A fixed job scheduling problem with machine-dependent job weights

This study considers the identical parallel machines operational fixed job scheduling problem with machine-dependent job weights. A job is either processed in a fixed interval or is not processed at all. Our aim is to maximise the total weight of the processed jobs. We show that the problem with machine eligibility constraints resides as a special case of this problem. We identify some special polynomially solvable cases and propose a branch-and-bound (BB) algorithm that employs efficient bounding schemes and dominance conditions. Computational experience on large-sized problem examples reveals the satisfactory performance of the BB algorithm.     

A hybrid artificial bee colony algorithm for a flexible job shop scheduling problem with overlapping in operations

Overlapping in operations is an effective technology for productivity improvement in modern manufacturing systems. Thus far, however, there are still rare works on flexible job shop scheduling problems (FJSPs) concerning this strategy. In this paper, we present a hybrid artificial bee colony (hyABC) algorithm to minimise the total flowtime for a FJSP with overlapping in operations. In the proposed hyABC, a dynamic scheme is introduced to fine-tune the search scope adaptively. In view of poor exploitation ability of artificial bee colony algorithm, a modified migrating birds optimisation algorithm (MMBO) is developed and integrated into the search process for better balancing global exploration and local exploitation. In MMBO, a forward share strategy with one-job based crossover is designed to make good use of valuable information from behind solutions. Besides, an improved downward share scheme is adopted to increase diversification of the population, and thus alleviate the premature convergence. Extensive experiments based on benchmark instances with different scales are carried out and comparisons with other recent algorithms identify the effectiveness of the proposed hyABC.     

A parallel-machine scheduling problem with two competing agents

Scheduling with two competing agents has become popular in recent years. Most of the research has focused on single-machine problems. This article considers a parallel-machine problem, the objective of which is to minimize the total completion time of jobs from the first agent given that the maximum tardiness of jobs from the second agent cannot exceed an upper bound. The NP-hardness of this problem is also examined. A genetic algorithm equipped with local search is proposed to search for the near-optimal solution. Computational experiments are conducted to evaluate the proposed genetic algorithm.     

A novel imperialist competitive algorithm for bi-criteria scheduling of the assembly flowshop problem

This paper deals with the two-stage assembly flowshop scheduling problem with minimisation of weighted sum of makespan and mean completion time as the objective. The problem is NP-hard, hence we proposed a meta-heuristic named imperialist competitive algorithm (ICA) to solve it. Since appropriate design of the parameters has a significant impact on the algorithm efficiency, we calibrate the parameters of this algorithm using the Taguchi method. In comparison with the best algorithm proposed previously, the ICA indicates an improvement. The results have been confirmed statistically.     

A branch-and-bound algorithm for a two-stage hybrid flowshop scheduling problem minimizing total tardiness

A two-stage hybrid flowshop-scheduling problem is considered with the objective of minimizing total tardiness of jobs. In the hybrid flowshop, there is one machine at the first stage and multiple identical parallel machines at the second stage. Dominance properties and lower bounds are developed for the problem and a branch-and-bound algorithm is suggested using them. Results of computational experiments show that the suggested algorithm can find optimal solutions for problems with up to 15 jobs in a reasonable amount of central processing unit time.     

Proportionate flowshop scheduling with position-dependent weights

ABSTRACT

This article addresses proportionate flowshop scheduling problems with position-dependent weights wherein the weight is not related to the job but to the position in which the job is scheduled. Common and slack due date assignment models are discussed under a due date assignment framework. The goal is to determine a feasible schedule for all jobs and due dates of all jobs to minimize a total cost function wherein the objective function is of the minsum type. Optimal properties for the problems are proposed, based on which polynomial time algorithms are provided to solve these two problems optimally.     

A new heuristic for the flowshop scheduling problem to minimize makespan and maximum tardiness

This paper presents a new heuristic for solving the flowshop scheduling problem that aims to minimize makespan and maximize tardiness. The algorithm is able to take into account the aforementioned performance measures, finding a set of non-dominated solutions representing the Pareto front. This method is based on the integration of two different techniques: a multi-criteria decision-making method and a constructive heuristic procedure developed for makespan minimization in flowshop scheduling problems. In particular, the technique for order preference by similarity of ideal solution (TOPSIS) algorithm is integrated with the Nawaz–Enscore–Ham (NEH) heuristic to generate a set of potential scheduling solutions. To assess the proposed heuristic's performance, comparison with the best performing multi-objective genetic local search (MOGLS) algorithm proposed in literature is carried out. The test is executed on a large number of random problems characterized by different numbers of machines and jobs. The results show that the new heuristic frequently exceeds the MOGLS results in terms of both non-dominated solutions, set quality and computational time. In particular, the improvement becomes more and more significant as the number of jobs in the problem increases.     

A hybrid flowshop scheduling problem for a cold treating process in seamless steel tube production

Seamless steel tubes often have various categories and specifications, which further require complicated operations in production, especially in the cold treating process (CTP). This paper investigates the scheduling problem using the seamless tube plant of Baoshan Iron and Steel Complex as a study background. By considering the practical production constraints such as sequence-dependent setup times, maintenance schedule, intermediate material buffers, job-machine matches, we formulate the hybrid flowshop scheduling problem with a non-linear mixed integer programming model (NMIP). In addition, our model provides a flexibility to remove the permutation assumption, which is often a limitation in early studies. In order to obtain the solution of the above NMIP problem, a two-stage heuristic algorithm is proposed and it combines a modified genetic algorithm and a local search method. With real production instances, our computation experiments indicate that the proposed algorithm is efficient and it outperforms several other approaches. Industrial implementation also shows that such a scheduling tool brings a cost saving of more than 10% and it substantially reduces the computation time. Our study also illustrates the need of relaxing permutation assumption in such a scheduling problem with complicated operation sequences.     

作业车间调度问题中的协同优化算法

本文采用了多种优化算法 ,针对作业车间问题的特点设计一个比较有效的协同算法 ,解决了算法实现中的几个关键技术问题 ,为提高解决这一问题的效率提供了比较新颖的思路 ,并通过实际计算验证了该方法的可靠性和有效性 ,这一方法可以用于实际车间的调度安排 ,能够提高车间的生产效率。     

A heuristic for scheduling in flowshop and flowline-based manufacturing cell with multi-criteria

The problem of scheduling in flowshop and flowline-based manufacturing cell is considered with the bicriteria of minimizing makespan and total flowtime of jobs, The formulation of the scheduling problems for both the flowshop and the flowline-based manufacturing cell is first discussed. We then present the development of the proposed heuristic for flowshop scheduling. A heuristic preference relation is developed as the basis for the heuristic so that only the potential job interchanges are checked for possible improvement with respect to bicriteria, The proposed heuristic algorithm as well as the existing heuristic are evaluated in a large number of randomly generated large-sized flowshop problems. We also investigate the effectiveness of these heuristics with respect to the objective of minimizing total machine idletime. We then modify the proposed heuristic for scheduling in a cell, and evaluate its performance.     

Solving the n-job 3-stage flexible flowshop scheduling problem using an agent-based approach

In this paper, a general methodology of agent-based manufacturing systems scheduling, incorporating game theoretic analysis of agent cooperation is presented to solve the n-job 3-stage flexible flowshop scheduling problem. The flowshops are flexible in the sense that a job can be processed by any of the identical machines at each stage. Our objective is to schedule a set of n jobs so as to minimize the makespan. We perform error bound analysis using the lower bound estimates developed in the literature as a datum for comparing the agent-based scheduling solutions with other heuristic solutions. The results of the evaluation show that the agent-based scheduling approach outperforms existing heuristics for the majority of the testing problems.     

Parallel flowshop scheduling using Tabu search

Production scheduling problems in manufacturing systems with parallel machine flowshops are discussed. A mathematical programming model for combined part assignment and job scheduling is developed. The objective of solving the scheduling problem is to minimize a weighted sum of production cost and the cost incurred from late product delivery. The solution of the model is NP-hard. To solve the problem efficiently, a heuristic algorithm combining Tabu search and Johnson's method was proposed. Several numerical examples are presented to illustrate the developed model and the algorithm. Computational results from these example problems are very encouraging.     

Makespan minimisation for a parallel machine scheduling problem with preemption and job incompatibility

In this paper, an extension of the graph colouring problem is introduced to model a parallel machine scheduling problem with job incompatibility. To get closer to real-world applications, where the number of machines is limited and jobs have different processing times, each vertex of the graph requires multiple colours and the number of vertices with the same colour is bounded. In addition, several objectives related to scheduling are considered: makespan, number of pre-emptions and summation over the jobs’ throughput times. Different solution methods are proposed, namely, two greedy heuristics, two tabu search methods and an adaptive memory algorithm. The latter uses multiple recombination operators, each one being designed for optimising a subset of objectives. The most appropriate operator is selected dynamically at each iteration, depending on its past performance. Experiments show that the proposed algorithm is effective and robust, while providing high-quality solutions on benchmark instances for the graph multi-colouring problem, a simplification of the considered problem.     

Ant colony optimisation with parameterised search space for the job shop scheduling problem

The job-shop scheduling problem (JSSP) is known to be NP-hard. Due to its complexity, many metaheuristic algorithm approaches have arisen. Ant colony metaheuristic algorithm, lately proposed, has successful application to various combinatorial optimisation problems. In this study, an ant colony optimisation algorithm with parameterised search space is developed for JSSP with an objective of minimising makespan. The problem is modelled as a disjunctive graph where arcs connect only pairs of operations related rather than all operations are connected in pairs to mitigate the increase of the spatial complexity. The proposed algorithm is compared with a multiple colony ant algorithm using 20 benchmark problems. The results show that the proposed algorithm is very accurate by generating 12 optimal solutions out of 20 benchmark problems, and mean relative errors of the proposed and the multiple colony ant algorithms to the optimal solutions are 0.93% and 1.24%, respectively.     

A multi-objective iterated greedy search for flowshop scheduling with makespan and flowtime criteria

In this paper, we tackle the problem of total flowtime and makespan minimisation in a permutation flowshop. For this, we introduce a multi-criteria iterated greedy search algorithm. This algorithm iterates over a multicriteria constructive heuristic approach to yield a set of Pareto-efficient solutions (a posteriori approach). The proposed algorithm is compared against the best-so-far heuristic for the problem under consideration. The comparison shows the proposal to be very efficient for a wide number of multicriteria performance measures. Aside, an extensive computational experience is carried out in order to analyse the different parameters of the algorithm. The analysis shows the algorithm to be robust for most of the considered performance measures.     

A batch splitting method for a job shop scheduling problem in an MRP environment

The job shop scheduling problem has been a major target for many researchers. Unfortunately though, most of the previous research was based on assumptions that are different from the real manufacturing environment. Among those distorted assumptions, two assumptions about set-up time and job composition can greatly influence the performance of a schedule. First, most of the past studies ignored the impact of the before-arrival set-up time. If we know the sequence of operations in advance, we can obtain an improved schedule by preparing the setup before a job arrives. Secondly, most of the past studies assumed that a job consists of only a single part, that is a batch of size one. However, if we assume that a job consists of a batch size greater than one, as in many real manufacturing environments, then we can obtain an improved schedule because we can fill up the idle times of machines with jobs which have smaller processing times by splitting the original batches. However, the number of job orders may then increase due to the split, and the size of the scheduling problem would become too large to be solved in a practical time limit. Consequently, there may be an optimum batch size considering trade-off between better solution and tractability. The current study is the result of an attempt to find an acceptable solution when the production requirement from a MRP system for a planning period exceeds the capacity of a production system. We try to get an improved schedule by splitting the original batch into smaller batches, and consider setting up a machine before the actual arrival of jobs to that machine. Thereby we can meet the due date requirement without resorting to rescheduling of the master production schedule. For the given batch, we disaggregate it according to the algorithm we are proposing. A so-called 'modified shifting bottleneck procedure' is then applied to solve the job shop scheduling problem with a before-arrival family set-up time considering release date, transportation time and due date. The study also shows that we can adapt to unexpected dynamic events more elegantly by allowing the splitting of batches.     

A heuristic model for dynamic flexible job shop scheduling problem considering variable processing times

In real scheduling problems, unexpected changes may occur frequently such as changes in task features. These changes cause deviation from primary scheduling. In this article, a heuristic model, inspired from Artificial Bee Colony algorithm, is proposed for a dynamic flexible job-shop scheduling (DFJSP) problem. This problem consists of n jobs that should be processed by m machines and the processing time of jobs deviates from estimated times. The objective is near-optimal scheduling after any change in tasks in order to minimise the maximal completion time (Makespan). In the proposed model, first, scheduling is done according to the estimated processing times and then re-scheduling is performed after determining the exact ones considering machine set-up. In order to evaluate the performance of the proposed model, some numerical experiments are designed in small, medium and large sizes in different levels of changes in processing times and statistical results illustrate the efficiency of the proposed algorithm.     

Integrated production scheduling and vehicle routing problem with job splitting and delivery time windows

In this paper, we study a production scheduling and vehicle routing problem with job splitting and delivery time windows in a company working in the metal packaging industry. In this problem, a set of jobs has to be processed on unrelated parallel machines with job splitting and sequence-dependent setup time (cost). Then the finished products are delivered in batches to several customers with heterogeneous vehicles, subject to delivery time windows. The objective of production is to minimize the total setup cost and the objective of distribution is to minimize the transportation cost. We propose mathematical models for decentralized scheduling problems, where a production schedule and a distribution plan are built consecutively. We develop a two-phase iterative heuristic to solve the integrated scheduling problem. We evaluate the benefits of coordination through numerical experiments.     

A hybrid genetic algorithm and tabu search for a multi-objective dynamic job shop scheduling problem

In most real manufacturing environments, schedules are usually inevitable with the presence of various unexpected disruptions. In this paper, a rescheduling method based on the hybrid genetic algorithm and tabu search is introduced to address the dynamic job shop scheduling problem with random job arrivals and machine breakdowns. Because the real-time events are difficult to express and take into account in the mathematical model, a simulator is proposed to tackle the complexity of the problem. A hybrid policy is selected to deal with the dynamic feature of the problem. Two objectives, which are the schedule efficiency and the schedule stability, are considered simultaneously to improve the robustness and the performance of the schedule system. Numerical experiments have been designed to test and evaluate the performance of the proposed method. This proposed method has been compared with some common dispatching rules and meta-heuristic algorithms that have been widely used in the literature. The experimental results illustrate that the proposed method is very effective in various shop-floor conditions.