Distributed Scheduling Problem Research Articles

Energy-efficient multi-objective distributed assembly permutation flowshop scheduling by Q-learning based meta-heuristics

This study addresses energy-efficient multi-objective distributed assembly permutation flowshop scheduling problems with minimisation of maximum completion time, mean of earliness and tardiness, and total carbon emission simultaneously. A mathematical model is introduced to describe the concerned problems. Five meta-heuristics are employed and improved, including the artificial bee colony, genetic algorithms, particle swarm optimization, iterated greedy algorithms, and Jaya algorithms. To improve the quality of solutions, five critical path-based neighborhood structures are designed. Q-learning, a value-based reinforcement learning algorithm that learns an optimal strategy by repeatedly interacting with the environment, is embedded into meta-heuristics. The Q-learning guides algorithms intelligently select appropriate neighborhood structures in the iterative process. Then, two machine speed adjustment strategies are developed to further optimize the obtained solutions. Finally, extensive experimental results show that the Jaya algorithm with Q-learning has the best performance for solving the considered problems.

Integrated scheduling of multi-constraint open shop and vehicle routing: Mathematical model and learning-driven brain storm optimization algorithm

Recent years have witnessed a surge of interest in integrated production and distribution scheduling problems which can achieve an overall optimization of the production and distribution activities. However, integrated scheduling of open shop and distribution receives rare attention in existing studies. This work proposes an integrated scheduling problem of multi-constraint open shop and vehicle routing to minimize maximum completion time, where group and transportation operations are considered together in the production process. All jobs are divided into multiple groups, and then handled in an open shop with multiple machines. Subsequently, the jobs are delivered to their corresponding customers. First, a mixed integer programming model is formulated to define the problem. Second, a Q-learning-driven brain storm optimization algorithm is developed to address the formulated model. A Q-learning method is employed to choose search strategies for generating new individuals rather than using fixed probability parameters straightforwardly as basic brain storm optimizers. In addition, the solution encoding, heuristic decoding, population initialization, clustering, new individual generation and selection methods are specially devised in consideration of problem-specific knowledge. At last, the developed model and algorithm are verified by addressing a set of benchmark instances, and comparison experiments are conducted with an exact solver CPLEX and four meta-heuristics from existing literature. The results validate the competitive advantages of the formulated model and algorithm in solving the considered problems.

A biogeography-based optimization algorithm with local search for large-scale heterogeneous distributed scheduling with multiple process plans

Since modern production mode has shifted from a single factory to a multi-factory production network, distributed scheduling has been derived. Distributed scheduling problem (DSP) is characterized by many varieties, large scale, redundant production factories, flexible production processes, and high-value products. Each factory in the heterogeneous DSP can be considered an individual entity, and there may be several production process plans. To address the heterogeneous DSP with multiple process plans, we consider minimizing the global makespan over all factories containing the transportation time delivering tasks from factories to their destinations and propose a biogeography-based optimization algorithm combined with local search based on heuristic rules (BBO-LH) to find the optimal production plan and enhance productivity. First, a new encoding scheme with three-segment representation has been developed to avoid illegal solutions and realize the information sharing between solutions selecting different process plans. Then two efficient local search approaches have been proposed based on different heuristic rules on sequence and equipment allocation respectively, to improve the search efficiency. Besides, BBO-LH has adopted a cosine migration rate model to replace the linear one to strengthen the ability to jump out of local optima. BBO-LH is compared with a genetic algorithm (GA_X), using generated examples to test the performance of the proposed strategies, and simulation results show the effectiveness of the proposed BBO-LH on large-scale heterogeneous DSP with multiple process plans.

Online Integrated Production and Distribution Scheduling: Review and Extensions

As a growing number of manufacturers adopt the make-to-order business mode and a growing number of retailers sell online, we are seeing numerous decision problems that can be modeled as what are known in the literature as integrated production and distribution scheduling (IPDS) problems. In such problems, order processing and delivery must be scheduled jointly in order to achieve an optimal balance between total operational costs and overall customer service. Offline IPDS problems, in which the information about every order is known in advance with certainty, are extensively studied. However, research on online IPDS problems, in which orders arrive randomly with their information unknown until they arrive, is relatively recent but is growing rapidly. In this paper, we first describe several real-world applications to illustrate the importance of studying online IPDS problems from a practical point of view. We then review the existing literature on online IPDS problems with a focus on existing online algorithms for these problems and their theoretical performance. We also derive some new results to fill several gaps left in the literature and discuss possible topics for future research. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0305 .

Deep reinforcement learning for dynamic distributed job shop scheduling problem with transfers

Dynamic events and transportation constraints would significantly affect the full utilization of resources and the reduction of production costs in distributed job shops. Therefore, in this paper, a deep reinforcement learning algorithm (DRL)-based real-time scheduling method is developed to minimize the mean tardiness of the dynamic distributed job shop scheduling problem with transfers (DDJSPT) considering random job arrivals. Firstly, the proposed DDJSPT is modeled as a Markov decision process (MDP). Then, ten problem-oriented state features covering four aspects of factories, machines, jobs, and operations are elaborately extracted from the dynamic distributed job shop. After that, eleven composite rules considering the uniqueness of DDJSPT are constructed as a pool of actions to intelligently prioritize unfinished jobs and allocate the selected job to an appropriate factory. Moreover, a justified reward function adapted from the objective is designed for better convergence of DRLs. Subsequently, five DRLs are employed to address the DDJSPT, encompassing deep Q-network (DQN), double DQN (DDQN), dueling DQN (DlDQN), trust region policy optimization (TRPO), and proximal policy optimization (PPO). Finally, grounded in numerical comparison experiments under 243 production configurations of the DDJSPT, the effectiveness and generalization of DRL-based scheduling methods are credibly verified and confirmed.

Dynamic Intelligent Scheduling in Low-Carbon Heterogeneous Distributed Flexible Job Shops with Job Insertions and Transfers.

With the rapid development of economic globalization and green manufacturing, traditional flexible job shop scheduling has evolved into the low-carbon heterogeneous distributed flexible job shop scheduling problem (LHDFJSP). Additionally, modern smart manufacturing processes encounter complex and diverse contingencies, necessitating the ability to address dynamic events in real-world production activities. To date, there are limited studies that comprehensively address the intricate factors associated with the LHDFJSP, including workshop heterogeneity, job insertions and transfers, and considerations of low-carbon objectives. This paper establishes a multi-objective mathematical model with the goal of minimizing the total weighted tardiness and total energy consumption. To effectively solve this problem, diverse composite scheduling rules are formulated, alongside the application of a deep reinforcement learning (DRL) framework, i.e., Rainbow deep-Q network (Rainbow DQN), to learn the optimal scheduling strategy at each decision point in a dynamic environment. To verify the effectiveness of the proposed method, this paper extends the standard dataset to adapt to the LHDFJSP. Evaluation results confirm the generalization and robustness of the presented Rainbow DQN-based method.

An ensemble of brain storm optimization and Q-learning methods for distributed flexible job shop scheduling problems with distribution operations

Distributed manufacturing scheduling problems have attracted much concern from both industrial and academic areas. Nevertheless, distributed scheduling problems with distribution operations are seldom studied. This work proposes a distributed flexible job shop scheduling problem with distribution operations. A set of jobs is handled at distributed flexible job shops, and then the finished jobs are transported to their corresponding customers following given due dates. First, a mixed integer programming model is established to minimize total tardiness. Second, an ensemble of brain storm optimization and Q-learning methods is developed to solve the formulated model. Six heuristics are hybridized to generate a high-quality initial population. A Q-learning method is devised by fully employing found search information to guide subsequent search processes instead of using fixed parameters as basic brain storm optimization. A variable neighborhood search method combining problem-specific knowledge is designed to further refine the found best individual. At last, the formulated model and method are compared with three state-of-the-art metaheuristics and a mathematical programming solver CPLEX via using a group of problem instances. The results and analysis demonstrate that the developed model and algorithm have more powerful competitiveness in addressing the studied problem.

A Self-Adaptive Memetic Algorithm for Distributed Job Shop Scheduling Problem

Distributed scheduling has become a common manufacturing mode, and the distributed job scheduling problem (DJSP) has attracted more manufacturers and researchers in the field of operation research. For the distributed scheduling problem, it emphasizes the flexibility of factory assignment and determines the sequence of operation related to each machine in related factories. In this paper, a mixed-integer linear programming model for the DJSP is formulated to be optimized by an SMA. Also in this paper, a self-adaptive memetic algorithm (SMA) is proposed to obtain a near-optimal solution in a limited time for the DJSP. To strengthen the effectiveness of the SMA, an independent encoding is designed with jobs assigned to factories and the sequence of operation. In the proposed algorithm, various local search strategies related to the critical path in the critical factory are designed to enhance the quality of the solution. Moreover, the self-adaptive scheme for solution improvement is formulated to reduce the search time and avoid prematurity effectively. To demonstrate the performance of the proposed algorithm, numerical experiments are carried out on 120 different instances extended from the well-known job shop scheduling benchmarks. The proposed SMA has updated 30 instance records in 120 instances and it has obtained the 91 best records in 120 instances. According to the comparison, an SMA is a more effective algorithm that could update several records of benchmarks.

Bi-objective carbon-efficient distributed flow-shop scheduling with multistep electricity pricing

A bi-objective distributed flow-shop scheduling problem with multistep electricity pricing and carbon emissions is studied. One objective is to minimise the completion time of production, and the other is to minimise the total cost of multistep electricity pricing and carbon emissions. A mixed integer programming model and a two-stage knowledge based cooperative algorithm with a local reinforcement strategy are proposed for the problem. The extensive numerical experiments show that the two-stage algorithm was effective statistical significantly in generating non-dominated solution sets and Pareto frontiers. Simulations on Electricity Prices are applied to examine different multistep electricity pricing schemes, and management implications were drawn for both government and companies.

Investigation on distributed scheduling with lot-streaming considering setup time based on NSGA-II in a furniture intelligent manufacturing

Distributed flexible flowshop scheduling is getting more important in the large-scale panel furniture industry. It is vital for a higher manufacturing efficiency and economic profit. The distributed scheduling problem with lot-streaming in a flexible flow shop environment is investigated in this work. Furthermore, the actual constraints of packaging collaborative and machine setup times are considered in the proposed approach. The average order waiting time for packaging and average order delay rate is used as objectives. Non-dominated sorting method is used to handle this bi-objective optimization problem. An improved encoding method was proposed to address the large-scale orders that need to be divided into sub-lots based on genetic algorithm. The proposed approach is firstly validated by benchmark with other multi-objectives evolutionary algorithms. The results found that the proposed approach had a good convergence and diversity. Besides, the influence of the proportion of large-scale orders priority level and sub-lot size was investigated in a panel furniture manufacturing scenario. The results can be concluded that the enterprise could obtain shorter order average waiting time and delay rate when the sub-lot sizes were set as two and the order priority level was allocated in the proportion of 1:2:3:4:5.

The multi-factory two-stage assembly scheduling problem

The recent notable focus on distributed production management in academic and industrial contexts has underscored the importance of scheduling across multiple factories. Accordingly, this study investigates a new multi-factory configuration in which non-identical factories produce different components of a final product in the first stage. Each factory is considered as a classical flow-shop, which can manufacture a unique component. These components are assembled into final products in the assembly factory, which is located in the second stage. Unlike other distributed scheduling problems, to determine a united production sequence in such a system, there is no need to find a suitable factory to assign a job since each factory is qualified for a particular task. In real-world applications, these systems encounter challenges that span from information architectures and negotiation mechanisms to the development of scheduling algorithms. The objective of this research is to schedule the jobs in each factory to minimize the makespan of the entire process. For this purpose, a mixed-integer programming model is developed to deal with small-size instances. Then, the lower bound is derived and incorporated to develop a branch and bound method. Furthermore, to deal with larger instances, five heuristic methods are developed, and the worst-case analysis is carried out. Computational experiments are conducted for different test classes to compare and to highlight the performance of the proposed solution procedures.

New computational results for integrated production and outbound distribution scheduling problems for a product with a short lifespan

In this paper, we consider an integrated production and outbound distribution scheduling problem with a single production site, and its extension to multiple plants. A set of orders must be satisfied such that the required pieces from a single product must be first processed on a single machine in a plant, then must be delivered to the customers before their lifespan expire using a single vehicle. The goal is to minimize the makespan of the solution, which is the return time of the vehicle after its last trip. We propose an elementary variable neighborhood search to solve the problem, using two new local search operators. Our computational results show that this simple procedure outperforms the existing, sometimes complex approaches on the widely used benchmark dataset. We also review the existing computational results, and demonstrate that in some cases the comparisons in the literature are invalid due to the use of different rounding of the data. By re-evaluating the accessible solutions we provide a fair comparison for each rounding method. We also consider the extension of the problem to multiple plants, and adapt our solution approach for this extension. Our experiments show that our method is competitive in terms of solution quality with the existing solution approach for the problem.

Integrating Production Scheduling and Vehicle Routing Decisions at the Operational Decision Level: A Review and Discussion Extension

As a method of reducing costs and enhancing service quality, companies integrate production and distribution scheduling to improve performance. Thirty-two articles published between 2017 and 2022 are classified based on a review methodology as a continuation of a literature review of the integrated production and distribution scheduling problems at the operational level that was published in 2016. The characteristics of mathematical models and the solution algorithms used are discussed in order to identify gaps and determine future research directions. Through the review, it was found that some real-life characteristics still need further study. Future research may need to consider uncertainty, stochastic elements and evaluating different heuristics and metaheuristics in different production environments. Finally, additional research is necessary to determine under what conditions integration is most effective.

A deep reinforcement learning based algorithm for a distributed precast concrete production scheduling

The environmental-friendly production demands higher manufacturing efficiency and lower energy cost; therefore, time-of-use electricity price constraint and distributed production have attracted more attention. For concrete precast architecture construction, the tardiness penalty and warehouse cost cannot be ignored, which should be optimized for lower cost. In this study, the concrete precast process is investigated as the group scheduling of a distributed flexible job shop problem. Each concrete precast is managed in a group, the setup time between different groups is considered. Two objectives, total weighted earliness and tardiness and total time-of-use electricity cost are minimized, simultaneously. To solve the integrated problem, three coordinated double deep Q-networks (DQN) are applied, which are organized as a learn-to-improve reinforcement learning approach. For distributed scheduling problem, operators in a single factory or in multiple factories differs in solution improvement; so selection DQN is designed to decide the type of the operators according to scheduling circumstances. Other two DQNs, i.e., local DQN and global DQN, are to select the optimization operators in one factory or in multiple factories, respectively. Furthermore, two solution refinement strategies are designed to decrease the objectives after reinforcement learning component. Numerical experiment and statistical analysis suggest that the proposed deep reinforcement learning based algorithm has superiority in solving the considered problem.

A Q-learning-based multi-objective evolutionary algorithm for integrated green production and distribution scheduling problems

In recent years, integrated production and distribution scheduling (IPDS) has received growing attention from academia and industry. With increasingly global economic activities, it is vital to extend IPDS to distributed environments. Besides, the production and distribution systems are the main contributors to carbon emissions due to their high energy consumption. Driven by this, this work introduces an integrated green distributed production and distribution scheduling problem with the objectives of total tardiness and total carbon emissions minimization. To provide a clear definition, a mixed-integer mathematical programming model is created. Considering the problem's NP-hard nature, a Q-learning-based multi-objective evolutionary algorithm (Q-MEA) is designed to handle it. To evaluate the performance of Q-MEA, a comparison pool including four variants, five meta-heuristics, and an exact optimizer named CPLEX is constructed to implement numerical experiments. The results demonstrate that Q-MEA has clear advantages over its rivals in tackling our problems. Furthermore, comparing the integrated model with a separate one shows that the former can achieve an average decrease of about 13.10% in total tardiness and 21.02% in total carbon emissions.

A biogeography-based optimization algorithm with modified migration operator for large-scale distributed scheduling with transportation time

To expand production scale and enhance enterprise competitiveness, modern supply chains and manufacturing systems have shifted from the single factory production to the multi-factory production network with the characteristics of large scale, diversification of varieties, redundant production factories, flexible production processes, and high-value products. This production mode is called distributed scheduling. The transportation time caused by geographically distributed factories in Distributed Scheduling Problem (DSP) with a series-parallel network plays an important role in the scheduling scheme. To minimize the global makespan over all factories, a two-segment representation has been taken as an encoding scheme while the decoding procedure applies the First Come First Served (FCFS) heuristic rule. A Biogeography-Based Optimization with Modified Migration Operator (BBO-MMO) is then proposed to address the heterogeneous DSP with transportation time between factories at adjacent processing stages, which improves the migration operator by modifying the immigration rate according to processing time and transportation time. A cosine migration model has been adopted to enhance the ability of BBO-MMO to break through local optimum. BBO-MMO is compared with the Improved Memetic Algorithm (IMA), and several groups of examples with various parameters have been generated to test the performance of BBO-MMO. The results show that the proposed BBO-MMO can effectively solve the large-scale heterogeneous DSP with transportation time.

Q-learning-based multi-objective particle swarm optimization with local search within factories for energy-efficient distributed flow-shop scheduling problem

Q-learning-based multi-objective particle swarm optimization with local search within factories for energy-efficient distributed flow-shop scheduling problem

Multi-Objective Q-Learning-Based Brain Storm Optimization for Integrated Distributed Flow Shop and Distribution Scheduling Problems

In recent years, integrated production and distribution scheduling (IPDS) has become an important subject in supply chain management. However, IPDS considering distributed manufacturing environments is rarely researched. Moreover, reinforcement learning is seldom combined with metaheuristics to deal with IPDS problems. In this work, an integrated distributed flow shop and distribution scheduling problem is studied, and a mathematical model is provided. Owing to the problem’s NP-hard nature, a multi-objective Q-learning-based brain storm optimization is designed to minimize makespan and total weighted earliness and tardiness. In the presented approach, a double-string representation method is utilized, and a dynamic clustering method is developed in the clustering phase. In the generating phase, a global search strategy, a local search strategy, and a simulated annealing strategy are introduced. A Q-learning process is performed to dynamically choose the generation strategy. It consists of four actions defined as the combinations of these strategies, four states described by convergence and uniformity metrics, a reward function, and an improved ε-greedy method. In the selecting phase, a newly defined selection method is adopted. To assess the effectiveness of the proposed approach, a comparison pool consisting of four prevalent metaheuristics and a CPLEX optimizer is applied to conduct numerical experiments and statistical tests. The results suggest that the designed approach outperforms its competitors in acquiring promising solutions when handling the considered problem.

A tabu memory based iterated greedy algorithm for the distributed heterogeneous permutation flowshop scheduling problem with the total tardiness criterion

Distributed scheduling problems have been extensively studied due to their critical roles in industrial applications. Most research focuses on identical distributed factories and the objective of minimizing the makespan, ignoring the widely existing heterogeneous factories and delivery targets in reality. This paper aims to establish a distributed heterogeneous flowshop scheduling scenario with the objective of minimizing total tardiness (DHPFSP-t), and solve it using an improved iterative greedy algorithm. A mixed-integer programming model and several problem-specific properties are proposed for this novel scheduling scenario. Based on the distributed heterogeneous characteristics of the problem, four constructive algorithms are established to quickly generate initial solutions. Among them, the better solution is selected as the initial solution of the iterative greedy algorithm. To enhance the performance of the iterative greedy algorithm, the concept of tabu memory is incorporated and novel destruction and local search processes are devised. Thorough experiments are conducted to verify the effectiveness of the mixed-integer programming model of the scenario, the constructive heuristics and the improved iterative greedy algorithm. The result confirms the validity of the proposed model and the good performance of the proposed method.

Integrated production scheduling and vehicle routing problem with energy efficient strategies: Mathematical formulation and metaheuristic algorithms

This paper addresses integrated production and distribution scheduling problem in which orders/jobs are undergone a single operation on any one of the identical machines in parallel and upon the completion of the production they are distributed to destined customers by limited number of vehicles. Customers located in dispersed regions place their orders with predetermined demand size and time windows. On production side, machines operate under discrete speed modes, low of which requires less energy cost or vice versa. On distribution side, energy consumed by a vehicle varies depending on the size of load on it. Therefore, objective is minimizing the sum of the weighted cost emanating from early and tardy deliveries plus production and distribution costs. Operational decisions for (i) production are to determine the allocation of jobs to the machines and sequence of jobs on any machine as well as speed mode of each machine for a particular job. As for (ii) distribution: We need to decide vehicle assignment to specific subset of consolidated jobs and the sequence of customer visitation for each vehicle. We develop a formulation for the problem at hand involving parallel machine scheduling and vehicle routing to obtain solutions to optimality. Not surprisingly, however, CPLEX only provides optimum solution for all instances with customer number up to and 6, for which reason we present two metaheuristics, namely Memetic Algorithm (MA) and Iterated Local Search (ILS) for practical sized instances. Computational results indicate that ILS yields better solutions in shorter times as compared to its counterpart.