Modeling and heuristics for scheduling of distributed job shops

This paper deals with the problem of distributed job shop scheduling in which the classical single-facility job shop is extended to the multi-facility one. The mathematical formulation of the problem is comprehensively discussed. Two different mixed integer linear programming models in form of sequence and position based variables are proposed. Using commercial software of CPLEX, the small sized problems are optimally solved. To solve large sized problems, besides adapting three well-known heuristics, three greedy heuristics are developed. The basic idea behind the developed heuristics is to iteratively insert operations (one at each iteration) into a sequence to build up a complete permutation of operations. The permutation scheme, although having several advantages, suffers from redundancy which is having many different permutations representing the same schedule. The issue is analyzed to recognize the redundant permutation. That improves efficiency of heuristics. Comprehensive experiments are conducted to evaluate the performance of the two models and the six heuristics. The results show sequence based model and greedy heuristics equipped with redundancy exclusion are effective for the problem.     

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.     

Production scheduling for blocking flowshop in distributed environment using effective heuristics and iterated greedy algorithm

Production scheduling plays an important role in the intelligent decision support system and intelligent optimization decision technology. In the context of the globalization trend, the current production and management may extend from a single factory to a distributed production network. In this paper, we study the distributed blocking flowshop scheduling problem (DBFSP) that is an important generalization of the traditional blocking flowshop scheduling problem in the distributed environment. Six constructive heuristics and an iterated greedy (IG) algorithm are proposed to minimize the makespan, which provides procedures for obtaining efficient and effective solutions to make decision-making sounder. The first five heuristics are developed based on the well-known NEH2 heuristic [B. Naderi, R. Ruiz, The distributed permutation flowshop scheduling problem, Computers & Operations Research, 37 (4) (2010) 754–768.] and the last heuristic is presented by extending the PW heuristic [Q.K. Pan, L. Wang, Effective heuristics for the blocking flowshop scheduling problem with makespan minimization, Omega, 40 (2) (2012) 218–229.] to DBFSP in an effective way. The composite heuristics that combining constructive heuristics and local searches are also studied. The proposed composite heuristics are chosen to generate an initial solution with a high level of quality. Keeping the simplicity of the IG algorithm, three local search procedures, two destruction procedures, an improved reconstruction procedure, and a simulated annealing-like acceptance criterion are well designed based on the problem-specific knowledge to enhance the IG algorithm. The computational experiments are carried out based on the 720 benchmark instances from the literature. The results show that the proposed heuristics are very effective for solving the problem under consideration and the presented IG algorithm performs significantly better than the other state-of-the-art metaheuristics from the literature.     

基于TSP方法求解等待时间受限的置换流水车间调度

等待时间受限的置换流水车间调度问题要求工件在连续两个机器间的等待时间满足上限值约束.对此,分析了工件序列中相邻工件的加工持续时间及其上下界关系,并且提出一种启发式方法.首先,建立旅行商间题（TSP）以生成初始调度;然后,采用扩展插入方法优化调度解.为了衡量算法性能,给出问题下界的计算方法和相关评价指标,并通过数据实验验证了该启发式和下界计算方法的可行性和有效性.     

On the Use of Genetic Algorithm for Solving Re-entrant Flowshop Scheduling with Sum-of-processing-times-based Learning Effect to Minimize Total Tardiness

Most research studies on scheduling problems assume that a job visits certain machines only one time. However, this assumption is invalid in some real-life situations. For example, a job may be processed by the same machine more than once in semiconductor wafer manufacturing or in a printed circuit board manufacturing machine. Such a setting is known as the “re-entrant flowshop”. On the other hand, the importance of learning effect present in many practical situations such as machine shop, in different branches of industry and for a variety of corporate activities, in shortening life cycles, and in an increasing diversity of products in the manufacturing environment. Inspired by these observations, this paper addresses a re-entrant m-machine flowshop scheduling problems with time-dependent learning effect to minimize the total tardiness. The complexity of the proposed problem is very difficult. Therefore, in this paper we first present four heuristic algorithms, which are modified from existing algorithms to solve the problem. Then, we use the solutions as four initials to a genetic algorithm. Finally, we report experimental performances of all the proposed methods for the small and big numbers of jobs, respectively     

A hybrid discrete artificial bee colony algorithm for permutation flowshop scheduling problem

To minimize the makespan in permutation flowshop scheduling problems, a hybrid discrete artificial bee colony (HDABC) algorithm is presented. In the HDABC, each solution to the problem is called a food source and represented by a discrete job permutation. First, the initial population with certain quality and diversity is generated from Greedy Randomized Adaptive Search Procedure (GRASP) based on Nawaz–Enscore–Ham (NEH) heuristics. Second, the discrete operators and algorithm, such as insert, swap, path relinking and GRASP are applied to generate new solution for the employed bees, onlookers and scouts. Moreover, local search is applied to the best one. The presented algorithm is tested on scheduling problem benchmarks. Experimental results show its efficiency.     

Effective constructive heuristics and meta-heuristics for the distributed assembly permutation flowshop scheduling problem

This paper addresses a novel distributed assembly permutation flowshop scheduling problem that has important applications in modern supply chains and manufacturing systems. The problem considers a number of identical factories, each one consisting of a flowshop for part-processing plus an assembly line for product-processing. The objective is to minimize the makespan. To suit the needs of different CPU time and solution quality, we present a mixed integer linear model, three constructive heuristics, two variable neighborhood search methods, and an iterated greedy algorithm. Important problem-specific knowledge is obtained to enhance the effectiveness of the algorithms. Accelerations for evaluating solutions are proposed to save computational efforts. The parameters and operators of the algorithms are calibrated and analyzed using a design of experiments. To prove the algorithms, we present a total of 16 adaptations of other well-known and recent heuristics, variable neighborhood search algorithms, and meta-heuristics for the problem and carry out a comprehensive set of computational and statistical experiments with a total of 810 instances. The results show that the proposed algorithms are very effective and efficient to solve the problem under consideration as they outperform the existing methods by a significant margin.     

A comprehensive review and evaluation of permutation flowshop heuristics to minimize flowtime

In recent years, a large number of heuristics have been proposed for the minimization of the total or mean flowtime/completion time of the well-known permutation flowshop scheduling problem. Although some literature reviews and comparisons have been made, they do not include the latest available heuristics and results are hard to compare as no common benchmarks and computing platforms have been employed. Furthermore, existing partial comparisons lack the application of powerful statistical tools. The result is that it is not clear which heuristics, especially among the recent ones, are the best. This paper presents a comprehensive review and computational evaluation as well as a statistical assessment of 22 existing heuristics. From the knowledge obtained after such a detailed comparison, five new heuristics are presented. Careful designs of experiments and analyses of variance (ANOVA) techniques are applied to guarantee sound conclusions. The comparison results identify the best existing methods and show that the five newly presented heuristics are competitive or better than the best performing ones in the literature for the permutation flowshop problem with the total completion time criterion.     

An efficient stochastic hybrid heuristic for flowshop scheduling

The paper addresses the problem of flowshop scheduling in order to minimize the makespan objective. Three probabilistic hybrid heuristics are presented for solving permutation flowshop scheduling problem. The proposed methodology combines elements from both constructive heuristic search and a stochastic improvement technique. The stochastic method used in this paper is simulated annealing (SA). Experiments have been run on a large number of randomly generated test problems of varying jobs and machine sizes. Our approach is shown to outperform best-known existing heuristics, including the classical NEH technique (OMEGA, 1983) and the SA based on (OMEGA, 1989) of Osman and Potts . Statistical tests of significance are performed to substantiate the claims of improvement.     

Scheduling in a two-machine flowshop for the minimization of the mean absolute deviation from a common due date

This paper addresses the minimization of the mean absolute deviation from a common due date in a two-machine flowshop scheduling problem. We present heuristics that use an algorithm, based on proposed properties, which obtains an optimal schedule for a given job sequence. A new set of benchmark problems is presented with the purpose of evaluating the heuristics. Computational experiments show that the developed heuristics outperform results found in the literature for problems up to 500 jobs.     

A beam-search-based constructive heuristic for the PFSP to minimise total flowtime

In this paper we present a beam-search-based constructive heuristic to solve the permutation flowshop scheduling problem with total flowtime minimisation as objective. This well-known problem is NP-hard, and several heuristics have been developed in the literature. The proposed algorithm is inspired in the logic of the beam search, although it remains a fast constructive heuristic.The results obtained by the proposed algorithm outperform those obtained by other constructive heuristics in the literature for the problem, thus modifying substantially the state-of-the-art of efficient approximate procedures for the problem. In addition, the proposed algorithm even outperforms two of the best metaheuristics for many instances of the problem, using much lesser computation effort. The excellent performance of the proposal is also proved by the fact that the new heuristic found new best upper bounds for 35 of the 120 instances in Taillard’s benchmark.     

基于遗传算法的某航空发动机装配车间优化调度

航空发动机装配车间装配生产线的调度问题,是一类比较典型的混合Flowshop问题,同时还带有工件可重人等特点,这就区别于一般的Flowshop和Jobshop调度问题,因此,将可重入混合车间调度问题划为第三类调度问题。关于重入式混合车间生产调度的优化问题通常来说都是属于NP难问题。文中通过某航空发动机装配车间生产线的研究,以最小化最大完工时间为目标函数,借助随机矩阵的编码方式和改进的交叉方法与变异方法,提出了基于遗传算法的调度优化方法。最后实验结果表明,文中提出的改进算法能够有效地实现装配车间调度的优化。     

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.     

两机无等待流水车间调度问题的性质

针对两机无等待流水车间调度问题,提出目标函数最大完工时间最小化的快速算法,并给出算法的复杂度。分析两机无等待流水车间调度问题的排列排序性质,证明了两机无等待流水车间调度问题的可行解只存在于排列排序中,排列排序的最优解一定是两机无等待流水车间调度问题的最优解。最后研究了同时包含普通工件和无等待工件的两机流水车间调度问题的复杂性,为进一步研究两机无等待流水车间调度问题提供了理论依据。     

Parallel machine scheduling problems using memetic algorithms

In this paper, we investigate how to apply the hybrid genetic algorithms (the memetic algorithms) to solve the parallel machine scheduling problem. There are two essential issues to be dealt with for all kinds of parallel machine scheduling problems: job partition among machines and job sequence within each machine. The basic idea of the proposed method is that (a) use the genetic algorithms to evolve the job partition and then (b) apply a local optimizer to adjust the job permutation to push each chromosome climb to his local optima. Preliminary computational experiments demonstrate that the hybrid genetic algorithm outperforms the genetic algorithms and the conventional heuristics.     

Simulation-based two-phase genetic algorithm for the capacitated re-entrant line scheduling problem

In this paper, we develop a simulation-based two-phase genetic algorithm for the capacitated re-entrant line scheduling problem. The structure of a chromosome consists of two sub-chromosomes for buffer allocation and server allocation, respectively, while considering all possible states of the system in terms of buffer levels of workstations and assigning a preferred job stage to each component of the chromosome. As an implementation of the suggested algorithm, a job priority-based randomized policy is defined, which reflects the job priority and the properness of local non-idling in allocating buffering and processing capacity to available job instances. The algorithm is combined with a polynomial time sub-optimal deadlock avoidance policy, namely, Bankers algorithm, and the fitness of a chromosome was evaluated based on simulation. The performance of the proposed algorithm is evaluated through a numerical experiment, showing that the suggested approach holds considerable promise for providing effective and computationally efficient approximations to the optimal scheduling policy that consistently outperforms the typically employed heuristics.     

A variable iterated greedy algorithm with differential evolution for the no-idle permutation flowshop scheduling problem

This paper presents a variable iterated greedy algorithm (IG) with differential evolution (vIG_DE), designed to solve the no-idle permutation flowshop scheduling problem. In an IG algorithm, size d of jobs are removed from a sequence and re-inserted into all possible positions of the remaining sequences of jobs, which affects the performance of the algorithm. The basic concept behind the proposed vIG_DE algorithm is to employ differential evolution (DE) to determine two important parameters for the IG algorithm, which are the destruction size and the probability of applying the IG algorithm to an individual. While DE optimizes the destruction size and the probability on a continuous domain by using DE mutation and crossover operators, these two parameters are used to generate a trial individual by directly applying the IG algorithm to each target individual depending on the probability. Next, the trial individual is replaced with the corresponding target individual if it is better in terms of fitness. A unique multi-vector chromosome representation is presented in such a way that the first vector represents the destruction size and the probability, which is a DE vector, whereas the second vector simply consists of a job permutation assigned to each individual in the target population. Furthermore, the traditional IG and a variable IG from the literature are re-implemented as well. The proposed algorithms are applied to the no-idle permutation flowshop scheduling (NIPFS) problem with the makespan and total flowtime criteria. The performances of the proposed algorithms are tested on the Ruben Ruiz benchmark suite and compared to the best-known solutions available at http://soa.iti.es/rruiz as well as to those from a recent discrete differential evolution algorithm (HDDE) from the literature. The computational results show that all three IG variants represent state-of-art methods for the NIPFS problem.     

Non-permutation flowshop scheduling with dual resources

Typically, in order to process jobs in a flowshop both machines and labor are required. However, in traditional scheduling problems, labor is assumed to be plentiful and only machine is considered to be a constraint. This assumption could be due to the lower cost of labor compared to machines or the complexity of dual-resource constrained problems. In this paper a mathematical model is developed to minimize the work-in-process inventory while maximizing the service level in a flowshop with dual resources. The model focuses on optimizing a non-permutation flowshop. There are different skill levels considered for labor and the setup times on machines are sequence-dependent. Jobs are allowed to skip one or more stages in the flowshop. Job release and machine availability times are considered to be dynamic. The problem is solved in two layers. The outer layer is a search algorithm to find the schedule of jobs on the machine (traditional flowshop scheduling problem) and the inner layer is a three-step heuristic to find a schedule of jobs on labor in accordance to the machine schedule. Three different search algorithms are developed to solve the proposed NP-hard problem. First algorithm can solve a permutation flowshop while the other two are developed to solve a non-permutation flowshop. The comparison between the optimal solution and the search algorithms in small examples shows a good performance of the algorithms with an average deviation of only 2.00%. An experimental design analyzes the effectiveness and efficiency of the algorithms statistically. The results show that non-permutation algorithms perform better than the permutation algorithm, although the former are less efficient. The effectiveness and efficiency in all three algorithms have an inverse relation. To the best of our knowledge, this research is the first of its kind to provide a comprehensive mathematical model for dual resource flowshop scheduling problem.     

The distributed permutation flowshop scheduling problem

This paper studies a new generalization of the regular permutation flowshop scheduling problem (PFSP) referred to as the distributed permutation flowshop scheduling problem or DPFSP. Under this generalization, we assume that there are a total of F identical factories or shops, each one with m machines disposed in series. A set of n available jobs have to be distributed among the F factories and then a processing sequence has to be derived for the jobs assigned to each factory. The optimization criterion is the minimization of the maximum completion time or makespan among the factories. This production setting is necessary in today's decentralized and globalized economy where several production centers might be available for a firm. We characterize the DPFSP and propose six different alternative mixed integer linear programming (MILP) models that are carefully and statistically analyzed for performance. We also propose two simple factory assignment rules together with 14 heuristics based on dispatching rules, effective constructive heuristics and variable neighborhood descent methods. A comprehensive computational and statistical analysis is conducted in order to analyze the performance of the proposed methods.     

Permutation flowshop problems with bi-criterion makespan and total completion time objective and position-weighted learning effects

In this paper, we study the problem of minimizing the weighted sum of makespan and total completion time in a permutation flowshop where the processing times are supposed to vary according to learning effects. The processing time of a job is a function of the sum of the logarithms of the processing times of the jobs already processed and its position in the sequence. We present heuristic algorithms, which are modified from the optimal schedules for the corresponding single machine scheduling problem and analyze their worst-case error bound. We also adopt an existing algorithm as well as a branch-and-bound algorithm for the general m-machine permutation flowshop problem. For evaluation of the performance of the algorithms, computational experiments are performed on randomly generated test problems.