Auction-based approach for a flexible job-shop scheduling problem with multiple process plans

This study addresses the flexible job-shop scheduling problem with multiple process plans with the objective of minimizing the overall makespan. A nonlinear programming model is formulated to allocate machines and schedule jobs. An auction-based approach is proposed to address the integrated production route selection and resource allocation problem and focus on improving resource utilization and productive efficiency to reduce the makespan. The approach consists of an auction for process plans and an auction for machines. The auctions are evaluated to select a more suitable route for production and allocate resources to a more desirable job. Numerical experiments are conducted by testing new large benchmark instances. A comparison of Lingo and other existing algorithms demonstrates the effectiveness and stability of the proposed auction-based approach. Furthermore, SPSS is used to prove that the proposed method exhibits an absolute advantage, particularly for medium-scale or large-scale instances.     

Extracting priority rules for dynamic multi-objective flexible job shop scheduling problems using gene expression programming

In this paper, two new approaches are proposed for extracting composite priority rules for scheduling problems. The suggested approaches use simulation and gene expression programming and are able to evolve specific priority rules for all dynamic scheduling problems in accordance with their features. The methods are based on the idea that both the proper design of the function and terminal sets and the structure of the gene expression programming approach significantly affect the results. In the first proposed approach, modified and operational features of the scheduling environment are added to the terminal set, and a multigenic system is used, whereas in the second approach, priority rules are used as automatically defined functions, which are combined with the cellular system for gene expression programming. A comparison shows that the second approach generates better results than the first; however, all of the extracted rules yield better results than the rules from the literature, especially for the defined multi-objective function consisting of makespan, mean lateness and mean flow time. The presented methods and the generated priority rules are robust and can be applied to all real and large-scale dynamic scheduling problems.     

Integrated process planning and scheduling for large-scale flexible job shops using metaheuristics

In this paper, we discuss an integrated process planning and scheduling problem in large-scale flexible job shops (FJSs). We assume that products can be manufactured in different ways, i.e. using different bills of materials (BOM) and routes for the same product. The total weighted tardiness is the performance measure of interest. A Mixed Integer Programming formulation is provided for the researched problem. Because of the NP-hardness of the investigated problem, an iterative scheme is designed that is based on variable neighbourhood search (VNS) on the process planning level. Appropriate neighbourhood structures for VNS are proposed. Because the evaluation of each move within VNS requires the solution of a large-scale FJS scheduling problem instance, efficient heuristics based on local search from previous research are considered on the scheduling level. Extensive computational experiments based on new randomly generated problem instances are conducted. In addition, a parallel version of the VNS is investigated within the computational experiments. The proposed iterative scheme is benchmarked against a genetic algorithm (GA) from the literature that simultaneously considers process planning and scheduling for the special case where a single BOM is available for each product. It turns out that the new iterative scheme outperforms the GA and a memetic algorithm based on the GA. It is able to solve even large-size problem instances in reasonable amount of time.     

Reactive scheduling in a make-to-order flexible job shop with re-entrant process and assembly: a mathematical programming approach

A mixed-integer linear programming model is presented for the scheduling of flexible job shops, a production mode characteristic of make-to-order industries. Re-entrant process (multiple visits to the same machine group) and a final assembly stage are simultaneously considered in the model. The formulation uses a continuous time representation and optimises an objective function that is a weighted sum of order earliness, order tardiness and in-process inventory. An algorithm for predictive-reactive scheduling is derived from the proposed model to deal with the arrival of new orders. This is illustrated with a realistic example based on data from the mould making industry. Different reactive scheduling scenarios, ranging from unchanged schedule to full re-scheduling, are optimally generated for order insertion in a predictive schedule. Since choosing the most suitable scenario requires balancing criteria of scheduling efficiency and stability, measures of schedule changes were computed for each re-scheduling solution. The short computational times obtained are promising regarding future application of this approach in the manufacturing environment studied.     

Scheduling algorithms to minimise the total family flow time for job shops with job families

This paper considers the job scheduling problem in which jobs are grouped into job families, but they are processed individually. The decision variable is the sequence of the jobs assigned to each machine. This type of job shop scheduling can be found in various production systems, especially in remanufacturing systems with disassembly, reprocessing and reassembly shops. In other words, the reprocessing shop can be regarded as the job shop with job families since it performs the operations required to bring parts or sub-assemblies disassembled back to like-new condition before reassembling them. To minimise the deviations of the job completion times within each job family, we consider the objective of minimising the total family flow time. Here, the family flow time implies the maximum among the completion times of the jobs within a job family. To describe the problem clearly, a mixed integer programming model is suggested and then, due to the complexity of the problem, two types of heuristics are suggested. They are: (a) priority rule based heuristics; and (b) meta-heuristics. Computational experiments were performed on a number of test instances and the results show that some priority rule based heuristics are better than the existing ones. Also, the meta-heuristics improve the priority rule based heuristics significantly.     

Variable neighbourhood search for dual-resource constrained flexible job shop scheduling

Dual-resource constrained flexible job shop scheduling problem (FJSP) is considered and an effective variable neighbourhood search (VNS) is presented, in which the solution to the problem is indicated as a quadruple string of the ordered operations and their resources. Two neighbourhood search procedures are sequentially executed to produce new solutions for two sub-problems of the problem, respectively. The search of VNS is restarted from a slightly perturbed version of the current solution of VNS when the determined number of iterations is reached. VNS is tested on some instances and compared with methods from literature. Computational results show the significant advantage of VNS on the problem.     

遗传算法的双目标柔性作业车间调度研究

研究了FMS环境下先进制造车间路径柔性的优化调度问题.同时考虑现代生产准时制的要求,建立了柔性作业车间调度问题的双目标数学优化模型,并给出了求解模型的遗传算法的具体实现过程;针对模型的特殊性,提出了染色体两层编码结构,将AOV网络图应用到解码和适应度函数的计算中,通过一个调度实例进行验证,给出了相应的选择、交叉、变异操作设计方案.     

Robust scheduling for multi-objective flexible job-shop problems with flexible workdays

This study determines a robust schedule for a flexible job-shop scheduling problem with flexible workdays. The performance criteria considered in this study are tardiness, overtime and robustness. Furthermore, the problem is addressed in a Pareto manner, and a set of Pareto-optimal solutions is determined for this purpose. In consideration of all the aforementioned features, a goal-guided neighbourhood function is proposed based on efficient problem-dependent move-filtering methods. Two metaheuristic algorithms, named goal-guided multi-objective tabu search and goal-guided multi-objective hybrid search, are proposed in this work based on this neighbourhood function. The effectiveness of these approaches is demonstrated via empirical studies.     

A shuffled frog-leaping algorithm for flexible job shop scheduling with the consideration of energy consumption

Flexible job shop scheduling problem (FJSP) has been extensively investigated and objectives are often related to time. Energy-related objective should be considered fully in FJSP with the advent of green manufacturing. In this study, FJSP with the minimisation of workload balance and total energy consumption is considered and the conflicting between two objectives is analysed. A shuffled frog-leaping algorithm (SFLA) is proposed based on a three-string coding approach. Population and a non-dominated set are used to construct memeplexes according to tournament selection and the search process of each memeplex is done on its non-dominated member. Extensive experiments are conducted to test the search performance of SFLA and computational results show the conflicting between two objectives of FJSP and the promising advantages of SFLA on the considered FJSP.     

Correlation among tardiness-based measures for scheduling using priority dispatching rules

One of the most commonly used methods to schedule manufacturing systems is to use priority dispatching rules (pdrs). It is frequently desired to distinguish the behaviour of pdrs with regard to tardiness-based performance measures. However, the relation among these performance measures is generally not obvious even for simple scheduling strategies such as pdrs. In this paper, we first focus on the maximum tardiness, which is a very interesting performance measure for the decision-maker on the shop floor. However, because of its singularity, it is not trivial to assess. We conducted a simulation study on a benchmark model of a dynamic job-shop system to evaluate the relative performance of a set of pdrs chosen either because they are used extensively or because they exhibit very good performance. Based upon the distribution of the maximum tardiness of these benchmark pdrs, we identify two sub-sets of pdrs. From this, we conducted experiments on the root-mean-square tardiness, which is used to distinguish a system with a few very tardy jobs from a system with a lot of less tardy jobs. The experiments show a positive correlation between maximum tardiness and root-mean-square tardiness. Because of the fact that the root-mean-square tardiness is an aggregate measure, it is much easier to assess than the maximum tardiness. This provides an opportunity to predict the relative performance of pdrs with regard to the maximum tardiness as well as the width of the tardiness by evaluating the root-mean-square tardiness only.     

Automatic design of scheduling policies for dynamic flexible job shop scheduling via surrogate-assisted cooperative co-evolution genetic programming

At present, a lot of references use discrete event simulation to evaluate the fitness of evolved rules, but which simulation configuration can achieve better evolutionary rules in a limited time has not been fully studied. This study proposes three types of hyper-heuristic methods for coevolution of the machine assignment rules (MAR) and job sequencing rules (JSR) to solve the DFJSP, including the cooperative coevolution genetic programming with two sub-populations (CCGP), the genetic programming with two sub-trees (TTGP) and the genetic expression programming with two sub-chromosomes (GEP). After careful parameter tuning, a surrogate simulation model is used to evaluate the fitness of evolved scheduling policies (SP). Computational simulations and comparisons demonstrate that the proposed surrogate-assisted CCGP method (CCGP-SM) shows competitive performance with other evolutionary approaches using the same computation time. Furthermore, the learning process of the proposed methods demonstrates that the surrogate-assisted GP methods help accelerating the evolutionary process and improving the quality of the evolved SPs without a signi?cant increase in the length of SP. In addition, the evolved SPs generated by the CCGP-SM show superior performance as compared with existing rules in the literature. These results demonstrate the effectiveness and robustness of the proposed method.     

A hybrid artificial bee colony algorithm for flexible job shop scheduling with worker flexibility

The traditional flexible job shop scheduling problem (FJSP) considers machine flexibility but not worker flexibility. Given the influence and potential of human factors in improving production efficiency and decreasing the cost in practical production systems, we propose a mathematical model of an extended FJSP with worker flexibility (FJSPW). A hybrid artificial bee colony algorithm (HABCA) is presented to solve the proposed FJSPW. For the HABCA, effective encoding, decoding, crossover and mutation operators are designed, and a new effective local search method is developed to improve the speed and exploitation ability of the algorithm. The Taguchi method of Design of Experiments is used to obtain the best combination of key parameters of the HABCA. Extensive computational experiments carried out to compare the HABCA with some well-performing algorithms from the literature confirm that the proposed HABCA is more effective than these algorithms, especially on large-scale FJSPW instances.     

A generalized permutation approach to job shop scheduling with genetic algorithms

In order to sequence the tasks of a job shop problem (JSP) on a number of machines related to the technological machine order of jobs, a new representation technique — mathematically known as permutation with repetition is presented. The main advantage of this single chromosome representation is — in analogy to the permutation scheme of the traveling salesman problem (TSP) — that it cannot produce illegal operation sequences. As a consequence of the representation scheme a new crossover operator preserving the initial scheme structure of permutations with repetition will be sketched. Its behavior is similar to the well known Order-Crossover for simple permutation schemes. Actually theGOX operator for permutations with repetition arises from aGeneralisation ofOX. Computational experiments show, that GOX passes the information from a couple of parent solutions efficiently to offspring solutions. Together, the new representation and GOX support the cooperative aspect of genetic search for scheduling problems strongly.Supported by the Deutsche Forschungsgemeinschaft (Project Parnet)     

An evaluation of worker cross training and flexible workdays in job shops

Capacity flexibility is becoming increasingly important as a means for reducing inventory while maintaining customer service levels. We examine two means to increase capacity flexibility. In particular, we examine an environment where both cross training and flexible workdays are available to respond to workload variability. Flexible workdays are under consideration in the US Legislature. This proposed legislation provides the opportunity for workers to exchange overtime for time off. From a managerial perspective, flexible workdays allow management to shift capacity from periods of light load to periods of heavy load. We simulate the operation of a job shop with both cross training and flexible workdays. Our results indicate that cross training is a far more effective tool for improving performance as compared to flexible workdays. Flexible workdays can be valuable particularly in volatile conditions. However, our results indicate that the degree of cross training is a critical consideration in determining the impact of flexible workdays.     

A hybrid Pareto-based local search algorithm for multi-objective flexible job shop scheduling problems

This paper presents a hybrid Pareto-based local search (PLS) algorithm for solving the multi-objective flexible job shop scheduling problem. Three minimisation objectives are considered simultaneously, i.e. the maximum completion time (makespan), the total workload of all machines, and the workload of the critical machine. In this study, several well-designed neighbouring approaches are proposed, which consider the problem characteristics and thus can hold fast convergence ability while keep the population with a certain level of quality and diversity. Moreover, a variable neighbourhood search (VNS) based self-adaptive strategy is embedded in the hybrid algorithm to utilise the neighbouring approaches efficiently. Then, an external Pareto archive is developed to record the non-dominated solutions found so far. In addition, a speed-up method is devised to update the Pareto archive set. Experimental results on several well-known benchmarks show the efficiency of the proposed hybrid algorithm. It is concluded that the PLS algorithm is superior to the very recent algorithms, in term of both search quality and computational efficiency.     

A heuristic model for dynamic flexible job shop scheduling problem considering variable processing times

In real scheduling problems, unexpected changes may occur frequently such as changes in task features. These changes cause deviation from primary scheduling. In this article, a heuristic model, inspired from Artificial Bee Colony algorithm, is proposed for a dynamic flexible job-shop scheduling (DFJSP) problem. This problem consists of n jobs that should be processed by m machines and the processing time of jobs deviates from estimated times. The objective is near-optimal scheduling after any change in tasks in order to minimise the maximal completion time (Makespan). In the proposed model, first, scheduling is done according to the estimated processing times and then re-scheduling is performed after determining the exact ones considering machine set-up. In order to evaluate the performance of the proposed model, some numerical experiments are designed in small, medium and large sizes in different levels of changes in processing times and statistical results illustrate the efficiency of the proposed algorithm.     

Multi-period lot sizing and job shop scheduling with compressible process times for multilevel product structures

This paper presents mathematical modelling of joint lot sizing and scheduling problem in job shop environment under a set of working conditions. The main feature of the problem is to deal with flexible machines able to change their working speeds, known as process compressibility. Furthermore, produced items should be assembled together to make final products. In other words, the products have a multilevel structure, shown with bill of materials. As the problem is proved to be strongly NP-hard, it is solved by a memetic algorithm here. Computational experiences on the data of ‘Mega Motor’ company are reported. Also, further experiences on random test data confirm the performance of the proposed method with less than 5.02% optimality gap while solving the problems in very shorter times than CPLEX 12.0.     

An effective discrete harmony search algorithm for flexible job shop scheduling problem with fuzzy processing time

This study addresses flexible job shop scheduling problem (FJSP) with fuzzy processing time. The fuzzy or uncertainty of processing time is one of seven characteristics in remanufacturing. A discrete harmony search (DHS) algorithm is proposed for FJSP with fuzzy processing time. The objective is to minimise maximum fuzzy completion time. A simple and effective heuristic rule is proposed to initialise harmony population. Extensive computational experiments are carried out using five benchmark cases with eight instances from remanufacturing. The proposed heuristic rule is evaluated using five benchmark cases. The proposed DHS algorithm is compared to six metaheuristics. The results and comparisons show the effectiveness and efficiency of DHS for solving FJSP with fuzzy processing time.     

A generic deadlock-free reactive scheduling approach

In this paper, a generic deadlock-free reactive scheduling (GDRS) approach is proposed. The approach can react to the occurrence of a variety of disruptions in flexible job shops, in real time. Internal and external disruptions such as machine breakdown, process time variation, urgent job, arrival of a new job order, and order cancellation are considered. Performance comparisons of the proposed approach with that of Total Rescheduling (TR), and with the modified Affected Operations Rescheduling (mAOR) heuristic proposed earlier in the literature are presented by considering scheduling efficiency and stability. The results show that, for most of the disruptions considered, GDRS retains the rescheduling efficiency of TR while providing superior system stability over the other two approaches.     

Mathematical modelling and a meta-heuristic for flexible job shop scheduling

This study develops new solution methodologies for the flexible job shop scheduling problem (F-JSSP). As a first step towards dealing with this complex problem, mathematical modellings have been used; two novel effective position- and sequence-based mixed integer linear programming (MILP) models have been developed to fully characterise operations of the shop floor. The developed MILP models are capable of solving both partially and totally F-JSSPs. Size complexities, solution effectiveness and computational efficiencies of the developed MILPs are numerically explored and comprehensively compared vis-à-vis the makespan optimisation criterion. The acquired results demonstrate that the proposed MILPs, by virtue of its structural efficiencies, outperform the state-of-the-art MILPs in literature. The F-JSSP is strongly NP-hard; hence, it renders even the developed enhanced MILPs inefficient in generating schedules with the desired quality for industrial scale problems. Thus, a meta-heuristic that is a hybrid of Artificial Immune and Simulated Annealing (AISA) Algorithms has been proposed and developed for larger instances of the F-JSSP. Optimality gap is measured through comparison of AISA’s suboptimal solutions with its MILP exact optimal counterparts obtained for small- to medium-size benchmarks of F-JSSP. The AISA’s results were examined further by comparing them with seven of the best-performing meta-heuristics applied to the same benchmark. The performed comparative analysis demonstrated the superiority of the developed AISA algorithm. An industrial problem in a mould- and die-making shop was used for verification.