A fixed job scheduling problem with machine-dependent job weights

This study considers the identical parallel machines operational fixed job scheduling problem with machine-dependent job weights. A job is either processed in a fixed interval or is not processed at all. Our aim is to maximise the total weight of the processed jobs. We show that the problem with machine eligibility constraints resides as a special case of this problem. We identify some special polynomially solvable cases and propose a branch-and-bound (BB) algorithm that employs efficient bounding schemes and dominance conditions. Computational experience on large-sized problem examples reveals the satisfactory performance of the BB algorithm.     

A hybrid artificial bee colony algorithm for a flexible job shop scheduling problem with overlapping in operations

Overlapping in operations is an effective technology for productivity improvement in modern manufacturing systems. Thus far, however, there are still rare works on flexible job shop scheduling problems (FJSPs) concerning this strategy. In this paper, we present a hybrid artificial bee colony (hyABC) algorithm to minimise the total flowtime for a FJSP with overlapping in operations. In the proposed hyABC, a dynamic scheme is introduced to fine-tune the search scope adaptively. In view of poor exploitation ability of artificial bee colony algorithm, a modified migrating birds optimisation algorithm (MMBO) is developed and integrated into the search process for better balancing global exploration and local exploitation. In MMBO, a forward share strategy with one-job based crossover is designed to make good use of valuable information from behind solutions. Besides, an improved downward share scheme is adopted to increase diversification of the population, and thus alleviate the premature convergence. Extensive experiments based on benchmark instances with different scales are carried out and comparisons with other recent algorithms identify the effectiveness of the proposed hyABC.     

A modified harmony search algorithm for the multi-objective flowshop scheduling problem with due dates

This paper presents a modified harmony search optimisation algorithm (MHSO), specifically designed to solve two- and three-objective permutation flowshop scheduling problems, with due dates. To assess its capability, five sets of scheduling problems have been used to compare the MHSO with a known and highly efficient genetic algorithm (GA) chosen as the benchmark. Obtained results show that the new procedure is successful in exploring large regions of the solution space and in finding a significant number of Pareto non-dominated solutions. For those cases where the exhaustive evaluation of sequences can be applied the algorithm is able to find the whole non-dominated Pareto border, along with a considerable number of solutions that share the same optimal values for the considered optimisation parameters. To validate the algorithm, five sets of scheduling problems are investigated in-depth in comparison with the GA. Results obtained by both methods (exhaustive solutions have been provided as well for small sized problems) are fully described and discussed.     

A differential evolution algorithm for the no-idle flowshop scheduling problem with total tardiness criterion

In this paper, we investigate the use of a continuous algorithm for the no-idle permutation flowshop scheduling (NIPFS) problem with tardiness criterion. For this purpose, a differential evolution algorithm with variable parameter search (vpsDE) is developed to be compared to a well-known random key genetic algorithm (RKGA) from the literature. The motivation is due to the fact that a continuous DE can be very competitive for the problems where RKGAs are well suited. As an application area, we choose the NIPFS problem with the total tardiness criterion in which there is no literature on it to the best of our knowledge. The NIPFS problem is a variant of the well-known permutation flowshop (PFSP) scheduling problem where idle time is not allowed on machines. In other words, the start time of processing the first job on a given machine must be delayed in order to satisfy the no-idle constraint. The paper presents the following contributions. First of all, a continuous optimisation algorithm is used to solve a combinatorial optimisation problem where some efficient methods of converting a continuous vector to a discrete job permutation and vice versa are presented. These methods are not problem specific and can be employed in any continuous algorithm to tackle the permutation type of optimisation problems. Secondly, a variable parameter search is introduced for the differential evolution algorithm which significantly accelerates the search process for global optimisation and enhances the solution quality. Thirdly, some novel ways of calculating the total tardiness from makespan are introduced for the NIPFS problem. The performance of vpsDE is evaluated against a well-known RKGA from the literature. The computational results show its highly competitive performance when compared to RKGA. It is shown in this paper that the vpsDE performs better than the RKGA, thus providing an alternative solution approach to the literature that the RKGA can be well suited.     

A bounded-search iterated greedy algorithm for the distributed permutation flowshop scheduling problem

As the interest of practitioners and researchers in scheduling in a multi-factory environment is growing, there is an increasing need to provide efficient algorithms for this type of decision problems, characterised by simultaneously addressing the assignment of jobs to different factories/workshops and their subsequent scheduling. Here we address the so-called distributed permutation flowshop scheduling problem, in which a set of jobs has to be scheduled over a number of identical factories, each one with its machines arranged as a flowshop. Several heuristics have been designed for this problem, although there is no direct comparison among them. In this paper, we propose a new heuristic which exploits the specific structure of the problem. The computational experience carried out on a well-known testbed shows that the proposed heuristic outperforms existing state-of-the-art heuristics, being able to obtain better upper bounds for more than one quarter of the problems in the testbed.     

A parallel-machine scheduling problem with two competing agents

Scheduling with two competing agents has become popular in recent years. Most of the research has focused on single-machine problems. This article considers a parallel-machine problem, the objective of which is to minimize the total completion time of jobs from the first agent given that the maximum tardiness of jobs from the second agent cannot exceed an upper bound. The NP-hardness of this problem is also examined. A genetic algorithm equipped with local search is proposed to search for the near-optimal solution. Computational experiments are conducted to evaluate the proposed genetic algorithm.     

A branch-and-bound algorithm for a two-stage hybrid flowshop scheduling problem minimizing total tardiness

A two-stage hybrid flowshop-scheduling problem is considered with the objective of minimizing total tardiness of jobs. In the hybrid flowshop, there is one machine at the first stage and multiple identical parallel machines at the second stage. Dominance properties and lower bounds are developed for the problem and a branch-and-bound algorithm is suggested using them. Results of computational experiments show that the suggested algorithm can find optimal solutions for problems with up to 15 jobs in a reasonable amount of central processing unit time.     

A novel imperialist competitive algorithm for bi-criteria scheduling of the assembly flowshop problem

This paper deals with the two-stage assembly flowshop scheduling problem with minimisation of weighted sum of makespan and mean completion time as the objective. The problem is NP-hard, hence we proposed a meta-heuristic named imperialist competitive algorithm (ICA) to solve it. Since appropriate design of the parameters has a significant impact on the algorithm efficiency, we calibrate the parameters of this algorithm using the Taguchi method. In comparison with the best algorithm proposed previously, the ICA indicates an improvement. The results have been confirmed statistically.     

Proportionate flowshop scheduling with position-dependent weights

ABSTRACT

This article addresses proportionate flowshop scheduling problems with position-dependent weights wherein the weight is not related to the job but to the position in which the job is scheduled. Common and slack due date assignment models are discussed under a due date assignment framework. The goal is to determine a feasible schedule for all jobs and due dates of all jobs to minimize a total cost function wherein the objective function is of the minsum type. Optimal properties for the problems are proposed, based on which polynomial time algorithms are provided to solve these two problems optimally.     

Green permutation flowshop scheduling problem with sequence-dependent setup times: a case study

Increasing global energy consumption, large variations in its cost and the environmental degradation effects are good reasons for the manufacturing industries to become greener. Green shop floor scheduling is increasingly becoming a vital factor in the sustainable manufacturing. In this paper, a green permutation flowshop scheduling problem with sequence-dependent setup times is studied. Two objectives are considered including minimisation of makespan as a measure of service level and minimisation of total energy consumption as a measure of environmental sustainability. We extend a bi-objective mixed-integer linear programming model to formulate the stated problem. We develop a constructive heuristic algorithm to solve the model. The constructive heuristic algorithm includes iterated greedy (CHIG) and local search (CHLS) algorithms. We develop an efficient energy-saving method which decreases energy consumption, on average, by about 15%. To evaluate the effectiveness of the constructive heuristic algorithm, we compare it with the famous augmented ?-constraint method using various small-sized and large-sized problems. The results confirm that the heuristic algorithm obtains high-quality non-dominated solutions in comparison with the augmented ?-constraint method. Also, they show that the CHIG outperforms the CHLS. Finally, this paper follows a case-study, with in-depth analysis of the model and the constructive heuristic algorithm.     

A divide-and-conquer strategy with particle swarm optimization for the job shop scheduling problem

An optimization algorithm based on the ‘divide-and-conquer’ methodology is proposed for solving large job shop scheduling problems with the objective of minimizing total weighted tardiness. The algorithm adopts a non-iterative framework. It first searches for a promising decomposition policy for the operation set by using a simulated annealing procedure in which the solutions are evaluated with reference to the upper bound and the lower bound of the final objective value. Subproblems are then constructed according to the output decomposition policy and each subproblem is related to a subset of operations from the original operation set. Subsequently, all these subproblems are sequentially solved by a particle swarm optimization algorithm, which leads directly to a feasible solution to the original large-scale scheduling problem. Numerical computational experiments are carried out for both randomly generated test problems and the real-world production data from a large speed-reducer factory in China. Results show that the proposed algorithm can achieve satisfactory solution quality within reasonable computational time for large-scale job shop scheduling problems.     

A new heuristic for the flowshop scheduling problem to minimize makespan and maximum tardiness

This paper presents a new heuristic for solving the flowshop scheduling problem that aims to minimize makespan and maximize tardiness. The algorithm is able to take into account the aforementioned performance measures, finding a set of non-dominated solutions representing the Pareto front. This method is based on the integration of two different techniques: a multi-criteria decision-making method and a constructive heuristic procedure developed for makespan minimization in flowshop scheduling problems. In particular, the technique for order preference by similarity of ideal solution (TOPSIS) algorithm is integrated with the Nawaz–Enscore–Ham (NEH) heuristic to generate a set of potential scheduling solutions. To assess the proposed heuristic's performance, comparison with the best performing multi-objective genetic local search (MOGLS) algorithm proposed in literature is carried out. The test is executed on a large number of random problems characterized by different numbers of machines and jobs. The results show that the new heuristic frequently exceeds the MOGLS results in terms of both non-dominated solutions, set quality and computational time. In particular, the improvement becomes more and more significant as the number of jobs in the problem increases.     

Heuristics for the two-machine flowshop scheduling problem to minimise makespan with bounded processing times

The two-machine flowshop scheduling problem of minimising makespan is addressed where jobs have random processing times that are bounded within certain intervals. The probability distributions of job processing times within intervals are not known. The only known information about job processing times is the lower and upper bounds. The decision concerning the solution to the problem, i.e. finding a sequence, has to be made based on these bounds. Different heuristics using the bounds are proposed, and the proposed heuristics are compared based on randomly generated data. Computational analysis has shown that three of the proposed heuristics perform well with an overall average error of less than one percent. Moreover, for symmetric distributions, it is also shown that one of the heuristics, which applies Johnson's algorithm to the average of the lower and upper bounds, performs best with an overall average percentage error of 0.71. The obtained results are also shown to be consistent with recent results reported in the literature.     

Permutation flowshop scheduling with simple linear deterioration

This article addresses permutation flowshop scheduling problems with simple linear deterioration. The objectives are to minimize logarithm of the makespan, total logarithm of the completion time, total weighted logarithm of the completion time, and the sum of the quadratic job logarithms of the completion times. Approximation algorithms and their worst-case bounds are presented and analysed. Branch-and-bound algorithms are also proposed to solve the problems optimally. Computational experiments are performed to illustrate the algorithms.     

A hybrid flowshop scheduling problem for a cold treating process in seamless steel tube production

Seamless steel tubes often have various categories and specifications, which further require complicated operations in production, especially in the cold treating process (CTP). This paper investigates the scheduling problem using the seamless tube plant of Baoshan Iron and Steel Complex as a study background. By considering the practical production constraints such as sequence-dependent setup times, maintenance schedule, intermediate material buffers, job-machine matches, we formulate the hybrid flowshop scheduling problem with a non-linear mixed integer programming model (NMIP). In addition, our model provides a flexibility to remove the permutation assumption, which is often a limitation in early studies. In order to obtain the solution of the above NMIP problem, a two-stage heuristic algorithm is proposed and it combines a modified genetic algorithm and a local search method. With real production instances, our computation experiments indicate that the proposed algorithm is efficient and it outperforms several other approaches. Industrial implementation also shows that such a scheduling tool brings a cost saving of more than 10% and it substantially reduces the computation time. Our study also illustrates the need of relaxing permutation assumption in such a scheduling problem with complicated operation sequences.     

作业车间调度问题中的协同优化算法

本文采用了多种优化算法 ,针对作业车间问题的特点设计一个比较有效的协同算法 ,解决了算法实现中的几个关键技术问题 ,为提高解决这一问题的效率提供了比较新颖的思路 ,并通过实际计算验证了该方法的可靠性和有效性 ,这一方法可以用于实际车间的调度安排 ,能够提高车间的生产效率。     

Solving the n-job 3-stage flexible flowshop scheduling problem using an agent-based approach

In this paper, a general methodology of agent-based manufacturing systems scheduling, incorporating game theoretic analysis of agent cooperation is presented to solve the n-job 3-stage flexible flowshop scheduling problem. The flowshops are flexible in the sense that a job can be processed by any of the identical machines at each stage. Our objective is to schedule a set of n jobs so as to minimize the makespan. We perform error bound analysis using the lower bound estimates developed in the literature as a datum for comparing the agent-based scheduling solutions with other heuristic solutions. The results of the evaluation show that the agent-based scheduling approach outperforms existing heuristics for the majority of the testing problems.     

A heuristic for scheduling in flowshop and flowline-based manufacturing cell with multi-criteria

The problem of scheduling in flowshop and flowline-based manufacturing cell is considered with the bicriteria of minimizing makespan and total flowtime of jobs, The formulation of the scheduling problems for both the flowshop and the flowline-based manufacturing cell is first discussed. We then present the development of the proposed heuristic for flowshop scheduling. A heuristic preference relation is developed as the basis for the heuristic so that only the potential job interchanges are checked for possible improvement with respect to bicriteria, The proposed heuristic algorithm as well as the existing heuristic are evaluated in a large number of randomly generated large-sized flowshop problems. We also investigate the effectiveness of these heuristics with respect to the objective of minimizing total machine idletime. We then modify the proposed heuristic for scheduling in a cell, and evaluate its performance.     

A tabu search algorithm for solving a multicriteria flexible job shop scheduling problem

The problem that we consider in this article is a flexible job shop scheduling problem issued from the printing and boarding industry. Two criteria have to be minimised, the makespan and the maximum lateness. Two tabu search algorithms are proposed for finding a set of non-dominated solutions: the first is based on the minimisation of one criterion subject to a bound on the second criterion (ε-constraint approach) and the second is based on the minimisation of a linear combination of criteria. These algorithms are tested on benchmark instances from the literature and the results are discussed. The total tardiness is considered as a third criterion for the second tabu search and results are presented and discussed.