Minimizing makespan on parallel machines with batch arrivals

Most studies in the scheduling literature assume that jobs arrive at time zero, while some studies assume that jobs arrive individually at non-zero times. However, both assumptions may not be valid in practice because jobs usually arrive in batches. In this article, a scheduling model for an identical parallel machine problem with batch arrivals is formulated. Because of the NP-hardness of the problem, a heuristic based on a simplified version of lexicographical search is proposed. To verify the heuristic, two lower bounding schemes are developed, where one lower bound is tight, and the list scheduling heuristic is compared. Extensive computational experiments demonstrate that the proposed heuristic is quite efficient in obtaining near optimal solution with an average error of less than 1.58%. The percentage improvement (from the lower bound) of the heuristic solution on the solution by the list scheduling is as large as 31.68.     

Loading and sequencing heuristics for job scheduling on two unrelated parallel machines with long,sequence-dependent set-up times

The purpose of this paper is to develop and test intelligible heuristics for the scheduling of production orders that can easily be used in practice. Grounded in a case study, this paper examines the combined effects of assignment and sequencing heuristics on commonly used performance indicators. Discrete event simulation is used in the analysis to adequately capture the complexity found in the case study: production orders differing in many aspects, two unrelated parallel machines with varying and product-specific speed, and set-up times that depend on the (dis)similarity of successive orders. Evaluating 108 strategy–scenario combinations including the base case derived from the case study, it is found that a loading heuristic based on order quantity and scheduled capacity in combination with the shortest set-up heuristic performs best. When compared to the heuristic approach used by the case company, this strategy saves about 13.9% of total machine busy time and increases service level by 10.2%. In addition, using a reduced set of 40 production orders we are able to demonstrate that the best heuristic strategies comes close to results generated in a two-stage optimisation. The gap to optimality is only 3.1% in total busy time on average over all scenarios.     

Parallel machine scheduling with tool loading: a constraint programming approach

This paper presents constraint programming models that aim to solve scheduling and tool assignment problems in parallel machine environments. There are a number of jobs to be processed on parallel machines. Each job requires a set of tools, but limited number of tools are available in the system due to economic restrictions. The problem is to assign the jobs and the required tools to machines and to determine the schedule so that the makespan is minimised. Three constraint programming models are developed and compared with existing methods described in the literature.     

A branch and bound algorithm for scheduling unit size jobs on parallel batching machines to minimize makespan

In this paper, we present a branch and bound algorithm for the parallel batch scheduling of jobs having different processing times, release dates and unit sizes. There are identical machines with a fixed capacity and the number of jobs in a batch cannot exceed the machine capacity. All batched jobs are processed together and the processing time of a batch is given by the greatest processing time of jobs in that batch. We compare our method to a mixed integer program as well as a method from the literature that is capable of optimally solving instances with a single machine. Computational experiments show that our method is much more efficient than the other two methods in terms of solution time for finding the optimal solution.     

Scheduling of machines and automated guided vehicles in FMS using differential evolution

This paper addresses the problem of simultaneous scheduling of machines and two identical automated guided vehicles (AGVs) in a flexible manufacturing system (FMS). For solving this problem, a new meta-heuristic differential evolution (DE) algorithm is proposed. The problem consists of two interrelated problems, scheduling of machines and scheduling of AGVs. A simultaneous scheduling of these, in order to minimise the makespan will result in a FMS being able to complete all the jobs assigned to it at the earliest time possible, thus saving resources. An increase in the performance of the FMS under consideration would be expected as a result of making the scheduling of AGVs as an integral part of the overall scheduling activity. The algorithm is tested by using problems generated by various researchers and the makespan obtained by the algorithm is compared with that obtained by other researchers and analysed.     

Parallel machine scheduling problem with ready times,due times and sequence-dependent setup times using meta-heuristic algorithms

This article considers a parallel machine scheduling problem with ready times, due times and sequence-dependent setup times. The objective of this problem is to determine the allocation policy of jobs and the scheduling policy of machines to minimize the weighted sum of setup times, delay times and tardy times. A mathematical model for optimal solution is derived. An in-depth analysis of the model shows that it is very complicated and difficult to obtain optimal solutions as the problem size becomes large. Therefore, two meta-heuristics, genetic algorithm (GA) and a new population-based evolutionary meta-heuristic called self-evolution algorithm (SEA), are proposed. The performances of the meta-heuristic algorithms are evaluated through comparison with optimal solutions using several randomly generated examples.     

A reactive GRASP and Path Relinking for balancing reconfigurable transfer lines

A line balancing problem for reconfigurable transfer lines with sequence-dependent setup times and parallel machines was studied. These lines are paced and serial, i.e. a part to be machined passes through a sequence of stations. Stations are composed of CNC (Computer Numerical Control) machines. At least one CNC machine is installed at each station. These CNC machines are mono-spindle head machines, hence setup times between operations have to be taken into account. The origins of setup times are various, for example, the necessity to rotate the part, change and displace the tool, etc. Because of setup times, the station workload depends on the sequence in which the operations are assigned to the station. In addition, accessibility constraints have to be considered. The objective consists of assigning a given set of operations as well as machines to a sequence of workstations in order to minimise the total cost of the line. Keeping in mind the industrial importance of this problem and the lack of available methods in the literature tackling it efficiently, we propose a new heuristic based on GRASP combined with Path Relinking. A MIP approach is used to select the sequences of operations on workstations. Numerical experiments are presented and show that the proposed heuristic can provide good solutions even for large-sized instances while requiring a computational time that is fully compatible with a practical application. An industrial case study is also described.     

MIP-based fix-and-optimise algorithms for the parallel machine capacitated lot-sizing and scheduling problem

This paper examines the capacitated lot-sizing and scheduling problem (CLSP) with sequence-dependent setup times, time windows, machine eligibility and preference constraints. Such a problem frequently arises in the semiconductor manufacturing industry by which this paper is motivated. A mixed integer programming (MIP) model is constructed for the problem. Two MIP-based fix-and-optimise algorithms are proposed in which the binary decision variables associated with the assignment of machines are first fixed using the randomised least flexible machine (RLFM) rule and the rest of the decision variables are settled by an MIP solver. Extensive experiments show that the proposed algorithms outperform the state-of-the-art MIP-based fix-and-optimise algorithms in the literature, especially for instances with high machine flexibility and high demand variation.     

考虑序列相关准备时间的分布式柔性作业车间调度研究

针对考虑序列相关准备时间的分布式柔性作业车间调度问题,提出以最小化最大完工时间为优化目标的混合整数线性规划模型,并提出一种改进遗传算法。采用基于负荷均衡的种群初始化方法提高初始种群质量,根据问题特性构造6个局部扰动算子,设计多重局部扰动策略提高算法的局部搜索能力。通过扩展柔性作业车间调度基准生成测试算例,使用正交实验确定算法参数。实验结果表明,所提改进策略能够有效提高算法性能,求解结果优于对比算法,验证了调度模型和所提算法的可行性和有效性。     

A multi-phase covering Pareto-optimal front method to multi-objective parallel machine scheduling

This paper considers the problem of parallel machine scheduling with sequence-dependent setup times to minimise both makespan and total earliness/tardiness in the due window. To tackle the problem considered, a multi-phase algorithm is proposed. The goal of the initial phase is to obtain a good approximation of the Pareto-front. In the second phase, to improve the Pareto-front, non-dominated solutions are unified to constitute a big population. In this phase, based on the local search in the Pareto space concept, three multi-objective hybrid metaheuristics are proposed. Covering the whole set of Pareto-optimal solutions is a desired task of multi-objective optimisation methods. So in the third phase, a new method using an e-constraint hybrid metaheuristic is proposed to cover the gaps between the non-dominated solutions and improve the Pareto-front. Appropriate combinations of multi-objective methods in various phases are considered to improve the total performance. The multi-phase algorithm iterates over a genetic algorithm in the first phase and three hybrid metaheuristics in the second and third phases. Experiments on the test problems with different structures show that the multi-phase method is a better tool to approximate the efficient set than the global archive sub-population genetic algorithm presented previously.     

平行机系统生产调度与维护计划联合优化

针对平行机系统中生产调度和维护计划的联合决策问题,假设随机故障服从威布尔分布,将作业在设备上加工位置以及设备上预防性维护位置作为决策变量,以最小化最大完工时间和最小化单位维护成本作为优化目标建立了多目标优化模型.建立了基于混合编码的遗传算法,针对不同编码类型采用合适的遗传算子,并引入了自适应交叉和变异概率使算法在收敛速度和求解精度上得到较好平衡.通过与枚举算法对比,证明遗传算法具有较好的时间效率和求解精度.通过与独立决策模型对比,证明联合优化模型能更好地解决联合优化问题,提高企业整体效益.     

A comparison of mixed-integer linear programming models for workforce scheduling with position-dependent processing times

Only a few studies in the available scientific literature address the problem of having a group of workers that do not share identical levels of productivity during the planning horizon. This study considers a workforce scheduling problem in which the actual processing time is a function of the scheduling sequence to represent the decline in workers’ performance, evaluating two classical performance measures separately: makespan and maximum tardiness. Several mathematical models are compared with each other to highlight the advantages of each approach. The mathematical models are tested with randomly generated instances available from a public e-library.     

Parallel machine scheduling with preference of machines

This paper considers a scheduling problem in the manufacturing of anodic electro-etching aluminium foil. To reduce cost and increase efficiency, the manufacturer of aluminium foil usually designs the equipment for electro-etching of aluminium foil into specialised equipment that is dedicated to produce high voltage or medium voltage aluminium foil based on the range the aluminium foil can bear. Nevertheless, high voltage equipment can be used to produce medium voltage aluminium foil with longer processing time, and vice versa. The problem is to schedule jobs on the high and medium voltage equipment, each having several pieces in parallel, with setup times to minimise to the total completion time. In this paper, we propose a three-stage heuristic for this problem and computationally evaluate the performance of the heuristic in comparison to a heuristic for unrelated parallel machines and a branch-and-bound algorithm.     

A method combining rules with genetic algorithm for minimizing makespan on a batch processing machine with preventive maintenance

This paper considers the problem of minimising makespan on a single batch processing machine with flexible periodic preventive maintenance. This problem combines two sub-problems, scheduling on a batch processing machine with jobs’ release dates considered and arranging the preventive maintenance activities on a batch processing machine. The preventive maintenance activities are flexible but the maximum continuous working time of the machine, which is allowed, is determined. A mathematical model for integrating flexible periodic preventive maintenance into batch processing machine problem is proposed, in which the grouping of jobs with incompatible job families, the starting time of batches and the preventive maintenance activities are optimised simultaneously. A method combining rules with the genetic algorithm is proposed to solve this model, in which a batching rule is proposed to group jobs with incompatible job families into batches and a modified genetic algorithm is proposed to schedule batches and arrange preventive maintenance activities. The computational results indicate the method is effective under practical problem sizes. In addition, the influences of jobs’ parameters on the performance of the method are analyzed, such as the number of jobs, the number of job families, jobs’ processing time and jobs’ release time.     

Scheduling policies in multi-product manufacturing systems with sequence-dependent setup times and finite buffers

Multi-product production systems with sequence-dependent setup times are typical in the manufacturing of semiconductor chips and other electronic products. In such systems, the scheduling policies coordinating the production of multiple product types play an important role. In this paper, we study a multi-product manufacturing system with finite buffers, sequence-dependent setup times and various scheduling policies. Using continuous-time Markov chain models, we evaluate the performance of such systems under seven scheduling policies, i.e. cyclic, shortest queue, shortest processing time, shortest overall time (including setup time and processing time), longest queue, longest processing time, and longest overall time. The impacts of these policies on system throughput are compared, and the conditions characterising the superiority of each policy are investigated. The results of this work can provide production engineers and supervisors practical guidance to operate multi-product manufacturing systems with sequence-dependent setups.