Distributed Scheduling Problem Research Articles

A multi-objective discrete differential evolution algorithm for energy-efficient distributed blocking flow shop scheduling problem

ABSTRACT The energy problem in green manufacturing has attracted enormous attention from researchers and practitioners in the manufacturing domain with the global energy crisis and the aggravation of environmental pollution. The distributed blocking flow shop scheduling problem (DBFSP) has considerable application scenarios in connection with its widespread application in the industry under the background of intelligent manufacturing. A multi-objective discrete differential evolution (MODE) algorithm is proposed to solve the energy-efficient distributed blocking flow shop scheduling problem (EEDBFSP) with the objectives of the makespan and total energy consumption (TEC) in this paper. The cooperative initialisation strategy is proposed to generate the initial population of the EEDBFSP. The mutation, crossover, and selection operators are redesigned to enable the MODE algorithm as applied to discrete space. A local search strategy based on the knowledge of five operators is introduced to enhance the exploitation capability of the MODE algorithm in the EEDBFSP. The non-critical path energy-efficient strategy is proposed to reduce energy consumption according to the specific constraints in the EEDBFSP. The effectiveness of each strategy in the MODE algorithm is verified and compared with the state-of-the-art algorithms. The numerical results demonstrate that the MODE algorithm is the efficient optimiser for solving the EEDBFSP.

An improved iterative greedy athm for energy-efficient distributed assembly no-wait flow-shop scheduling problem

An improved iterative greedy athm for energy-efficient distributed assembly no-wait flow-shop scheduling problem

N-list-enhanced heuristic for distributed three-stage assembly permutation flow shop scheduling

AbstractSystem-wide optimization of distributed manufacturing operations enables process improvement beyond the standalone and individual optimality norms. This study addresses the production planning of a distributed manufacturing system consisting of three stages: production of parts (subcomponents), assembly of components in Original Equipment Manufacturer (OEM) factories, and final assembly of products at the product manufacturer’s factory. Distributed Three Stage Assembly Permutation Flowshop Scheduling Problems (DTrSAPFSP) models this operational situation; it is the most recent development in the literature of distributed scheduling problems, which has seen very limited development for possible industrial applications. This research introduces a highly efficient constructive heuristic to contribute to the literature on DTrSAPFSP. Numerical experiments considering a comprehensive set of operational parameters are undertaken to evaluate the performance of the benchmark algorithms. It is shown that the N-list-enhanced Constructive Heuristic algorithm performs significantly better than the current best-performing algorithm and three new metaheuristics in terms of both solution quality and computational time. It can, therefore, be considered a competitive benchmark for future studies on distributed production scheduling and computing.

Multi-Objective brain storm optimization for integrated scheduling of distributed flow shop and distribution with maximal processing quality and minimal total weighted earliness and tardiness

At present, integrated production and distribution scheduling problems have obtained amounts of concern due to their essential roles in enhancing the supply chain performance. Along with the economic globalization, many manufacturing enterprises adopt distributed production structures to reduce operation costs and improve service quality. Besides, processing quality becomes a fundamental standard for manufacturing enterprises to keep their competitiveness. In the distributed production and distribution process, the jobs are first produced on machines in different factories at the production stage, and then shipped to their associated customers using vehicles at the distribution stage. To realize an overall optimization of these two stages, this work investigates a multi-objective integrated distributed flow shop and distribution scheduling problem to reach maximal processing quality and minimal total weighted earliness and tardiness. To define it mathematically, a mixed integer programming model is established. Given the problem’s NP-hard nature, a multi-objective brain storm optimization algorithm is addressed to settle it. Through performing numerical experiments and statistical tests on some test instances, the effectiveness of the developed method is demonstrated..

A cooperative memetic algorithm for energy-aware distributed welding shop scheduling problem

Facing globalization trends and sustainable industrial development, energy-aware distributed manufacturing has become an emerging topic. Meanwhile, welding is a kind of indispensable processing in the development of manufacturing and its effective scheduling can improve production efficiency and reduce energy consumption. However, it is difficult to solve the energy-aware distributed welding shop scheduling problem (EADWSP) due to the characteristics of large scale and multiple objectives. Thus, this paper presents a mathematical model and a cooperative memetic algorithm (CMA) to addresses the EADWSP with minimization both makespan and total energy consumption. To improve the quality and diversity of initial population, a hybrid initialization is developed with a modified NEH based heuristic. Via taking full advantage of historical information, a cooperative search based on feedback is designed and a cooperative selection strategy is employed to balance the exploration and exploitation. In addition, multiple problem-specific operators are presented and a local intensification with Q-learning is designed to enhance exploitation capability. Numerical experiments are carried out and the results demonstrate the effectiveness of the above specific designs. The comparisons to the existing algorithms show superiority of the proposed CMA. Moreover, the application to a real-life case also verifies the effectiveness and practicability in solving the EADWSP.

Multi-stage hybrid evolutionary algorithm for multiobjective distributed fuzzy flow-shop scheduling problem.

In the current global cooperative production mode, the distributed fuzzy flow-shop scheduling problem (DFFSP) has attracted much attention because it takes the uncertain factors in the actual flow-shop scheduling problem into account. This paper investigates a multi-stage hybrid evolutionary algorithm with sequence difference-based differential evolution (MSHEA-SDDE) for the minimization of fuzzy completion time and fuzzy total flow time. MSHEA-SDDE balances the convergence and distribution performance of the algorithm at different stages. In the first stage, the hybrid sampling strategy makes the population rapidly converge toward the Pareto front (PF) in multiple directions. In the second stage, the sequence difference-based differential evolution (SDDE) is used to speed up the convergence speed to improve the convergence performance. In the last stage, the evolutional direction of SDDE is changed to guide individuals to search the local area of the PF, thereby further improving the convergence and distribution performance. The results of experiments show that the performance of MSHEA-SDDE is superior to the classical comparison algorithms in terms of solving the DFFSP.

Improved Meta-Heuristics for Solving Distributed Lot-Streaming Permutation Flow Shop Scheduling Problems

This paper addresses a distributed lot-streaming permutation flow shop scheduling problem that has various applications in real-life manufacturing systems. We aim to optimally assign jobs to multiple distributed factories and sequence them to minimize the maximum completion time (Makespan). A mathematic model is first developed to describe the considered problem. Then, five meta-heuristics are executed to solve it, including particle swarm optimization, genetic algorithm, harmony search, artificial bee colony, and Jaya algorithm. To improve the performance of these meta-heuristics, we employ Nawaz-Enscore-Ham (NEH) heuristic to initialize populations and propose improved strategies based on the problem’s feature. Finally, experiments are carried out based on 120 instances. The performance of improved strategies is verified. Comparisons and discussions show that the artificial bee colony algorithm with improved strategies has the best competitiveness for solving the proposed problem with makespan criteria. Note to Practitioners—In contemporary manufacturing industry, the traditional single-factory environment is being replaced by a distributed multi-factory environment, as a distributed pattern can effectively improve the production efficiency through the reasonable resource allocation strategies. The distributed lot-streaming permutation flow shop scheduling problem in such a pattern is of significance to practitioners. Although intelligent optimization can provide an effective tool to solve such problems, most of the algorithms are parameter-sensitive. A challenge for engineers is parameter selection, which greatly impacts the algorithm performance. To ensure the robustness of the algorithms, we develop five improved meta-heuristics by employing some strategies. Furthermore, parameter setting test is carried out to select the appropriate parameter values. As a result, the proposed algorithms can obtain resource allocation schemes with high-quality. It is shown that the artificial bee colony algorithm with improved strategies outperforms other algorithms well. The proposed methodology can be readily applied to real distributed scheduling problems.

A New Mathematical Model for the Integration of Production and Distribution in Mobile Centers

In today's competitive environment, having the best sequence of operations for production and distribution activities is a basic need for survival. As a result, one of the major challenges in fixed supply chain systems is unnecessary transportation costs and the inability to meet customer demand as quickly as possible. In order to meet these challenges, factories and mobile equipment have been considered in this study, and have recently been used in several industries, including pharmaceutical, chemical, and dairy. In the course of this study, a novel mathematical model was put forward for an integrated production and distribution scheduling problem taking into account some real-world features, focusing on reducing customer waiting time and also reducing production costs. A small-scale problem was resolved to check the model’s accuracy. The accuracy of the model is affirmed given the example and its solution acquired from GAMS software. The results of the study prove the effectiveness of this model in reducing customer waiting time and production costs and also demonstrate that the model has the capacity to be utilized by all organizations that produce and distribute perishable products, including dairy and pharmaceutical products, chemical compounds and masks during the Coronavirus pandemic.

A network memetic algorithm for energy and labor-aware distributed heterogeneous hybrid flow shop scheduling problem

With the penetration of decentralization into factories, the production scheduling among non-identical factories has emerged as a hot issue for industrial demand response. However, little attention has been paid to differentiated production resources for distributed production scheduling. This paper studies an energy and labor-aware distributed heterogeneous hybrid flow shop scheduling problem (ELDHHFSP). The heterogeneous factors, i.e. different numbers and capabilities of machines, time-of-use electricity price, labor shift, salary and bonus of workers, are included in the ELDHHFSP. The mixed-integer linear programming (MILP) model of ELDHHFSP is presented with the objectives of minimization of total tardiness, total production cost, and total carbon emission. A network memetic algorithm (NMA) is proposed for the ELDHHFSP from the solution and strategy space. The NMA mainly includes two critical parts, i.e., probability network model and learning-based local search, corresponding to global and local search. A probability network model is established to guide the search towards the optimal regions from different directions by employing multiple objective weight vectors. The sampling part samples from the probability matrix of each node in the network to construct new solutions. The learning-based local search integrates several local search operators and a reward learning mechanism is designed to find suitable local search operators when evolutionary. A comprehensive experiment on extensive testing instances is conducted to investigate the effectiveness of the probability network and local-learning strategy. The comparison of NMA and other related algorithms shows the effectiveness and efficiency of NMA.

Integrated scheduling of distributed production and distribution in group manufacturing with uncertain travel time

This paper presents a novel integrated distributed production and distribution scheduling problem in group manufacturing with uncertain travel time (IDPDSP-GM-UTT), in which products are firstly produced in several distributed hybrid flow shops and then delivered to several retailers in batches. The proposed model considers both geographical dispersion of multi-factories and variable travel time between factories and retailers caused by time-varying dynamics of road network, which describes the production environment more authentic. Additionally, a mathematical model is developed to find the optimal quantity of raw material, delivery plan, and punishment of earliness and tardiness with the objective of minimizing total costs. Then, an improved genetic algorithm with two-stage heuristic mutation scheduling strategy and tabu search for local optimization (GA-2HMS&TS) is designed to solve the proposed model. To verify the performances of the proposed method, several experiments by adopting test experimental examples with different scales are performed. The computational results exhibit that the GA-2HMS&TS not only significantly reduces the total cost of production and distribution, but also outperforms all of its rivals. In addition, the robustness of the proposed models is also analyzed with regard to the different road conditions.

Two-stage knowledge-driven evolutionary algorithm for distributed green flexible job shop scheduling with type-2 fuzzy processing time

• The distributed green FJSP with type-2 fuzzy processing time is considered. • A two-stage knowledge-driven evolutionary algorithm is proposed. • An efficient energy-saving strategy is designed. • The results indicate the superior performance of our approach. This study is investigated on multi-objective distributed green flexible job shop scheduling problem with type-2 fuzzy processing time. Minimizing makespan and total energy consumption simultaneously is considered. A mixed integer linearity programming model is developed to describe the considered problem. To solve such a hard problem, a two-stage knowledge-driven evolutionary algorithm is proposed (TS-KEA) which divided evolutionary process into two stage. On the first stage, an initial strategy mixed with five problem-specific heuristics is applied to provide a high-quality initial population. Next, a Pareto-based multi-objective evolutionary algorithm is designed for quickly converging to the high quality solutions. Then, a full-active scheduling strategy is designed to reduce total energy consumption. On the second stage, five problem-specific neighborhood structures are proposed to search the non-dominated solutions around the elite solutions. Finally, to evaluate the performance of the proposed algorithm, a number of experiments are adopted on a benchmark with 20 instances. The experiment results show that the proposed TS-KEA can efficiently solve this problem.

Modeling and solving the waste valorization production and distribution scheduling problem

Bio-based waste valorization is one of the current trends in municipal waste management. It decreases the amount of waste to be disposed of, reduces the sourcing of limited chemical compounds used in fertilizer production, and promotes a circular economy perspective vital in big cities. However, modeling and optimizing a biorefinery plant’s operations is challenging and requires innovative approaches and solutions. In this paper, we model and solve the integrated production and distribution scheduling problem faced by an industrial partner. We propose three models for the waste valorization production and distribution scheduling problem: a time-discretized integer linear program, and two mixed-integer linear program with continuous timing variables. Moreover, several powerful and problem-specific valid inequalities and variable reduction procedures are proposed. We study some variants of the problem and propose a simple heuristic algorithm that mimics the logic of a decision maker. Through a series of computational experiments, we determine how critical operational parameters affect the performance of the system and demonstrate how significant improvements can be achieved in our industrial partner’s biorefinery plant.

A reinforcement learning-driven brain storm optimisation algorithm for multi-objective energy-efficient distributed assembly no-wait flow shop scheduling problem

A reinforcement learning-driven brain storm optimisation idea (RLBSO) is proposed in this paper to solve multi-objective energy-efficient distributed assembly no-wait flow shop scheduling problem. The objectives of the problem include minimising the maximum assembly completion time (), minimising the total energy consumption (TEC) and achieving resource allocation balanced . Four operations, which are critical factory insert, critical factory swap, critical factory insert to other factories, critical factory swap with other factories, are designed to optimise the objective of maximum assembly completion time. Q-learning mechanism is utilised to guide the selection of operations to avoid blind search in the iteration process. The learning mechanism based on clustering mechanism in brain storm optimisation algorithm is utilised to assign products to factories in the objective space according to the processing time of products to balance the resources allocation. The speed of operations on non-critical path is slowed down to reduce TEC regarded with the characteristics of no-wait flow shop scheduling problem. The experimental results under 810 large-scale instances by RLBSO show that the RLBSO outperforms the comparison algorithm for addressing the problem.

Solving a multi-objective distributed scheduling problem for building material equipment group enterprises by measuring quality indicator with a product gene evaluation approach

In building material equipment group enterprises (BME-GEs), unstable manufacturing quality and insufficient delivery capacity are the common problems, where their on-time delivery capacity is greatly affected by manufacturing quality. Therefore, improving manufacturing quality control ability is the key approach to improve their core competitiveness. The manufacturing quality of a product is determined by the attributes of multiple manufacturing resources, therefore, optimizing the utilization of manufacturing resources can improve product manufacturing quality and reduce quality problems in BME-GEs, so as to reduce delivery delay caused by quality problems. Aiming at achieving the goal mentioned above, we were inspired by biological genetic engineering, and a product gene recombination mechanism was analyzed and designed based on our existing studies on product gene. And a multi-objective scheduling model considering minimizing total costs and makespan while maximizing quality for the distributed collaborative manufacturing mode of BME-GEs was established, where a comprehensive measurement method of quality according to our research on product gene evaluation method was presented. To deal with the multi-objective problem, the Fuzzy Analytic Hierarchy Process (FAHP) was applied to determine the weight of each objective. To solve the above model, a hybrid genetic algorithm and discrete particle swarm optimization (H-GA-DPSO) based on multi-level encoding method was designed, which optimized the operation-sequencing, job-to-cell assignment and operation-to-machine assignment by considering the frequent operation outsourcing in BME-GEs. To verify the performance of the above model and algorithm, several comparison experiments including tabu search (TS), GA, DPSO and H-GA-DPSO were presented. The results indicate that the proposed model and algorithm can effectively solve the optimization problem of manufacturing resources in BME-GEs, and compared with the three single algorithms, the hybrid algorithm has significant advantages on optimization ability as well as comprehensive performance for solving the problem studied in this research.

A hash map-based memetic algorithm for the distributed permutation flowshop scheduling problem with preventive maintenance to minimize total flowtime

Distributed scheduling problems have been an active research topic due to their close connection with the multifactory production environment in today’s decentralized economy. In this paper, the distributed permutation flowshop scheduling problem with preventive maintenance is studied with the goal of minimizing the total flowtime. A mathematical model and a hash map-based algorithm are presented to tackle the problem. The Nawaz–Enscore–Ham heuristic is improved and incorporated with the distributed Liu–Reeves heuristic to provide a promising initial solution in a finite number of steps. The proposed algorithm employs the data structure of the hash map to store all the candidate solutions in the form of key–value pairs. The selection, crossover, and mutation operators are also modified to expand the scope of exploration in the discrete domain. The local search hybridizes the job insertion operator and the job swap operator to further improve the obtained offspring solutions and utilizes the characteristic of the population hash map to reduce the efforts of solution evaluations. The candidate solution obtained by the local search is hashed by a rotating hash method and then placed at the node with the corresponding hash code. A series of experiments were conducted to verify the effectiveness of the hybrid local search operators and hash map strategy. Computational results indicate that the multiple strategies not only help to escape from the local optimization but also improve the computational efficiency. When compared with 10 state-of-the-art algorithms, the proposed algorithm generates an average relative percentage deviation of 0.134%, which is significant improvement.

Rescheduling of Distributed Manufacturing System with Machine Breakdowns

This study attempts to explore the dynamic scheduling problem from the perspective of operational research optimization. The goal is to propose a rescheduling framework for solving distributed manufacturing systems that consider random machine breakdowns as the production disruption. We establish a mathematical model that can better describe the scheduling of the distributed blocking flowshop. To realize the dynamic scheduling, we adopt an “event-driven” policy and propose a two-stage “predictive-reactive” method consisting of two steps: initial solution pre-generation and rescheduling. In the first stage, a global initial schedule is generated and considers only the deterministic problem, i.e., optimizing the maximum completion time of static distributed blocking flowshop scheduling problems. In the second stage, that is, after the breakdown occurs, the rescheduling mechanism is triggered to seek a new schedule so that both maximum completion time and the stability measure of the system can be optimized. At the breakdown node, the operations of each job are classified and a hybrid rescheduling strategy consisting of “right-shift repair + local reorder” is performed. For local reorder, we designed a discrete memetic algorithm, which embeds the differential evolution concept in its search framework. To test the effectiveness of DMA, comparisons with mainstream algorithms are conducted on instances with different scales. The statistical results show that the ARPDs obtained from DMA are improved by 88%.

A Non-Cooperative Game-Based Distributed Beam Scheduling Framework for 5G Millimeter-Wave Cellular Networks

This paper studies the problem of distributed beam scheduling for 5G millimeter-Wave (mm-Wave) cellular networks where base stations (BSs) belonging to different operators share the same spectrum without centralized coordination among them. Our goal is to design efficient distributed scheduling algorithms to maximize the network utility, which is a function of the achieved throughput by the user equipment (UEs), subject to the average and instantaneous power consumption constraints of the BSs. We propose a Media Access Control (MAC) and a power allocation/adaptation mechanism utilizing the Lyapunov stochastic optimization framework and non-cooperative games. In particular, we first decompose the original utility maximization problem into two sub-optimization problems for each time frame, which are a convex optimization problem and a non-convex optimization problem, respectively. By formulating the distributed scheduling problem as a non-cooperative game where each BS is a player attempting to optimize its own utility, we provide a distributed solution to the non-convex sub-optimization problem via finding the Nash Equilibrium (NE) of the game whose weights are determined optimally by the Lyapunov optimization framework. Finally, we conduct simulation under various network settings to show the effectiveness of the proposed game-based beam scheduling algorithm in comparison to that of several reference schemes.

Anarchy in the UJ: Coordination mechanisms for minimizing the number of late jobs

We consider the distributed scheduling problem on parallel machines with the central objective of maximizing the number of on-time jobs. Jobs are self-interested utility-maximizers that can choose the machines they are processed on and are exclusively interested in reducing their own private objective function. Each machine processes the jobs according to a local policy. We discuss Nash equilibria in the resulting schedules and perform a thorough analysis of the resulting (absolute) prices of anarchy for various parallel machine environments, utilities of the agents, and local policies of the machines. We show that local policies that are based on simple sorting-based procedures like shortest processing time first (SPT) and earliest due date first (EDD) lead to big losses in welfare compared to the global optimum. However, when employing Moore-Hodgson’s algorithm as a local policy, we can prove a price of anarchy of (2m−1)/m for identical machines and a price of anarchy of 2 for related and unrelated parallel machines. Moreover, we show how these results can be used to prove approximation ratios for greedy scheduling algorithms. This paper is the first to prove approximation ratios for two greedy scheduling procedures, turning them from simple heuristics into actual approximation ratios with a provable approximation ratio.

Supply chain-oriented two-stage assembly flowshops with sequence-dependent setup times

Supply chain-oriented scheduling problems have received recent recognition among production research scholars due to their ability in integrating production planning and control across manufacturing systems. This study contributes to the literature of the distributed scheduling problems developing an original Mixed-Integer Linear Programming (MILP) formulation to the Distributed Two-Stage Assembly Flowshop Scheduling Problem with Sequence-Dependent Setup Times (DTSAFSP-SDSTs). Besides, the Iterated Greedy algorithm is extended to effectively solve this relatively complex production scheduling situation considering the makespan as the optimization criterion. Extensive numerical tests and statistical analyses are conducted to evaluate the effectiveness of the developed solution algorithm. Results showed that the Improved Iterated Greedy (IIG) algorithm yields the best solution in nearly all of the large-scale instances. The statistical test of significance confirmed that IIG is superior to the current-best-performing algorithm. This study contributes to the transition from standalone optimization to integrated production planning and control of distributed manufacturing systems.

Modelling and optimization of integrated distributed flow shop scheduling and distribution problems with time windows

Production and distribution are two essential activities in supply chain management. Currently, integrated production and distribution problems receive much attention because decision-makers devote to improving the operation efficiency of both stages and try to achieve an optimal solution. This work proposes an integrated distributed production and distribution problem with consideration of time windows, in which a set of jobs (i.e., customer orders) needs to be assigned among factories and the jobs are processed on flow shop environments at their associated factories. Then, the completed jobs are delivered by capacitated vehicles to customers in different regions while satisfying given time windows as much as possible. Accordingly, to optimally solve the proposed problem, a mixed integer programming model with minimizing total weighted earliness and tardiness has been established. For the optimization task, an enhanced brain storm optimization algorithm with some particular strategies is designed to handle the considered problem. To assess the performance of the proposed optimization method, several experiments by adopting a set of benchmark test problems are performed, and state-of-the-art optimizers are chosen for comparisons. The obtained optimization results exhibit that the designed algorithm significantly outperforms its rivals and can be considered as an excellent optimizer for solving the studied problem. Besides, compared with the CPLEX solver, the designed optimizer also performs much better for solving large-size problems.