A survey of scheduling problems with setup times or costs

The first comprehensive survey paper on scheduling problems with separate setup times or costs was conducted by [Allahverdi, A., Gupta, J.N.D., Aldowaisan, T., 1999. A review of scheduling research involving setup considerations. OMEGA The International Journal of Management Sciences 27, 219–239], who reviewed the literature since the mid-1960s. Since the appearance of that survey paper, there has been an increasing interest in scheduling problems with setup times (costs) with an average of more than 40 papers per year being added to the literature. The objective of this paper is to provide an extensive review of the scheduling literature on models with setup times (costs) from then to date covering more than 300 papers. Given that so many papers have appeared in a short time, there are cases where different researchers addressed the same problem independently, and sometimes by using even the same technique, e.g., genetic algorithm. Throughout the paper we identify such areas where independently developed techniques need to be compared. The paper classifies scheduling problems into those with batching and non-batching considerations, and with sequence-independent and sequence-dependent setup times. It further categorizes the literature according to shop environments, including single-machine, parallel machines, flow shop, no-wait flow shop, flexible flow shop, job shop, open shop, and others.     

Solving the serial batching problem in job shop manufacturing systems

This paper addresses the serial batch scheduling problem embedded in a job shop environment to minimize makespan. Sequence dependent family setup times and a job availability assumption are also taken into account. In consideration of batching decisions, we propose a tabu search algorithm which consists of various neighborhood functions, multiple tabu lists and a sophisticated diversification structure. Computational experiments show that our algorithm outperforms a well-known tabu search approach which is developed for solving the traditional job shop problem. These results also confirm the benefits of batching.     

Trapezoidal type inequalities for n-time differentiable functions

In this paper we consider the flow shop scheduling problems with the effects of learning and deterioration. In this model the processing times of a job is defined as a function of its starting time and position in a sequence. The scheduling objective functions are makespan and total completion time. We prove that even with the introduction of learning effect and deteriorating jobs to job processing times, some special flow shop scheduling problems remain polynomially solvable.     

安装、加工和拆卸时间分离的两台机器混合作业问题

混合作业是经典的自由作业和异序作业的一种综合,其中一些工件可以按任意的机器顺序进行处理,而另一些工件必须遵守预先指定的机器顺序.本文研究安装、加工和拆卸时间分离的两台机器混合作业排序问题,该问题已经被知道是强NP困难的,本文把流水作业中的同顺序作业概念推广到混合作业,并得到这个混合作业问题在同顺序意义下的最优解,这个解对于一般情形是3/2近似解,但对于一些有意义的特殊情形是整体最优的.     

Multi-objective sequence dependent setup times permutation flowshop: A new algorithm and a comprehensive study

The permutation flowshop scheduling problem has been thoroughly studied in recent decades, both from single objective as well as from multi-objective perspectives. To the best of our knowledge, little has been done regarding the multi-objective flowshop with Pareto approach when sequence dependent setup times are considered. As setup times and multi-criteria problems are important in industry, we must focus on this area. We propose a simple, yet powerful algorithm for the sequence dependent setup times flowshop problem with several criteria. The presented method is referred to as Restarted Iterated Pareto Greedy or RIPG and is compared against the best performing approaches from the relevant literature. Comprehensive computational and statistical analyses are carried out in order to demonstrate that the proposed RIPG method clearly outperforms all other algorithms and, as a consequence, it is a state-of-art method for this important and practical scheduling problem.     

Genetic algorithm-based subproblem solution procedures for a modified shifting bottleneck heuristic for complex job shops

In this paper, we consider 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 (Wafer Fabs) are typical examples for manufacturing systems with these characteristics. Our primary performance measure is total weighted tardiness (TWT). The shifting bottleneck heuristic uses a disjunctive graph to decompose the overall scheduling into scheduling problems for single tool groups. The scheduling algorithms for these scheduling problems are called subproblem solution procedures (SSPs). In previous research, only subproblem solution procedures based on dispatching rules have been considered. In this paper, we are interested in how much we can gain in terms of TWT if we apply more sophisticated subproblem solution procedures like genetic algorithms for parallel machine scheduling. We conduct simulation experiments in a dynamic job shop environment in order to assess the performance of the suggested subproblem solution procedures. It turns out that using near to optimal subproblem solution procedures leads in many situations to improved results compared to dispatching-based subproblem solution procedures.     

Optimization of setup times in the furniture industry

The aim of this paper is to develop a scheduling policy oriented towards minimizing setup times in the made-to-order furniture industry. The task is treated as a dynamic job shop scheduling problem, with the exception that customers?? orders collected over a?specified period of time are combined into a?production plan and released together. A?simulation of a production flow based on technological routes of real subassemblies was performed. The proposed method of calculating a setup time eliminates the need to determine machine setup time matrices. Among the tested priority rules the best performance was observed in the case of the hierarchical rule that combines similar setup, the earliest due date and the shortest processing time. This rule allowed the setup time per operation to be reduced by 58?% compared to a combination of the earliest due date with the shortest setup and processing time rule and by over 70?% compared to the single shortest processing time rule.     

Mixed integer goal programming models for the flexible job-shop scheduling problems with separable and non-separable sequence dependent setup times

The optimization problem addressed in this paper is an advanced form of the flexible job shop scheduling problem (FJSP) which also covers process plan flexibility and separable/non-separable sequence dependent setup times in addition to routing flexibility. Upon transforming the problem into an equivalent network problem, two mixed integer goal programming models are formulated. In the first model (Model A) the sequence dependent setup times are non-separable. In the second one (Model B) they are separable. Model B is obtained from Model A with a minor modification. The formulation of the models is described on a small sized numerical example and the solutions are interpreted. Finally, computational results are obtained on test problems.     

考虑机器调整次数和产品质量的卷烟批量计划和柔性流水车间调度集成问题

针对卷烟企业生产中的批量计划和柔性流水车间调度集成问题,构建了整数规划模型,目标函数由卷烟生产时间、生产线调整次数、卷烟质量、库存成本四部分组成。鉴于该问题的NP-hard性,设计遗传算法进行求解,通过合理设计遗传算子,避免不可行解出现。应用某卷烟企业数据得到优化排产结果,与该企业之前依照经验排产方案进行对比,发现优化排程结果在减少品牌转换次数,提高生产的连续性方面具有明显优势。该算法已作为某卷烟企业排产人员的排产参考,应用于排产决策中,取得了良好的效果,对卷烟企业制定排产计划具有一定的实际指导意义。     

A new neighborhood and tabu search for the Blocking Job Shop

The Blocking Job Shop is a version of the job shop scheduling problem with no intermediate buffers, where a job has to wait on a machine until being processed on the next machine. We study a generalization of this problem which takes into account transfer operations between machines and sequence-dependent setup times. After formulating the problem in a generalized disjunctive graph, we develop a neighborhood for local search. In contrast to the classical job shop, there is no easy mechanism for generating feasible neighbor solutions. We establish two structural properties of the underlying disjunctive graph, the concept of closures and a key result on short cycles, which enable us to construct feasible neighbors by exchanging critical arcs together with some other arcs. Based on this neighborhood, we devise a tabu search algorithm and report on extensive computational experience, showing that our solutions improve most of the benchmark results found in the literature.     

Single-machine scheduling with deteriorating jobs and past-sequence-dependent setup times

In many realistic scheduling settings a job processed later consumes more time than the same job processed earlier – this is known as scheduling with deteriorating jobs. Most research on scheduling with deteriorating jobs assumes that the actual processing time of a job is an increasing function of its starting time. Thus a job processed late may incur an excessively long processing time. On the other hand, setup times occur in manufacturing situations where jobs are processed in batches whereby each batch incurs a setup time. This paper considers scheduling with deteriorating jobs in which the actual processing time of a job is a function of the logarithm of the total processing time of the jobs processed before it (to avoid the unrealistic situation where the jobs scheduled late will incur excessively long processing times) and the setup times are proportional to the actual processing times of the already scheduled jobs. Under the proposed model, we provide optimal solutions for some single-machine problems.     

基于遗传算法的多目标柔性工作车间调度问题求解

本文针对柔性工作车间调度问题给出了一个有意义的综合目标尽可能缩短制造周期的同时尽可能的减少机器负荷。由于传统遗传算法在多目标柔性工作车间调度问题上的局限性，我们提出了一种改进遗传算法：首先，我们给出了针对综合目标的工序调度算法获得初始集合；接着，针对柔性工作车间调度问题的特点，我们在常用的基于工序顺序的编码方法上融入了基于机器分配的编码方法，并据此设计了相应的交叉变异操作；最后借鉴了物种进化现象中的环境迁移思想设计了解决多目标优化问题的迁移操作。实验结果表明，改进的遗传算法在多目标柔性工作车间调度问题的解决上要优于传统遗传算法。     

Fuzzy job shop scheduling with lot-sizing

This paper deals with a problem of determining lot-sizes of jobs in a real-world job shop-scheduling in the presence of uncertainty. The main issue discussed in this paper is lot-sizing of jobs. A fuzzy rule-based system is developed which determines the size of lots using the following premise variables: size of the job, the static slack of the job, workload on the shop floor, and the priority of the job. Both premise and conclusion variables are modelled as linguistic variables represented by using fuzzy sets (apart from the priority of the job which is a crisp value). The determined lots’ sizes are input to a fuzzy multi-objective genetic algorithm for job shop scheduling. Imprecise jobs’ processing times and due dates are modelled by using fuzzy sets. The objectives that are used to measure the quality of the generated schedules are average weighted tardiness of jobs, the number of tardy jobs, the total setup time, the total idle time of machines and the total flow time of jobs. The developed algorithm is analysed on real-world data obtained from a printing company.     

A Rollout Metaheuristic for Job Shop Scheduling Problems

In this paper we deal with solution algorithms for a general formulation of the job shop problem, called alternative graph. We study in particular the job shop scheduling problem with blocking and/or no-wait constraints. Most of the key properties developed for solving the job shop problem with infinite capacity buffer do not hold in the more general alternative graph model. In this paper we report on an extensive study on the applicability of a metaheuristic approach, called rollout or pilot method. Its basic idea is a look-ahead strategy, guided by one or more subheuristics, called pilot heuristics. Our results indicate that this method is competitive and very promising for solving complex scheduling problems.     

Vehicle scheduling with combinable delivery and pickup operations

Motivated by the logistics operations in an express delivery company, we develop and study a new scheduling model. The problem seems similar to scheduling with sequence-dependent setup times and scheduling with release times, however, the ability to combine or separate the job operations makes our problem unique.     

A Model for Shop Makespans and Lead Times

A model has been constructed which enables a component manufacturing shop to be interactively defined at a V.D.U., and used to calculate the average job makespan (time taken on the shop) under a variety of assumptions relating to work content, capacity and operational procedures. A second phase of the model allows the production controller to define a scheduling technique and lead-time assignment method, and provides guidance on how the makespan should be converted to lead times (time allowed on the shop). The model uses a mixture of queueing theory and simulation. This paper principally describes the methodology, but uses of the model are briefly discussed.     

The equal allocation policy in open shop batch scheduling

We study the optimality of the very practical policy of equal allocation of jobs to batches in batch scheduling problems on an m-machine open shop. The objective is minimum makespan. We assume unit processing time jobs, machine-dependent setup times and batch availability. We show that equal allocation is optimal for a two-machine and a three-machine open shop. Although, this policy is not necessarily optimal for larger size open shops, it is shown numerically to produce very close-to-optimal schedules.     

Approximation algorithms for two-machine flow shop scheduling with batch setup times

In many practical situations, batching of similar jobs to avoid setups is performed while constructing a schedule. This paper addresses the problem of non-preemptively scheduling independent jobs in a two-machine flow shop with the objective of minimizing the makespan. Jobs are grouped into batches. A sequence independent batch setup time on each machine is required before the first job is processed, and when a machine switches from processing a job in some batch to a job of another batch. Besides its practical interest, this problem is a direct generalization of the classical two-machine flow shop problem with no grouping of jobs, which can be solved optimally by Johnson's well-known algorithm. The problem under investigation is known to be NP-hard. We propose two O(n logn) time heuristic algorithms. The first heuristic, which creates a schedule with minimum total setup time by forcing all jobs in the same batch to be sequenced in adjacent positions, has a worst-case performance ratio of 3/2. By allowing each batch to be split into at most two sub-batches, a second heuristic is developed which has an improved worst-case performance ratio of 4/3. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.     

Scheduling jobs with a general learning effect model

The paper deals with machine scheduling problems with a general learning effect. By the general learning effect, we mean that the actual processing time of a job is not only a non-increasing function of the total weighted normal processing times of the jobs already processed, but also a non-increasing function of the job’s position in the sequence, where the weight is a position-dependent weight. We show that even with the introduction of a general learning effect to job processing times, some single machine scheduling problems are still polynomially solvable under the proposed model. We also show that some special cases of the flow shop scheduling problems can be solved in polynomial time.     

Flow shop scheduling jobs with position-dependent processing times

The paper is devoted to some flow shop scheduling problems, where job processing times are defined by functions dependent on their positions in the schedule. An example is constructed to show that the classical Johnson's rule is not the optimal solution for two different models of the two-machine flow shop scheduling to minimize makespan. In order to solve the makespan minimization problem in the two-machine flow shop scheduling, we suggest Johnson's rule as a heuristic algorithm, for which the worst-case bound is calculated. We find polynomial time solutions to some special cases of the considered problems for the following optimization criteria: the weighted sum of completion times and maximum lateness. Some furthermore extensions of the problems are also shown.