A hybrid artificial bee colony algorithm for the job shop scheduling problem

The job shop scheduling problem (JSSP) has attracted much attention in the field of both information sciences and operations research. In terms of the objective function, most existing research has been focused on the makespan criterion (i.e., minimizing the overall completion time). However, for contemporary manufacturing firms, the due date related performance is usually more important because it is crucial for maintaining a high service reputation. Therefore, in this study we aim at minimizing the total weighted tardiness in JSSP. Considering the high complexity, a novel artificial bee colony (ABC) algorithm is proposed for solving the problem. A neighborhood property of the problem is discovered, and then a tree search algorithm is devised to enhance the exploitation capability of ABC. According to extensive computational tests, the proposed approach is efficient in solving the job shop scheduling problem with total weighted tardiness criterion.     

A new approach to job shop scheduling problems with due date constraints considering operation subcontracts

We consider a kind of job shop scheduling problems with due-date constraints, where temporal relaxation of machine capacity constraint is possible through subcontracts. In practice, this kind of problem is frequently found in manufacturing industries where outsourcing of manufacturing operation is possible through subcontract. We present a heuristic algorithm that addresses the problem by solving a series of smaller subproblems to optimality. For the sake of efficiency, the algorithm repeatedly executes in two steps—(1) improving the sequence of operations and (2) picking out the operations to be subcontracted—on bottleneck machines. Experiments are conducted for example problems, and the result of the experiment confirms the viability of the suggested algorithm.     

Two-machine flow shop scheduling of polyurethane foam production

This paper studies a two-machine flow shop scheduling problem with a supporting precedence relation. The model originates from a real production context of a chemical factory that produces foam-rubber products. We extend the traditional two-machine flow shop by dividing the operations into two categories: supporting tasks and regular jobs. In the model, several different compositions of foam rubber can be mixed at the foam blooming stage, and products are processed at the manufacturing stage. Each job (product) on the second machine cannot start until its supporting tasks (parts) on the first machine are all finished and the second machine is not occupied. The objective is to find a schedule that minimizes the total job completion time. The studied problem is strongly NP-hard. In this paper, we propose a branch-and-bound algorithm incorporating a lower bound and two dominance rules. We also design a simple heuristic and an iterated local search (ILS) algorithm to derive approximate solutions. The performances of the proposed algorithms are examined through computational experiments.     

A simple and effective evolutionary algorithm for multiobjective flexible job shop scheduling

This paper addresses the multiobjective flexible job shop scheduling problem (MOFJSP) regarding minimizing the makespan, total workload, and maximum workload. The problem is solved in a Pareto manner, whose goal is to seek for the set of Pareto optimal solutions. We propose a multiobjective evolutionary algorithm, which utilizes effective genetic operators and maintains population diversity carefully. A main feature of the proposed algorithm is its simplicity—it needs only two parameters. Performance of our algorithm is compared with seven state-of-the-art algorithms on fifteen popular benchmark instances. Only our algorithm can find 70% or more non-dominated solutions for every instance.     

Flexible job shop scheduling with due window—a two-pheromone ant colony approach

Recently, the companies reduce the manufacturing costs and increase capacity efficiency in the competitive environment. Therefore, to balance workstation loading, the hybrid production system is necessary, so that, the flexible job shop system is the most common production system, and there are parallel machines in each workstation. In this study, the due window and the sequential dependent setup time of jobs are considered. To satisfy the customers’ requirement, and reduce the cost of the storage costs at the same time, the sum of the earliness and tardiness costs is the objective. In this study, to improve the traditional ant colony system, we developed the two pheromone ant colony optimization (2PH-ACO) to approach the flexible job shop scheduling problem. Computational results indicate that 2PH-ACO performs better than ACO in terms of sum of earliness and tardiness time.     

Johnson's algorithm: A key to solve optimally or approximately flow shop scheduling problems with unavailability periods

Johnson's algorithm (JA) is perhaps the most classical algorithm in the scheduling area. JA gives the optimal solution to the two machine flow shop to minimize the makespan in polynomial time. Researchers have tried to extend this notorious result to obtain polynomial time algorithms for more general cases. Such importance motivated us to devote this paper to JA applied to three flow shop problems with unavailability periods to minimize the makespan. First we focus on the optimality condition of JA. Then we propose a modification of JA. After we calculate new performances of JA as a heuristic. Last we deal with an extension of JA.     

流水工序调度与生产效率的关系模型分析

提出一种基于粒子群算法的流水工序调度任务优化模型。利用流水工序调度任务的特点得到流水工序时间约束条件,利用粒子群算法的原理建立流水工序调度任务优化模型,利用粒子群算法对模型进行求解。仿真实验表明,利用该算法能够得到流水工序调度问题的最优解,提高生产效率。     

A hybrid approach based on the variable neighborhood search and particle swarm optimization for parallel machine scheduling problems—A case study for solar cell industry

This paper studies a solar cell industry scheduling problem which is similar to the traditional hybrid flow shop scheduling (HFS). In a typical HFS with parallel machines problem, the allocation of machine resources for each order should be scheduled in advance and then the optimal multiprocessor task scheduling in each stage could be determined. However, the challenge in solar cell manufacturing is the number of machines can be dynamically adjusted to complete the job within the shortest possible time. Therefore, the paper addresses a multi-stage HFS scheduling problem with characteristics of parallel processing, dedicated machines, sequence-independent setup time, and sequence-dependent setup time. The objective is to schedule the job production sequence, number of sublots, and dynamically allocate sublots to parallel machines such that the makespan time is minimized. The problem is formulated as a mixed integer linear programming (MILP) model. A hybrid approach based on the variable neighborhood search and particle swarm optimization (VNPSO) is developed to obtain the near-optimal solution. Preliminary computational study indicates that the developed VNPSO not only provides good quality solutions within a reasonable amount of time but also outperforms the classic branch and bound method and the current industry heuristic practiced by the case company.     

A Pareto approach to multi-objective flexible job-shop scheduling problem using particle swarm optimization and local search

The job-shop scheduling problem is one of the most arduous combinatorial optimization problems. Flexible job-shop problem is an extension of the job-shop problem that allows an operation to be processed by any machine from a given set along different routes. This paper present a new approach based on a hybridization of the particle swarm and local search algorithm to solve the multi-objective flexible job-shop scheduling problem. The particle swarm optimization is a highly efficient and a new evolutionary computation technique inspired by birds’ flight and communication behaviors. The multi-objective particle swarm algorithm is applied to the flexible job-shop scheduling problem based on priority. Also the presented approach will be evaluated for their efficiency against the results reported for similar algorithms (weighted summation of objectives and Pareto approaches). The results indicate that the proposed algorithm satisfactorily captures the multi-objective flexible job-shop problem and competes well with similar approaches.     

Optimization analysis of supply chain scheduling in mass customization

How to deal with the contradiction between scale production effect and customized demand is the key problem on studying mass customization (MC). When MC is operating in supply chain environment, on one hand, the excellent operating character of the supply chain will give conditions for solving this problem. On the other hand, it will bring out several complicated contradictions and increase the difficulties of the analysis and research on the supply chain operating and scheduling, so it is important to settle the contradictions. Based on our earlier work, the dominant contradictions of the supply chain scheduling in MC and the ways to relieve them are briefly summarized in this paper. A dynamic and multi-objective optimization mathematical model and the appropriate solving algorithm are set up by introducing these relieving methods into the operating process. It is pointed out that the characteristics of the model and algorithm cannot only reflect the unique operating requirements for this special production mode, but also merge with the thought of relieving the dominant contradictions. The feasibility of the model and algorithm in practical application to improve the scheduling efficiency and to settle the key problem mentioned above ultimately gets validated through the analysis of an application case we followed and through the algorithm simulation of a numerical scheduling case.     

Supply chain scheduling and coordination with dual delivery modes and inventory storage cost

We study a two-echelon supply chain scheduling problem in which a manufacturer acquires supplies from an upstream supplier and processes orders from the downstream retailers. The supply chain sells a single short-life product in a single season. We consider the scenario where the manufacturer can only accept some of the orders from the retailers due to its supplier's common production time window and its own two common production and delivery time windows. The upstream supplier processes materials and delivers the semi-finished products to the manufacturer within its time window. Then the manufacturer further processes these products to produce finished products and delivers them to the retailers within its two time windows, where one window is for production and normal delivery, and the other is for production and express delivery. Having to store the materials before processing them, the supplier incurs a storage cost, which depends on the order size and storage time. The manufacturer pays the transportation cost for delivering the finished products to the retailers. Due to double marginalization, the performance of the supply chain is sub-optimal. We model the supply chain problem as a flow shop scheduling problem with multiple common time windows. We derive some dominance properties and establish some theorems that help solve the sequencing problems for the orders and eliminate the idle time among the orders. Based on these results, we develop fast pseudo-polynomial dynamic algorithms to optimally solve the problem. We prove that the problem is NP-hard in the ordinary sense only. We develop two practically relevant and robust methods for the supply chain to achieve optimal profit-making performance through channel coordination.     

Scheduling a single batch processing machine with arbitrary job sizes and incompatible job families

Motivated by a bottleneck operation in a multi-layer ceramic capacitor production line, we study a scheduling problem of batch processing machine in which a number of jobs are processed simultaneously as a batch. The performance measures considered include makespan, total completion time, and total weighted completion time. We first present a new simple integer programming formulation for the problem, and using this formulation, one can easily find optimal solutions for small problems. However, since the problem is NP-hard and the size of a real problem is very large, we propose a number of heuristic algorithms and design a hybrid genetic algorithm to solve practical big-size problems in a reasonable computational time. To verify performance of the algorithms, we compare them with lower bounds for the problems. From the results of these computational experiments the heuristic algorithms including the genetic algorithm show different performances for the three problems.     

Hybrid flow shop scheduling with parallel batching

In this research the problem of parallel batch scheduling in a hybrid flow shop environment with minimizing C_max is studied. In parallel batching it is assumed that machines in some stages are able to process a number of operations simultaneously. Since the problem is NP-hard, three heuristic algorithms are developed to give near optimal solutions. Since this problem has not been studied previously, therefore, a lower bound is developed for evaluating the performance of the proposed heuristics. Several test problems have been solved using these heuristics and results compared. To further enhance the solution quality, a three dimensional genetic algorithm (3DGA) is also developed. Several test problems have been solved using 3DGA and the results indicate its superiority to the other heuristics.     

Metaheuristics for drilling operation scheduling in Taiwan PCB industries

Among all types of production environment, identical parallel machines are frequently used to increase the manufacturing capacity of the drilling operation in Taiwan printed circuit board (PCB) industries. Additionally, multiple but conflicting objectives are usually considered when a manager plans the production scheduling. Compared to the single objective problem, the multiple-objective version no longer looks for an individual optimal solution, but a Pareto front consisting of a set of non-dominated solutions will be needed and established. The manager then can select one of the alternatives from the set. This research aims at employing a variable neighborhood search (VNS) algorithm and a multiple ant colony optimization (MACO) algorithm to solve the identical parallel-machine scheduling problem with two conflicting objectives: makespan and total tardiness. In VNS, two neighborhoods are defined—insert a job to a different position or swap two jobs in the sequence. To save the computational expense, one of the neighborhoods is randomly selected for the target solution which is also arbitrarily chosen from the current Pareto front. In MACO, a two-phase construction procedure where three colonies are employed in each phase is proposed. These two algorithms are tested on a set of real data collected from a leading PCB factory in Taiwan and their performances are compared. The computational results show that VNS outperforms all competing algorithms—SPGA, MOGA, NSGA-II, SPEA-II, and MACO in terms of solution quality and computational time.     

A modified artificial bee colony algorithm for order acceptance in two-machine flow shops

We consider a two-stage make-to-order production system characterized by limited production capacity and tight order due dates. We want to make joint decisions on order acceptance and scheduling to maximize the total net revenue. The problem is computationally intractable. In view of the fact that artificial bee colony algorithm has been shown to be an effective evolutionary algorithm to handle combinatorial optimization problems, we first conduct a pilot study of applying the basic artificial bee colony algorithm to treat our problem. Based on the results of the pilot study and the problem characteristics, we develop a modified artificial bee colony algorithm. The experimental results show that the modified artificial bee colony algorithm is able to generate good solutions for large-scale problem instances.     

A genetic algorithm based heuristic for two machine no-wait flowshop scheduling problems with class setup times that minimizes maximum lateness

Machine scheduling problem has been extensively studied by researchers for many decades in view of its numerous applications on solving practical problems. Due to the complexity of this class of scheduling problems, various approximation solution approaches have been presented in the literature. In this paper, we present a genetic algorithm (GA) based heuristic approach to solve the problem of two machine no-wait flowshop scheduling problems that the setup time on the machines is class dependent, and the objective is to minimize the maximum lateness of the jobs processed. This class of machine scheduling problems has many practical applications in manufacturing industry, such as metal refinery operations, food processing industry and chemical products production processes, in which no interruption between subsequent processes is allowed and the products can be grouped into families. Extensive computation experiments have been conducted to evaluate the effectiveness of the proposed algorithm. Results show the proposed methodology is suitable to be adopted for the development of an efficient scheduling plan for this class of problems in real life application.     

Economic lot and delivery scheduling problem for multi-stage supply chains

The economic lot and delivery scheduling problem for a multi-stage supply chain comprising multiple items is studied in this paper. It is required to develop a synchronized replenishment strategy, and specify the sequence of production and the replenishment cycle time that achieves synchronization through the supply chain at minimum cost. The problem is presented in a novel formulation based on the quadratic assignment representation. The common cycle time and the integer multipliers policies are adopted to accomplish the desired synchronization. The two policies are represented by nonlinear models handled through a hybrid algorithm. The algorithm combines linearization, outer approximation and Benders decomposition techniques. Results of the two policies demonstrate that a cost reduction up to16.3% can be attained by employing the integer multipliers policy instead of the common cycle time. Computational experiments show the efficiency of the new formulation and solution algorithm by reaching the optimal solution for large problem instances in short time.     

Tabu search for minimizing total tardiness in a job shop

This paper presents a tabu search approach to minimize total tardiness for the job shop scheduling problem. The method uses dispatching rules to obtain an initial solution and searches for new solutions in a neighborhood based on the critical paths of the jobs. Diversification and intensification strategies are suggested. For small problems the solutions’ quality is evaluated against optimal solution values and for large problems the tabu search performance is compared with two heuristics proposed in the literature.     

A tabu search approach for cell scheduling problem with makespan criterion

Scheduling problem in a cellular manufacturing system is treated as the group scheduling problem, assuming that intercellular moves can be eliminated by duplicating machines. However, in a typical CMS, duplicating bottleneck machines may be costly and infeasible. This fact limits the applicability of group scheduling. Scheduling problem in the presence of bottleneck machines is termed as cell scheduling. A mixed-integer linear programming model is proposed for the attempted cell scheduling problem and a nested application of tabu search approach is investigated in this paper to solve the problem heuristically. The effectiveness of the proposed nested tabu search (NTS) algorithm is evaluated on 16 problems selected from the literature. Comparison of the results of NTS with SVS-algorithm reveals the effectiveness and efficiency of the proposed algorithm.     

基于遗传禁忌算法的任务分配与调度的研究

任务分配与调度问题是公认的NP问题,为了合理的对备份任务进行分配与调度,使得最短时间内完成备份任务, 提出了基于遗传禁忌搜索的备份任务调度算法。 重点研究了遗传算法和禁忌搜索算法,并针对二者的不足,提出将其两种算法混合,相互取长补短,仿真实验结果和实例应用表明,笔者提出的算法其搜索效率比单一的遗传算法具有较好的效果。