Flexible Job-shop Problem Research Articles

Multi-Strategy Dynamic Evolution-Based Improved MOEA/D Algorithm for Solving Multi-Objective Fuzzy Flexible Job Shop Scheduling Problem

A scheduling model was developed to optimize the maximum completion time, total machine load, and maximum machine load for the fuzzy flexible job shop problem with uncertain processing times. To solve this problem, a multi-strategy dynamic evolution-based improved multi-objective evolutionary algorithm based on decomposition(IMOEA/D) was proposed. In order to enhance the quality of the non-dominated solution set and improve the algorithm efficiency. The algorithm firstly employs a strategy based on minimum processing time and workload, along with a non-dominated solution prioritization mechanism to generate the initial population. Secondly, three evolutionary strategies are incorporated, and their probabilities are dynamically adjusted with the increase of evolution generations. Finally, a variable neighborhood search method is introduced to improve the search performance of the algorithm. The effectiveness of the proposed algorithm was demonstrated through experimental validation.

A Mathematical Model for the Flexible Job Shop Scheduling Problem With Availability Constraints

We tackle the Flexible Job Shop Problem (FJSSP) subject to availability constraints due to maintenance tasks on machines. Previous studies explored meta-heuristic methods to address this problem and solved small-sized instances generated from classical FJSSP benchmark. We first introduce a new benchmark, comprising more than 2000 instances, for the problem based on the well-known FJSSP benchmarks. A mixed integer model is then developed to solve this problem. We carry out a computational study on the proposed benchmark and analyze its performances. Results show that our model can solve small and medium size instances efficiently. We also observe important variation in complexity depending on the class of instance which makes the proposed benchmark interesting to evaluate our approach and further improve the solving process in future works.

Distributed real-time production control for resilient manufacturing systems

To enable resilient manufacturing, production control systems must be able to adapt quickly and flexibly to unexpected changes. Motivated by Industrie 4.0, multi-agent systems offer a promising approach to meet these requirements. This paper presents a method for distributed production control that enables production entities to make optimal decisions regarding capacity utilization and the compliance of delivery dates in real-time despite disruptive events. Based on a multi-agent Markov Decision Process, production entities are modeled as autonomous software agents that can solve Flexible Job-Shop Problems through message passing. The performance of the proposed method is evaluated in a simulated production environment.

An MILP Model for Energy-Conscious Flexible Job Shop Problem with Transportation and Sequence-Dependent Setup Times

As environmental awareness grows, energy-aware scheduling is attracting increasing attention. Compared with traditional flexible job shop scheduling problem (FJSP), FJSP, with considering sequence-dependent setup times and transportation times (FJSP-SDST-T), is closer to real production. In existing research, little research has focused on FJSP-SDST-T with the minimization energy consumption. In order to make up the gap, a mixed integer linear programming (MILP) model has been formulated to solve FJSP-SDST-T with minimizing energy. Firstly, the total energy consumption of the workshop included the processing energy consumption, setup energy consumption, idle energy consumption, transportation energy consumption and common energy consumption, which were analyzed and formulated by introducing related decision variables. Then, the MILP model was detailedly formulated from the formulation of the energy consumption composition, the objective function, the decision variables and the constraint sets and the linearization. Finally, experiments were carried out on extended benchmark cases and the results showed the effectiveness of the MILP model.

Hybrid genetic algorithm with variable neighborhood search for flexible job shop scheduling problem in a machining system

This paper proposes an improved hybrid genetic algorithm with variable neighborhood search (HGA-VNS) for addressing the flexible job shop scheduling problem (FJSP) considering the machine work load balance in machining system, with the minimization of the makespan. In the HGA-VNS algorithm, each solution is represented by a chromosome consists of two parts, where the first part is the code of the machining machine number, and the second part chromosome is the code of the machining process number. Second, considering the slow convergence speed of the previous algorithms, a combined methods in crossover and mutation operators that considers the machine work load balance is proposed. Third, a local search approach that carry out for key processes on the critical path which reduces the number of invalid transformations is proposed. For the HGA-VNS, using the orthogonal experiment approach, the best combination of parameters is provided. Then, the proposed HGA-VNS is tested on sets of extended instances based on the well-known benchmarks. Experimental results show that the HGA-VNS is effective, and its performance is significantly better than other algorithms in solving flexible job shop problems in a machining system. Finally, the proposed HGA-VNS is applied to optimize practical FJSP in enterprise F. Compared with the original scheduling scheme, the makespan of the optimal scheduling scheme is reduced by 14.92%, and HGA-VNS can obtain more efficient and economic solutions.

Swarm intelligent based metaheuristics for a bi-objective flexible job shop integrated supply chain scheduling problems

This study introduces a bi-objective integrated supply chain (SC) scheduling (SCS) model to deal with the challenges of providing highly customized and on-time delivery requirements at the least cost. To address these real-life challenges, the model integrates the supply portfolio into production scheduling with a customer-imposed delivery time window. A set of conflicting factors is considered for the SC in which the manufacturer is modeled using the flexible job shop (FJS) problem to include greater flexibility in process routing. Since the proposed SCS model extends the strongly NP-hard FJS problem, two new meta-heuristic algorithms are developed, enhancing the performance of the multi-objective particle swarm optimization (MOPSO). A Tabu search inspired search mechanism and a problem-specific mutation operator are designed in both algorithms. As inadequate archive diversity leads to premature convergence and unsatisfactory Pareto solutions in many cases, this work employs two practical approaches separately (i.e., crowding distance (CD) and niche count preservation of reference point (RP)) in the proposed MOPSOs, called CD-MOPSO and RP-MOPSO, respectively. For leader selection, CD-MOPSO uses the swarm distance-based Roulette wheel, whereas the concept of RP is proposed in RP-MOPSO to expedite convergence. The performances of the proposed algorithms are validated against four existing algorithms and assessed by utilizing several criteria after solving 45 artificial instances. The simulation results and statistical analysis demonstrate the supremacy of the RP-MOPSO which increases the flexibility for a decision-maker in providing a higher number of Pareto solutions and more diverse and regular frontiers within reasonable computational time. Finally, a sensitivity analysis of the model is conducted, and managerial insights are provided.

Realtime scheduling heuristics for just-in-time production in large-scale flexible job shops

This study aims to enable jobs to go smoothly between shops on a production line by completing jobs in the upstream shop just in time (JIT) for the downstream shop. We propose solutions to a factory that is seeking ways for an upstream shop to complete every job at the precise time such that the downstream shop can process the job. We model the upstream shop as a flexible job shop and propose four methods that form a realtime scheduling and control system for JIT production. We first propose a method to set for each job a due date by which the job should be completed in the upstream shop. The due dates are set in such a manner that jobs would be completed JIT for the downstream shop, if they are completed JIT for their due dates. We then propose a method to estimate the minimum number of workers needed in the upstream shop for completing the jobs by their due dates. We further propose two methods that work dynamically to complete each job neither too early nor too late for its due date. One is a dispatching rule that dynamically sequences jobs in process according to urgency degree. The other is a job-selecting heuristic that dynamically assigns workers to jobs such that jobs not nearing completion will be given priority in processing. Simulations by using data from the factory show that the methods can achieve in real time (i.e. within 0.00 seconds) JIT production for a flexible job shop problem involving hundreds of operations. More extensive simulations by using a large number of randomly generated problem instances show that solutions obtained in real time by the proposed methods greatly outperform those obtained in much longer time by metaheuristics designed for solving similar problems, and that each proposed method outperforms its rivals in the literature. The findings imply that integrating fast and high-performing heuristics and rules can be a solution to solve large-scale scheduling problems in real time.

Hybrid energy-efficient scheduling measures for flexible job-shop problem with variable machining speeds

Production scheduling has a significant impact on energy savings in manufacturing system from the viewpoint of operation management. Taking the flexibility of machining speeds taken into account, the flexible job-shop scheduling problem will get closer to the real manufacturing environment, and the associated energy consumption for shifting speeds should also be noticeable. In this paper, a novel energy-aware estimation model is proposed to compute different energy consumptions for different running conditions of a machine. Then, a multi-objective optimization model is formulated for the dual flexible job-shop scheduling problem to minimize the makespan and total energy consumption. Hybrid energy-efficient scheduling measures are developed to reduce each kind of energy consumption on the machines. Finally, experimental results show the consistency between optimization objectives and demonstrate superior performance of these energy-efficient scheduling measures.

A hybrid genetic algorithm based on a two-level hypervolume contribution measure selection strategy for bi-objective flexible job shop problem

This study addresses the bi-objective flexible job shop problem (BOFJSP) with respect to minimization of the maximum completion time (makespan) and total tardiness. This study aims to propose an algorithm called Bi-objective Hybrid Genetic Algorithm – hypervolume contribution measure (BOHGA-HCM) that integrates GA with a multi-search algorithm and uses hypervolume contribution measure (Δs) in its two-level selection strategy. The initial population is created by randomly assigning operations to the available machines via dispatching rules to find better areas in the search space and enhance diversity to avoid premature convergence. The algorithm handles the objective functions simultaneously with the Pareto Optimality approach. The effectiveness and performance of the proposed algorithm are benchmarked and compared with other algorithms by using well-known data sets presented in the literature.

Dynamic Scheduling of Multi-Memory Process Flexible Job Shop Problem Based on Digital Twin

Dynamic Scheduling of Multi-Memory Process Flexible Job Shop Problem Based on Digital Twin

Improved chemical reaction optimization for distributed flexible job shop problem with transportation times

In this paper, we study a new variant of the Distributed Flexible Job shop Scheduling Problem introducing transportation time between machines as additional constraints. The problem is called Distributed Flexible Job shop Scheduling Problem with Transportation times and denoted by DFJSPT. In DFJSPT, each operation can be executed on one of the available machines in a set of geographically distributed factories. Each factory has a set of machines on which a set of jobs must be executed and the transport of jobs between machines is made by one or several transport robots. The DFJSPT combines three NP-Hard problems: The problem of assigning jobs to machines, the distribution problem of jobs to factories, and the robot routing problem. In this paper, we study the DFJSPT with a single robot in each factory and we propose an improved Chemical Reaction Optimization (CRO) metaheuristic to solve it in order to minimize the makespan to which we have made improvements in the classic CRO optimization phases in our algorithm. This phase consists of four functions: The crossover-Synthesis function, where we applied one point crossover known operator for the synthesis function, The mutation-OnWall function, where we applied the swap technique, The decomposition function, where we used the inversion mutation technique in this function and the Inter-Molecular, where we applied the two point crossover operator. We tested our approach on two different categories of instances that we designed on purpose, the first category is composed of instances of flexible job shop scheduling problem with transportation times to which we have integrated the constraints of jobs distribution between factories, the second category is composed of instances of distributed and flexible job shop scheduling problem to which we have integrated the constraints of Transportation times.

A Q-Learning Rescheduling Approach to the Flexible Job Shop Problem Combining Energy and Productivity Objectives

The flexible job shop problem (FJSP) has been studied in recent decades due to its dynamic and uncertain nature. Responding to a system’s perturbation in an intelligent way and with minimum energy consumption variation is an important matter. Fortunately, thanks to the development of artificial intelligence and machine learning, a lot of researchers are using these new techniques to solve the rescheduling problem in a flexible job shop. Reinforcement learning, which is a popular approach in artificial intelligence, is often used in rescheduling. This article presents a Q-learning rescheduling approach to the flexible job shop problem combining energy and productivity objectives in a context of machine failure. First, a genetic algorithm was adopted to generate the initial predictive schedule, and then rescheduling strategies were developed to handle machine failures. As the system should be capable of reacting quickly to unexpected events, a multi-objective Q-learning algorithm is proposed and trained to select the optimal rescheduling methods that minimize the makespan and the energy consumption variation at the same time. This approach was conducted on benchmark instances to evaluate its performance.

Enabling In-Depot Automated Routing and Recharging Scheduling for Automated Electric Bus Transit Systems

The bus transit system is promising to enable electric and autonomous vehicles for massive urban mobility, which relies on high-level automation and efficient resource management. Besides the on-road automation, the in-depot automated scheduling for battery recharging has not been adequately studied yet. This paper presents an integrated in-depot routing and recharging scheduling (IDRRS) problem, which is modeled as a constraint programming (CP) problem with Boolean satisfiability conditions (SAT). The model is converted to a flexible job-shop problem (FJSP) and is feasible to be solved by a CP-SAT solver for the optimal solution or feasible solutions with acceptable performance. This paper also presents a case study in Shanghai and compares the results from the FJSP model and the first-come first-serve (FCFS) method. The result demonstrates the allocation of routes and chargers under multiple scenarios with different numbers of chargers. The results show that the FJSP model shortens the delay and increases the time conservation for future rounds of operation than FCFS, while FCFS presents the simplicity of programming and better computational efficiency. The multiple random input test suggests that the proposed approach can decide the minimum number of chargers for stochastic charging requests. The proposed method can conserve the investment by increasing the utilization of automated recharging devices, improving vehicles’ in-depot efficiency.

Predictive maintenance integrated production scheduling by applying deep generative prognostics models: approach, formulation and solution

To harness the full potential of predictive maintenance (PdM), PdM information has to be used to optimally plan production and maintenance actions. Hence, operation-specific modelling of degradation, i.e. predictions of the health condition under time-varying operational conditions, has to be realized. By utilizing operation-specific degradation information, maintenance and production can be planned with regard to each other and thus, predictive maintenance integrated production scheduling (PdM-IPS) is enabled. This publication proposes a novel PdM-IPS approach consisting of two interacting modules: an operation-specific Prognostics and Health Management (PHM) module and an integrated production scheduling and maintenance planning (IPSMP) module. Specifically, the mathematical problem of the IPSMP module based on an extended version of the maintenance integrated flexible job shop problem is formulated. A two-stage genetic algorithm to efficiently solve this problem is designed and subsequently applied to simulated condition monitoring, as well as real industrial data. Results indicate that the approach is able to find feasible high quality PdM integrated production schedules.

Improved particle swarm optimization based on blockchain mechanism for flexible job shop problem

Improved particle swarm optimization based on blockchain mechanism for flexible job shop problem

Minimizing the maximum flow time for flexible job shop problem with parallel machines

ABSTRACT This paper studies a flexible job shop problem with parallel machines considering release time. The objective aims to minimize the maximum flow time. Based on the specific characteristics of the problem, we find a property which can reduce the dimension of solution space to dimension, where is the total number of operations. To solve the small-scale problem, a branch-and-bound algorithm is proposed. For the medium-scale problem, a heuristic based on a differential evolution algorithm is proposed. The LSPT-DS heuristic is tried to solve the large-scale problem. Through computational experiments, the proposed algorithms are proved to be both effective and efficient in solving this flexible job shop problem. Besides experiments are also conducted to verify that the objective to minimize the maximum flow time is reasonable.

An improved multi-objective optimization algorithm for solving flexible job shop scheduling problem with variable batches

In order to solve the flexible job shop scheduling problem with variable batches, we propose an improved multi-objective optimization algorithm, which combines the idea of inverse scheduling. First, a flexible job shop problem with the variable batches scheduling model is formulated. Second, we propose a batch optimization algorithm with inverse scheduling in which the batch size is adjusted by the dynamic feedback batch adjusting method. Moreover, in order to increase the diversity of the population, two methods are developed. One is the threshold to control the neighborhood updating, and the other is the dynamic clustering algorithm to update the population. Finally, a group of experiments are carried out. The results show that the improved multi-objective optimization algorithm can ensure the diversity of Pareto solutions effectively, and has effective performance in solving the flexible job shop scheduling problem with variable batches.

A Hybrid Iterated Greedy Algorithm for a Crane Transportation Flexible Job Shop Problem

In this study, we propose an efficient optimization algorithm that is a hybrid of the iterated greedy and simulated annealing algorithms (hereinafter, referred to as IGSA) to solve the flexible job shop scheduling problem with crane transportation processes (CFJSP). Two objectives are simultaneously considered, namely, the minimization of the maximum completion time and the energy consumptions during machine processing and crane transportation. Different from the methods in the literature, crane lift operations have been investigated for the first time to consider the processing time and energy consumptions involved during the crane lift process. The IGSA algorithm is then developed to solve the CFJSPs considered. In the proposed IGSA algorithm, first, each solution is represented by a 2-D vector, where one vector represents the scheduling sequence and the other vector shows the assignment of machines. Subsequently, an improved construction heuristic considering the problem features is proposed, which can decrease the number of replicated insertion positions for the destruction operations. Furthermore, to balance the exploration abilities and time complexity of the proposed algorithm, a problem-specific exploration heuristic is developed. Finally, a set of randomly generated instances based on realistic industrial processes is tested. Through comprehensive computational comparisons and statistical analyses, the highly effective performance of the proposed algorithm is favorably compared against several efficient algorithms. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The flexible job shop scheduling problem (FJSP) can be extended and applied to many types of practical manufacturing processes. Many realistic production processes should consider the transportation procedures, especially for the limited crane resources and energy consumptions during the transportation operations. This study models a realistic production process as an FJSP with crane transportation, wherein two objectives, namely, the makespan and energy consumptions, are to be simultaneously minimized. This study first considers the height of the processing machines, and therefore, the crane lift operations and lift energy consumptions are investigated. A hybrid iterated greedy algorithm is proposed for solving the problem considered, and several problem-specific heuristics are embedded to balance the exploration and exploitation abilities of the proposed algorithm. In addition, the proposed algorithm can be generalized to solve other types of scheduling problems with crane transportations.

Improved artificial immune algorithm for the flexible job shop problem with transportation time

The flexible job shop problem (FJSP), as one branch of the job shop scheduling, has been studied during recent years. However, several realistic constraints including the transportation time between machines and energy consumptions are generally ignored. To fill this gap, this study investigated a FJSP considering energy consumption and transportation time constraints. A sequence-based mixed integer linear programming (MILP) model based on the problem is established, and the weighted sum of maximum completion time and energy consumption is optimized. Then, we present a combinational meta-heuristic algorithm based on a simulated annealing (SA) algorithm and an artificial immune algorithm (AIA) for this problem. In the proposed algorithm, the AIA with an information entropy strategy is utilized for global optimization. In addition, the SA algorithm is embedded to enhance the local search abilities. Eventually, the Taguchi method is used to evaluate various parameters. Computational comparison with the other meta-heuristic algorithms shows that the improved artificial immune algorithm (IAIA) is more efficient for solving FJSP with different problem scales.

Robust scheduling based on extreme learning machine for bi-objective flexible job-shop problems with machine breakdowns

In modern manufacturing systems, a flexible job-shop schedule problem (FJSP) with random machine breakdown has been widely studied. Two objectives, namely makespan and robustness, were simultaneously considered in this study. Maximizing the workload and float time of each operation and the machine breakdowns, one surrogate measure named RMc was developed via an extreme learning machine (ELM) to evaluate robustness. Specifically, this measure determines the impact of float time on the robustness by the probability of machine breakdown and the location of float time. Simultaneously, the impact was automatically adjusted by the ELM. Then, a method combining an improved version of nondominated sorting genetic algorithm II and RMc was proposed to address the bi-objective FJSP. Computational results on the benchmarks show that RMc accurately evaluates the robustness of the schedules with a small amount of computation cost.