A GRASP algorithm for flexible job-shop scheduling with maintenance constraints

In most realistic situations, machines may be unavailable due to maintenance, pre-schedules and so on. The availability constraints are non-fixed in that the completion time of the maintenance task is not fixed and has to be determined during the scheduling procedure. In this paper a greedy randomised adaptive search procedure (GRASP) algorithm is presented to solve the flexible job-shop scheduling problem with non-fixed availability constraints (FJSSP-nfa). The GRASP algorithm is a metaheuristic algorithm which is characterised by multiple initialisations. Basically, it operates in the following manner: first a feasible solution is obtained, which is then further improved by a local search technique. The main objective is to repeat these two phases in an iterative manner and to preserve the best found solution. Representative FJSSP-nfa benchmark problems are solved in order to test the effectiveness and efficiency of the proposed algorithm.     

Flexible job-shop scheduling problem with resource recovery constraints

In this work, we introduce a Flexible Job-shop Scheduling Problem with Resource Recovery Constraints (FRRC). In the FRRC, besides the constraints of the classical Flexible Job-shop Scheduling Problem (FJSP), operations may require resources to be processed. The resources are available in batches and a recovery time is required between each batch. This problem is inspired by a real situation faced by a brewing company where different yeasts are available in a limited quantity and are recovered only once they have been completely used. The objective is to schedule the operations such that the makespan is minimised. A mathematical model and a metaheuristic based on a General Variable Neighborhood Search is proposed for the solution of the FRRC. Computational results over a large set of instances, adapted from the FJSP literature, are presented.     

Flexible job-shop scheduling problem under resource constraints

A flexible job-shop-scheduling problem is an extension of classical job-shop problems that permit an operation of each job to be processed by more than one machine. The research methodology is to assign operations to machines (assignment) and determine the processing order of jobs on machines (sequencing) such that the system objectives can be optimized. This problem can explore very well the common nature of many real manufacturing environments under resource constraints. A genetic algorithm-based approach is developed to solve the problem. Using the proposed approach, a resource-constrained operations–machines assignment problem and flexible job-shop scheduling problem can be solved iteratively. In this connection, the flexibility embedded in the flexible shop floor, which is important to today's manufacturers, can be quantified under different levels of resource availability.     

A variable neighbourhood search algorithm for the flexible job-shop scheduling problem

The flexible job-shop scheduling problem (FJSP) is a generalisation of the classical job-shop scheduling problem which allows an operation of each job to be executed by any machine out of a set of available machines. FJSP consists of two sub-problems which are assigning each operation to a machine out of a set of capable machines (routing sub-problem) and sequencing the assigned operations on the machines (sequencing sub-problem). This paper proposes a variable neighbourhood search (VNS) algorithm that solves the FJSP to minimise makespan. In the process of the presented algorithm, various neighbourhood structures related to assignment and sequencing problems are used for generating neighbouring solutions. To compare our algorithm with previous ones, an extensive computational study on 181 benchmark problems has been conducted. The results obtained from the presented algorithm are quite comparable to those obtained by the best-known algorithms for FJSP.     

A filtered-beam-search-based heuristic algorithm for flexible job-shop scheduling problem

Scheduling for the flexible job-shop is a very important issue in both fields of combinatorial optimization and production operations. However, due to combination of the routing and sequencing problems, flexible job-shop scheduling problem (FJSP) presents additional difficulty than the classical job-shop scheduling problem and requires more effective algorithms. This paper developed a filtered-beam-search-based heuristic algorithm (named as HFBS) to find sub-optimal schedules within a reasonable computational time for the FJSP with multiple objectives of minimising makespan, the total workload of machines and the workload of the most loaded machine. The proposed algorithm incorporates dispatching rules based heuristics and explores intelligently the search space to avoid useless paths, which makes it possible to improve the search speed. Through computational experiments, the performance of the presented algorithm is evaluated and compared with those of existing literature and those of commonly used dispatching rules, and the results demonstrate that the proposed algorithm is an effective and practical approach for the FJSP.     

A Pareto-based estimation of distribution algorithm for the multi-objective flexible job-shop scheduling problem

To solve the multi-objective flexible job-shop problem (MFJSP), an effective Pareto-based estimation of distribution algorithm (P-EDA) is proposed. The fitness evaluation based on Pareto optimality is employed and a probability model is built with the Pareto superior individuals for estimating the probability distribution of the solution space. In addition, a mechanism to update the probability model is proposed, and the new individuals are generated by sampling the promising searching region based on the probability model. To avoid premature convergence and enhance local exploitation, the population is divided into two sub-populations at certain generations according to a splitting criterion, and different operators are designed for the two sub-populations to generate the promising neighbour individuals. Moreover, multiple strategies are utilised in a combination way to generate the initial solutions, and a local search strategy based on critical path is proposed to enhance the exploitation ability. Furthermore, the influence of parameters is investigated based on the Taguchi method of design of experiment, and a suitable parameter setting is suggested. Finally, numerical simulation based on some well-known benchmark instances and comparisons with some existing algorithms are carried out. The comparative results demonstrate the effectiveness of the proposed P-EDA in solving the MFJSP.     

An effective estimation of distribution algorithm for the flexible job-shop scheduling problem with fuzzy processing time

Considering the fuzzy nature of the data in real-world scheduling, an effective estimation of distribution algorithm (EDA) is proposed to solve the flexible job-shop scheduling problem with fuzzy processing time. A probability model is presented to describe the probability distribution of the solution space. A mechanism is provided to update the probability model with the elite individuals. By sampling the probability model, new individuals can be generated among the search region with promising solutions. Moreover, a left-shift scheme is employed for improving schedule solution when idle time exists on the machine. In addition, some fuzzy number operations are used to calculate scheduling objective value. The influence of parameter setting is investigated based on the Taguchi method of design of experiment, and a suitable parameter setting is suggested. Numerical testing results and comparisons with some existing algorithms are provided, which demonstrate the effectiveness of the proposed EDA.     

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.     

A knowledge-guided fruit fly optimization algorithm for dual resource constrained flexible job-shop scheduling problem

Different from the classical job shop scheduling, the dual-resource constrained flexible job-shop scheduling problem (DRCFJSP) should deal with job sequence, machine assignment and worker assignment all together. In this paper, a knowledge-guided fruit fly optimisation algorithm (KGFOA) with a new encoding scheme is proposed to solve the DRCFJSP with makespan minimisation criterion. In the KGFOA, two types of permutation-based search operators are used to perform the smell-based search for job sequence and resource (machine and worker) assignment, respectively. To enhance the search capability, a knowledge-guided search stage is incorporated into the KGFOA with two new search operators particularly designed for adjusting the operation sequence and the resource assignment, respectively. Due to the combination of the knowledge-guided search and the smell-based search, global exploration and local exploitation can be balanced. Besides, the effect of parameter setting of the KGFOA is investigated and numerical tests are carried out using two sets of instances. The comparative results show that the KGFOA is more effective than the existing algorithms in solving the DRCFJSP.     

A memetic algorithm for multi-objective flexible job-shop problem with worker flexibility

In existing scheduling models, the flexible job-shop scheduling problem mainly considers machine flexibility. However, human factor is also an important element existing in real production that is often neglected theoretically. In this paper, we originally probe into a multi-objective flexible job-shop scheduling problem with worker flexibility (MO-FJSPW). A non-linear integer programming model is presented for the problem. Correspondingly, a memetic algorithm (MA) is designed to solve the proposed MO-FJSPW whose objective is to minimise the maximum completion time, the maximum workload of machines and the total workload of all machines. A well-designed chromosome encoding/decoding method is proposed and the adaptive genetic operators are selected by experimental studies. An elimination process is executed to eliminate the repeated individuals in population. Moreover, a local search is incorporated into the non-dominated sorting genetic algorithm II. In experimental phase, the crossover operator and elimination operator in MA are examined firstly. Afterwards, some extensive comparisons are carried out between MA and some other multi-objective algorithms. The simulation results show that the MA performs better for the proposed MO-FJSPW than other algorithms.     

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.     

Research on job-shop scheduling problem based on genetic algorithm

With job-shop scheduling (JSS) it is usually difficult to achieve the optimal solution with classical methods due to a high computational complexity (NP-hard). According to the nature of JSS, an improved definition of the JSS problem is presented and a JSS model based on a novel algorithm is established through the analysis of working procedure, working data, precedence constraints, processing performance index, JSS algorithm and so on. A decode select string (DSS) decoding genetic algorithm based on operation coding modes, which includes assembly problems, is proposed. The designed DSS decoding genetic algorithm (GA) can avoid the appearance of infeasible solutions through comparing current genes with DSS in the decoding procedure to obtain working procedure which can be decoded. Finally, the effectiveness and superiority of the proposed method is clarified compared to the classical JSS methods through the simulation experiments and the benchmark problem.     

A hybrid nested partitions algorithm for scheduling flexible resource in flow shop problem

Production scheduling with flexible resources is critical and challenging in many modern manufacturing firms. This paper applies the nested partitions (NP) framework to solve the flexible resource flow shop scheduling (FRFS) problem using an efficient hybrid NP algorithm. By considering the domain knowledge, the ordinal optimisation principle and the NEH heuristics are integrated into the partitioning scheme to search the feasible region. An efficient resource-allocation procedure is built into the sampling scheme for the FRFS problem. A large number of benchmark examples with flexible resources are tested. The test results show that the hybrid NP algorithm is more efficient than either generic NP or heuristics alone. The algorithm developed in this study is capable of selecting the most promising region for a manufacturing system with a high degree of accuracy. The algorithm is efficient and scalable for large-scale problems.     

Flexible job-shop scheduling with flexible workdays,preemption, overlapping in operations and satisfaction criteria: an industrial application

This paper addresses a real scheduling problem, namely, a complex flexible job-shop scheduling problem (FJSP) with special characteristics (flexible workdays, preemption and overlapping in operations), where the objective is to maximise a satisfaction criterion defined through goal programming. To allow for flexible workdays, the solution representation of the classical FJSP is extended to consider overtime decisions and a sequence of time-cell states, which is used to model resource capability. A new temporal-constraint-handling method is proposed to solve the problem of overlapping in operations in a flexible-workday environment. Three solution methods are proposed to solve this scheduling problem: a heuristic method based on priority rules, a goal-guided tabu search (GGTS) and an extended genetic algorithm (EGA). In the GGTS, the neighbourhood functions are defined based on elimination approaches, and five possible neighbourhood functions (N0???N1???N2???N3???N4) are presented. The effectiveness and efficiency of the three solution methods are verified using dedicated benchmark instances. Computational simulations and comparisons indicate that the proposed N4-based GGTS demonstrates performance competitive with that of the EGA and the GGTSs based on the other neighbourhood functions (N0, N1, N2 and N3) for solving the scheduling problem.     

A hybrid water flow algorithm for multi-objective flexible flow shop scheduling problems

In this article, the multi-objective flexible flow shop scheduling problem with limited intermediate buffers is addressed. The objectives considered in this problem consist of minimizing the completion time of jobs and minimizing the total tardiness time of jobs. A hybrid water flow algorithm for solving this problem is proposed. Landscape analysis is performed to determine the weights of objective functions, which guide the exploration of feasible regions and movement towards the optimal Pareto solution set. Local and global neighbourhood structures are integrated in the erosion process of the algorithm, while evaporation and precipitation processes are included to enhance the solution exploitation capability of the algorithm in unexplored neighbouring regions. An improvement process is used to reinforce the final Pareto solution set obtained. The performance of the proposed algorithm is tested with benchmark and randomly generated instances. The computational results and comparisons demonstrate the effectiveness and efficiency of the proposed algorithm.     

Tabu search for the job-shop scheduling problem with multi-purpose machines

In this paper we study the following generalization of the job-shop scheduling problem. Each operation can be performed by one machine out of a set of machines given for this operation. The processing time does not depend on the machine which has been chosen for processing the operation. This problem arises in the area of flexible manufacturing. As a generalization of the jobshop problem it belongs to the hardest problems in combinatorial optimization. We show that an application of tabu search techniques to this problem yields excellent results for benchmark problems.Supported by Deutsche Forschungsgemeinschaft, Project JoP-TAG     

A neural network decision-making model for job-shop scheduling

Scheduling in a job-shop system is a challenging task. Simulation modelling is a well-known approach for evaluating the scheduling plans of a job-shop system; however, it is costly and time-consuming, and developing a model and interpreting the results requires expertise. As an alternative, we have developed a neural network (NN) model focused on detailed scheduling that provides a versatile job-shop scheduling analysis framework for management to easily evaluate different possible scheduling scenarios based on internal or external constraints. A new approach is also proposed to enhance the quality of training data for better performance. Previous NN models in scheduling focus mainly on job sequencing and simple operations flow, and may not consider the complexities of real-world operations. The proposed model’s output proved statistically equivalent to the results of the simulation model. The study was accomplished using sensitivity analysis to measure the effectiveness of the input variables of the NN model and their impact on the output, revealing that the batch size variable had a significant impact on the scheduling results in comparison with other variables.     

A novel branch-and-bound algorithm for the chance-constrained resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) has been widely studied during the last few decades. In real-world projects, however, not all information is known in advance and uncertainty is an inevitable part of these projects. The chance-constrained resource-constrained project scheduling problem (CC-RCPSP) has been recently introduced to deal with uncertainty in the RCPSP. In this paper, we propose a branch-and-bound (B&B) algorithm and a mixed integer linear programming (MILP) formulation that solve a sample average approximation of the CC-RCPSP. We introduce two different branching schemes and eight different priority rules for the proposed B&B algorithm. The computational results suggest that the proposed B&B procedure clearly outperforms both a proposed MILP formulation and a branch-and-cut algorithm from the literature.     

A polynomial algorithm for the two machine job-shop scheduling problem with a fixed number of jobs

It is shown that the job-shop problem with two machines and a fixed number ofk jobs with makespan criterionJ2¦n=k¦C ^max is polynomially solvable. Sotskov and Shakhlevich (1993) have shown that problemJ3¦n=3¦C _maxisNP-hard. Furthermore it is well known that J¦n=2¦C _maxin polynomially solvable. Thus, our result settles the remaining open question concerning the complexity status of job-shop problems with fixed numbers of jobs and machines.Supported by Deutsche Forschungsgemeinschaft, Project Jop-TAG