime and schedule makespan. Experimental results show that the algorithm works very well for certain special cases and moderately well for others. In fact, it is able to produce optimal schedules for 500-job problems in which the second machine dominates the first machine. It is also shown that the algorithm developed to provide an upper bound for the branch-and-bound is optimal when processing times for jobs are the same on both machines. The primary reason for developing the branch-and-bound approach is that its results can be used to guide other heuristic techniques, such as simulated annealing, tabu search and genetic algorithms, in their search for optimal solutions for larger problems.     

Maximizing total job value on a single machine with job selection

This paper describes a single-machine scheduling problem of maximizing total job value with a machine availability constraint. The value of each job decreases over time in a stepwise fashion. Several solution properties of the problem are developed. Based on the properties, a branch-and-bound algorithm and a heuristic algorithm are derived. These algorithms are evaluated in the computational study, and the results show that the heuristic algorithm provides effective solutions within short computation times.     

Minimizing total tardiness on a two-machine re-entrant flowshop

We present a branch and bound algorithm for a two-machine re-entrant flowshop scheduling problem with the objective of minimizing total tardiness. In the re-entrant flowshop considered here, all jobs must be processed twice on each machine, that is, each job should be processed on machine 1, machine 2 and then machine 1 and machine 2. By regarding a job as a pair of sub-jobs, each of which represents a pass through the two machines, we develop dominance properties, a lower bound and heuristic algorithms for the problem, and use these to develop a branch and bound algorithm. For evaluation of the performance of the algorithms, computational experiments are performed on randomly generated test problems and results are reported. Results of the experiments show that the suggested branch and bound algorithm can solve problems with up to 20 sub-jobs in a reasonable amount of CPU time, and the average percentage gap of the heuristic solutions is about 13%.     

Scheduling of a Two-machine Flowshop with Processing Time Linearly Dependent on Job Waiting-time

This paper deals with the problem of finding the minimum finish-time schedule in a two-machine flowshop, where the processing times of jobs are linearly dependent on the job waiting-times. The problem is shown to be NP-hard. A heuristic algorithm is presented, and the worst-case bounds are derived for the different variations of the algorithm.     

A partial enumeration heuristic for multi-objective flowshop scheduling problems

This paper addresses the flowshop scheduling problem with multiple performance objectives in such a way as to provide the decision maker with approximate Pareto optimal solutions. It is well known that the partial enumeration constructive heuristic NEH and its adaptations perform well for single objectives such as makespan, total tardiness and flowtime. In this paper, we develop a similar heuristic using the concept of Pareto dominance when comparing partial and complete schedules. The heuristic is tested on problems involving combinations of the above criteria. For the two-machine case, and the pairs of objectives: (i) makespan and maximum tardiness, (ii) makespan and total tardiness, the heuristic is compared with branch-and-bound algorithms proposed in the literature. For two and more than two machines, and the criteria combinations considered in this article, the heuristic performance is tested against constructive heuristics reported in the literature. By means of an illustrative example, it is shown that a genetic algorithm from the literature performs better when starting from heuristic solutions rather than random solutions.     

Minimizing total weighted completion time in a two-machine flow shop scheduling under simple linear deterioration

In this paper, we address a two-machine flow shop scheduling problem under simple linear deterioration. By a simple linear deterioration function, we mean that the processing time of a job is a simple linear function of its execution start time. The objective is to find a sequence that minimizes total weighted completion time. Optimal schedules are obtained for some special cases. For the general case, several dominance properties and two lower bounds are derived to speed up the elimination process of a branch-and-bound algorithm. A heuristic algorithm is also proposed to overcome the inefficiency of the branch-and-bound algorithm. Computational analysis on randomly generated problems is conducted to evaluate the branch-and-bound algorithm and heuristic algorithm.     

Scheduling a single batch-processing machine with arbitrary job sizes and incompatible job families: An ant colony framework

This paper investigates the first attempt on the batch-processing machine scheduling problem, where the machine can process multiple jobs simultaneously, using an ant colony optimization metaheuristic. We consider the scheduling problem of a single batch-processing machine with incompatible job families and the performance measure of minimizing total weighted completion time. Jobs of a given family have an identical processing time and are characterized by arbitrary sizes and weights. Based on a number of developed heuristic approaches, we propose an ant colony framework (ACF) in two versions, which are distinguished by the type of embedded heuristic information. Each version is also investigated in two formats, that is the pure ACF and the hybridized ACF. To verify the performance of our framework, comparisons are made based on using a set of well-known existing heuristic and meta-heuristic algorithms taken from the literature, on a diverse set of artificially generated test problem instances. Computational results show the high performance of the proposed framework and signify its ability to outperform the comparator algorithms in most cases as the problem size increases.     

A No-Wait Flowshop Scheduling Heuristic to Minimize Makespan

The scheduling problem in the no-wait or constrained flowshop, with the makespan objective, is considered in this article. A simple heuristic algorithm is proposed on the basis of heuristic preference relations and job insertion. When evaluated over a large number of problems of various sizes, the solutions given by the proposed heuristic are found to be fairly accurate and much superior to those given by the two existing heuristics.     

A bi-criteria two-machine flowshop scheduling problem with a learning effect

This paper addresses a bi-criteria two-machine flowshop scheduling problem when the learning effect is present. The objective is to find a sequence that minimizes a weighted sum of the total completion time and the maximum tardiness. In this article, a branch-and-bound method, incorporating several dominance properties and a lower bound, is presented to search for the exact solution for small job-size problems. In addition, two heuristic algorithms are proposed to overcome the inefficiency of the branch-and-bound algorithm for large job-size problems. Finally, computational results for this problem are provided to evaluate the performance of the proposed algorithms.     

A branch-and-bound algorithm for a two-machine flowshop scheduling problem with limited waiting time constraints

In this paper, we consider a two-machine flowshop scheduling problem in which the waiting time of each job between the two machines cannot be greater than a certain time period. For the problem with the objective of minimizing makespan, we identify several dominance properties of the problem and develop a branch-and-bound (B&B) algorithm using the dominance properties. Computational tests are performed on randomly generated test problems for evaluation of performance of the B&B algorithm, and results show that the algorithm can solve problems with up to 150 jobs in a reasonable amount of CPU time.     

Crane scheduling with non-crossing constraint

In this paper, we examine crane scheduling for ports. This important component of port operations management is studied when the non-crossing spatial constraint, which is common to crane operations, is considered. We assume that ships can be divided into holds and that cranes can move from hold to hold but jobs are not pre-emptive, so that only one crane can work on one hold or job to complete it. Our objective is to minimize the latest completion time for all jobs. We formulate this problem as an integer programming problem. We provide the proof that this problem is NP-complete and design a branch-and-bound algorithm to obtain optimal solutions. A simulated annealing meta-heuristic with effective neighbourhood search is designed to find good solutions in larger size instances. The elaborate experimental results show that the branch-and-bound algorithm runs much faster than CPLEX and the simulated annealing approach can obtain near optimal solutions for instances of various sizes.     

An efficient heuristic for scheduling in a flowshop to minimize total weighted flowtime of jobs

The problem of scheduling in a flowshop is considered with the objective of minimizing the total weighted flowtime of jobs. A heuristic algorithm is developed by the introduction of lower bounds on the completion times of jobs and the development of heuristic preference relations for the scheduling problem under study. An improvement scheme is incorporated in the heuristic to enhance the quality of its solution. The proposed heuristic, with and without the improvement scheme, and the existing heuristics are evaluated by a large number of randomly generated problems. The results of an extensive computational investigation for various problem sizes are presented. It has been observed that both versions of the proposed heuristic perform better than the existing heuristics in giving a superior solution quality and that the proposed heuristic without the improvement scheme yields a good solution by requiring a negligible CPU time. In addition, an experimental investigation is carried out to evaluate the effectiveness of the improvement scheme when implemented in the proposed heuristic and the existing heuristics, as well as the effectiveness of a variant of the scheme. The results are also discussed.