Hybrid flexible flowshops with sequence-dependent setup times and machine availability constraints

One of the common assumptions in the field of scheduling is that machines are always available in the planning horizon. This may not be true in realistic problems since machines might be busy processing some jobs left from previous production horizon, breakdowns or preventive maintenance activities. Another common assumption is the consideration of setup times as a part of processing times, while in some industries, such as printed circuit board and automobile manufacturing, not only setups are an important factor but also setup magnitude of a job depends on its immediately preceding job on the same machine, known as sequence-dependent setup times. In this paper, we consider hybrid flexible flowshops with sequence-dependent setup times and machine availability constraints caused by preventive maintenance. The optimization criterion is the minimization of makespan. Since this problem is NP-hard in the strong sense, we propose three heuristics, based on SPT, LPT and Johnson rule and two metaheuristics based on genetic algorithm and simulated annealing. Computational experiments are performed to evaluate the efficiencies of the algorithms.     

Integrating non-preemptive open shops scheduling with sequence-dependent setup times using advanced metaheuristics

In this article, we consider non-preemptive open shops scheduling problem (OSSP) where setup times are sequence-dependent (SDST) on each machine to minimize makespan. The contributions of this article are threefold. Firstly, we incorporate a very practical assumption in our problem, SDST, which, according to Allahverdi et al. (2008) [Allahverdi, A., Ng, C. T., Cheung, T. C. E., & Kovalyov, Y. M. (2008). A survey of scheduling problems with setup times or costs. European Journal of Operational Research, 187(3), 985–1032], no paper has ever attempted to integrate into OSSP. Secondly, we propose two new advanced metaheuristics: multi-neighborhood search simulated annealing and hybrid simulated annealing to tackle the problem at hand. Thirdly, for the first time, we adapt two well-known constructive heuristics: longest total processing time and longest total remaining processing from the literature so as to consider the case of SDSTs. We also apply genetic algorithm from the literature of OSSP to embrace the concepts of SDST. Since there is no standard SDST-OSSP benchmark, we make certain adaptations on the Taillard’s benchmark [Taillard, E. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research, 64, 278–285] to include setup times. An experimental design based on foregoing benchmark is conducted to evaluate the competitiveness and robustness of our proposed algorithm against some effective algorithms in the literature. The obtained results strongly support the high performance of our proposed algorithms with respect to other well-known heuristic and metaheuristic algorithms.     

基于多班教学优化的多目标分布式混合流水车间调度

单工厂环境下的混合流水车间调度问题已受到广泛关注,而多工厂环境下的分布式混合流水车间调度问题(distributed hybrid flow shop scheduling problem,DHFSP)研究进展则较小.针对考虑顺序相关准备时间的DHFSP,提出一种多班教学优化(multi-class teaching-...     

Real-time scheduling for reentrant hybrid flow shops: A decision tree based mechanism and its application to a TFT-LCD line

A reentrant hybrid flow shop, typically found in the electronics industry, is an extended system of the ordinary flow shop in such a way that there exist one or more parallel machines at each serial stage and each job has the reentrant product flow, i.e., a job may visit a stage several times. Among the operational issues in reentrant hybrid flow shops, we focus on the scheduling problem that determines the allocation of jobs to the machines at each stage as well as the sequence of the jobs assigned to each machine. Unlike the theoretical approach on reentrant hybrid flow shop scheduling, we suggest a real-time scheduling mechanism with a decision tree when selecting appropriate dispatching rules. The decision tree, one of the commonly used data mining techniques, is adopted to eliminate the computational burden required to carry out simulation runs to select dispatching rules. To illustrate the mechanism suggested in this study, a case study was performed on a thin film transistor-liquid crystal display (TFT-LCD) manufacturing line and the results are reported for various system performance measures.     

Capacitated lot sizing and sequence dependent setup scheduling: an iterative approach for integration

We consider here the lot sizing and scheduling problem in single-level manufacturing systems. The shop floor is composed of unrelated parallel machines with sequence dependent setup times. We propose an integer programming model embedding precise capacity information due to scheduling constraints in a classical lot-sizing model. We also propose an iterative approach to generate a production plan taking into account scheduling constraints due to changeover setup times. The procedure executes two decision modules per iteration: a lot-sizing module and a scheduling module. The capacitated lot-sizing problem is solved to optimality considering estimated data and aggregate information, and the scheduling problem is solved by a GRASP heuristic. In the proposed scheme the information flow connecting the two levels is managed in each iteration. We report a set of computational experiments and discuss future work.     

Variable neighborhood search approaches for scheduling jobs on parallel machines with sequence-dependent setup times, precedence constraints, and ready times

In this paper, we discuss a scheduling problem for jobs on identical parallel machines. Ready times of the jobs, precedence constraints, and sequence-dependent setup times are considered. We are interested in minimizing the performance measure total weighted tardiness that is important for achieving good on-time delivery performance. Scheduling problems of this type appear as subproblems in decomposition approaches for large scale job shops with automated transport of the jobs as, for example, in semiconductor manufacturing. We suggest several variants of variable neighborhood search (VNS) schemes for this scheduling problem and compare their performance with the performance of a list based scheduling approach based on the Apparent Tardiness Cost with Setups and Ready Times (ATCSR) dispatching rule. Based on extensive computational experiments with randomly generated test instances we are able to show that the VNS approach clearly outperforms heuristics based on the ATCSR dispatching rule in many situations with respect to solution quality. When using the schedule obtained by ATCSR as an initial solution for VNS, then the entire scheme is also fast and can be used as a subproblem solution procedure for complex job shop decomposition approaches.     

A neighborhood for complex job shop scheduling problems with regular objectives

Due to the limited applicability in practice of the classical job shop scheduling problem, many researchers have addressed more complex versions of this problem by including additional process features, such as time lags, setup times, and buffer limitations, and have pursued objectives that are more practically relevant than the makespan, such as total flow time and total weighted tardiness. However, most proposed solution approaches are tailored to the specific scheduling problem studied and are not applicable to more general settings. This article proposes a neighborhood that can be applied for a large class of job shop scheduling problems with regular objectives. Feasible neighbor solutions are generated by extracting a job from a given solution and reinserting it into a neighbor position. This neighbor generation in a sense extends the simple swapping of critical arcs, a mechanism that is widely used in the classical job shop but that is not applicable in more complex job shop problems. The neighborhood is embedded in a tabu search, and its performance is evaluated with an extensive experimental study using three standard job shop scheduling problems: the (classical) job shop, the job shop with sequence-dependent setup times, and the blocking job shop, combined with the following five regular objectives: makespan, total flow time, total squared flow time, total tardiness, and total weighted tardiness. The obtained results support the validity of the approach.     

Optimizing distributed no-wait flow shop scheduling problem with setup times and maintenance operations via iterated greedy algorithm

Nowadays, distributed scheduling problem is a reality in many companies. Over the last years, an increasingly attention has been given to the distributed flow shop scheduling problem and the addition of constraints to the problem. This article introduces the distributed no-wait flow shop scheduling problem with sequence-dependent setup times and maintenance operations to minimize makespan. A mixed-integer linear programming (MILP) is to mathematically describe the problem and heuristic procedures to incorporate maintenance operations to job scheduling are proposed. An Iterated Greedy with Variable Search Neighborhood (VNS), named IG_NM, is proposed to solve small and large instances with size of 4,800 and 13,200 problems, respectively. Computational experiments were conducted to evaluate the performance of IG_NM in comparison with MILP and the most recent methods of literature of distributed flow shop scheduling problems. Statistical results show that in the trade-off between effectiveness and efficiency the proposed IG_NM outperformed other metaheuristics of the literature.     

Scheduling with multiple servers

In this paper, we consider the problem of scheduling a set of jobs on a set of identical parallel machines. Before the processing of a job can start, a setup is required which has to be performed by a given set of servers. We consider the complexity of such problems for the minimization of the makespan. For the problem with equal processing times and equal setup times we give a polynomial algorithm. For the problem with unit setup times, m machines and m − 1 servers, we give a pseudopolynomial algorithm. However, the problem with fixed number of machines and servers in the case of minimizing maximum lateness is proven to be unary NP-hard. In addition, recent algorithms for some parallel machine scheduling problems with constant precessing times are generalized to the corresponding server problems for the case of constant setup times. Moreover, we perform a worst case analysis of two list scheduling algorithms for makespan minimization.     

Design of a genetic algorithm for bi-objective unrelated parallel machines scheduling with sequence-dependent setup times and precedence constraints

This paper presents a novel, two-level mixed-integer programming model of scheduling N jobs on M parallel machines that minimizes bi-objectives, namely the number of tardy jobs and the total completion time of all the jobs. The proposed model considers unrelated parallel machines. The jobs have non-identical due dates and ready times, and there are some precedence relations between them. Furthermore, sequence-dependent setup times, which are included in the proposed model, may be different for each machine depending on their characteristics. Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time using traditional approaches or optimization tools is extremely difficult. This paper proposes an efficient genetic algorithm (GA) to solve the bi-objective parallel machine scheduling problem. The performance of the presented model and the proposed GA is verified by a number of numerical experiments. The related results show the effectiveness of the proposed model and GA for small and large-sized problems.     

A distributed shifting bottleneck heuristic for complex job shops

In this paper, we consider distributed versions of a modified shifting bottleneck heuristic for complex job shops. The considered job shop environment contains parallel batching machines, machines with sequence-dependent setup times and reentrant process flows. Semiconductor wafer fabrication facilities are typical examples for manufacturing systems with these characteristics. The used performance measure is total weighted tardiness (TWT). We suggest a two-layer hierarchical approach in order to decompose the overall scheduling problem. The upper (or top) layer works on an aggregated model. Based on appropriately aggregated routes it determines start dates and planned due dates for the jobs within each single work area, where a work area is defined as a set of parallel machine groups. The lower (or base) layer uses the start dates and planned due dates in order to apply shifting bottleneck heuristic type solution approaches for the jobs in each single work area. We conduct simulation experiments in a dynamic job shop environment in order to assess the performance of the heuristic. It turns out that the suggested approach outperforms a pure First In First Out (FIFO) dispatching scheme and provides a similar solution quality as the original modified shifting bottleneck heuristic.     

MIP formulation and heuristics for multi-stage capacitated lot-sizing and scheduling problem with availability constraints

In this paper, the problem of lot-sizing and scheduling of multiple product types in a capacitated flow shop with availability constraints for multi-period planning horizon is considered. In many real production systems, machines may be unavailable due to breakdowns or preventive maintenance activities, thus integrating lot-sizing and scheduling with maintenance planning is necessary to model real manufacturing conditions. Two variants are considered to deal with the maintenance activities. In the first, the starting times of maintenance tasks are fixed, whereas in the second one, maintenance must be carried out in a given time window. A new mixed-integer programming (MIP) model is proposed to formulate the problem with sequence-dependent setups and availability constraints. The objective is to find a production and preventive maintenance schedule that minimizes production, holding and setup costs. Three MIP-based heuristics with rolling horizon framework are developed to generate the integrated plan. Computational experiments are performed on randomly generated instances to show the efficiency of the heuristics. To evaluate the validity of the solution methods, problems with different scales have been studied and the results are compared with the lower bound. Computational experiments demonstrate that the performed methods have good-quality results for the test problems.     

Flow shop batching and scheduling with sequence-dependent setup times

This paper addresses the flow shop batching and scheduling problem where sequence-dependent family setup times are present and the objective is to minimize makespan. We consider violating the group technology assumption by dividing product families into batches. In order to reduce setup times, inconsistent batches are formed on different machines, which lead to non-permutation schedules. To the best of our knowledge, this is the first time that the splitting of job families into inconsistent batches has been considered in a flow shop system. A tabu search algorithm is developed which contains several neighbourhood functions, double tabu lists and a multilevel diversification structure. Compared to the state-of-the-art meta-heuristics for this problem, the proposed tabu search algorithm achieves further improvement when the group scheduling assumption is dropped. Also, various experiments conducted on the benchmark problem instances confirm the benefits of batching. Therefore, it will be prudent for the practitioners to consider adopting inconsistent batches and non-permutation schedules to improve their operational efficiency within a reasonable amount of computational effort.     

Unrelated parallel machine scheduling with setup times using simulated annealing

This paper presents a scheduling problem for unrelated parallel machines with sequence-dependent setup times, using simulated annealing (SA). The problem accounts for allotting work parts of L jobs into M parallel unrelated machines, where a job refers to a lot composed of N items. Some jobs may have different items while every item within each job has an identical processing time with a common due date. Each machine has its own processing times according to the characteristics of the machine as well as job types. Setup times are machine independent but job sequence dependent. SA, a meta-heuristic, is employed in this study to determine a scheduling policy so as to minimize total tardiness. The suggested SA method utilizes six job or item rearranging techniques to generate neighborhood solutions. The experimental analysis shows that the proposed SA method significantly outperforms a neighborhood search method in terms of total tardiness.     

时间约束混合流水车间调度问题综述

车间调度是智能制造领域中的核心问题之一, 在经典流水车间调度中, 所有工件按照相同的加工顺序在指 定机床上加工. 混合流水车间调度(HFS)作为流水车间调度的特例, 相比前者增加了机床选择的灵活性, 可以显著 优化系统目标, 但同时也增加了问题求解的难度. 由于时间约束HFS相比基本HFS问题更贴近实际生产过程, 近年 来, 综合考虑各类时间相关约束的HFS问题得到了深入研究. 因此, 本文围绕基本HFS、有限等待时间HFS、带准备 时间HFS、模糊/随机加工时间HFS、多时间约束HFS、时间约束相关多目标HFS等问题开展研究. 针对每一类时间 约束HFS问题, 按照问题规模对当前研究成果进行分类描述, 按照确定性算法、启发式方法、元启发式方法、算法混 合对相关成果进行算法分类, 按照实际工业应用对文献进行归类分析. 另一方面, 围绕交货期、能耗、成本等3类性 能指标, 分析了在各类时间约束HFS问题中的多目标优化相关成果. 最后详细分析了带时间约束HFS问题在问题层 面、算法层面和应用层面存在的挑战性问题和未来研究的方向.     

Study of stochastic sequence-dependent flexible flow shop via developing a dispatching rule and a hybrid GA

A flexible flow shop is a generalized flow shop with multiple machines in some stages. This system is fairly common in flexible manufacturing and in process industry. In most practical environments, scheduling is an ongoing reactive process where the presence of real time information continually forces reconsideration of pre-established schedules. This paper studies a flexible flow shop system considering non-deterministic and dynamic arrival of jobs and also sequence dependent setup times. The problem objective is to determine a schedule that minimizes average tardiness of jobs. Since the problem class is NP-hard, a novel dispatching rule and hybrid genetic algorithm have been developed to solve the problem approximately. Moreover, a discrete event simulation model of the problem is developed for the purpose of experimentation. The most commonly used dispatching rules from the literature and two new methods presented in this paper are incorporated in the simulation model. Simulation experiments have been conducted under various experimental conditions characterized by factors such as shop utilization, setup time level and number of stages. The results indicate that methods proposed in this study are much better than the traditional dispatching rules.     

Minimizing the makespan on a single machine subject to modular setups

Journal of Scheduling - Single machine scheduling with sequence-dependent setup times is one of the classical problems of production planning with widespread applications in many industries....     

Scheduling two-stage hybrid flow shops with parallel batch, release time, and machine eligibility constraints

This paper investigates a difficult scheduling problem on a specialized two-stage hybrid flow shop with multiple processors that appears in semiconductor manufacturing industry, where the first and second stages process serial jobs and parallel batches, respectively. The objective is to seek job-machine, job-batch, and batch-machine assignments such that makespan is minimized, while considering parallel batch, release time, and machine eligibility constraints. We first propose a mixed integer programming (MIP) formulation for this problem, then gives a heuristic approach for solving larger problems. In order to handle real world large-scale scheduling problems, we propose an efficient dispatching rule called BFIFO that assigns jobs or batches to machines based on first-in-first-out principle, and then give several reoptimization techniques using MIP and local search heuristics involving interchange, translocation and transposition among assigned jobs. Computational experiments indicate our proposed re-optimization techniques are efficient. In particular, our approaches can produce good solutions for scheduling up to 160 jobs on 40 machines at both stages within 10?min.     

Parallel-machine scheduling problems with sequence-dependent setup times using an ACO,SA and VNS hybrid algorithm

This paper proposes a hybrid metaheuristic for the minimization of makespan in scheduling problems with parallel machines and sequence-dependent setup times. The solution approach is robust, fast, and simply structured, and comprises three components: an initial population generation method based on an ant colony optimization (ACO), a simulated annealing (SA) for solution evolution, and a variable neighborhood search (VNS) which involves three local search procedures to improve the population. The hybridization of an ACO, SA with VNS, combining the advantages of these three individual components, is the key innovative aspect of the approach. Two algorithms of a hybrid VNS-based algorithm, SA/VNS and ACO/VNS, and the VNS algorithm presented previously are used to compare with the proposed hybrid algorithm to highlight its advantages in terms of generality and quality for large instances.     

A hybrid flowshop scheduling model considering dedicated machines and lot-splitting for the solar cell industry

This paper studies a solar cell industry scheduling problem, which is similar to traditional hybrid flowshop scheduling (HFS). In a typical HFS problem, the allocation of machine resources for each order should be scheduled in advance. However, the challenge in solar cell manufacturing is the number of machines that can be adjusted dynamically to complete the job. An optimal production scheduling model is developed to explore these issues, considering the practical characteristics, such as hybrid flowshop, parallel machine system, dedicated machines, sequence independent job setup times and sequence dependent job setup times. The objective of this model is to minimise the makespan and to decide the processing sequence of the orders/lots in each stage, lot-splitting decisions for the orders and the number of machines used to satisfy the demands in each stage. From the experimental results, lot-splitting has significant effect on shortening the makespan, and the improvement effect is influenced by the processing time and the setup time of orders. Therefore, the threshold point to improve the makespan can be identified. In addition, the model also indicates that more lot-splitting approaches, that is, the flexibility of allocating orders/lots to machines is larger, will result in a better scheduling performance.