Bottleneck-based heuristics to minimize total tardiness for the flexible flow line with unrelated parallel machines

This paper considers the flexible flow line problem with unrelated parallel machines at each stage and with a bottleneck stage on the line. The objective of the problem is to minimize the total tardiness. Two bottleneck-based heuristics with three machine selection rules are proposed to solve the problem. The heuristics first develop an indicator to identify a bottleneck stage in the flow line, and then separate the flow line into the upstream stages, the bottleneck stage, and the downstream stages. The upstream stages are the stages ahead of the bottleneck stage and the downstream stages are the stages behind the bottleneck stage. A new approach is developed to find the arrival times of the jobs at the bottleneck stage. Using the new approach, the bottleneck-based heuristics develop two decision rules to iteratively schedule the jobs at the bottleneck stage, the upstream stages, and the downstream stages. In order to evaluate the performance of the bottleneck-based heuristics, seven commonly used dispatching rules and a basic tabu search algorithm are investigated for comparison purposes. Seven experimental factors are used to design 128 production scenarios, and ten test problems are generated for each scenario. Computational results show that the bottleneck-based heuristics significantly outperform all the dispatching rules for the test problems. Although the effective performance of the bottleneck-based heuristics is inferior to the basic tabu search algorithm, the bottleneck-based heuristics are much more efficient than the tabu search algorithm. Also, a test of the effect of the experimental factors on the dispatching rules, the bottleneck-based heuristics, and the basic tabu search algorithm is performed, and some interesting insights are discovered.     

大规模流水线调度的瓶颈分解算法研究

为了克服大规模流水线调度问题的计算复杂度,提出一种瓶颈分解启发式算法．利用瓶颈特性将流水线分解为瓶颈机和非瓶颈机,对瓶颈机建立带有到达时间和传递时间约束的单机调度模型,并优化求解,而在非瓶颈机上则采用简单的分派规则,通过不断修正瓶颈机上工件的到达时间和传递时间来协调瓶颈机与非瓶颈机之间的关联．仿真结果验证了算法的有效性．     

瓶颈指向的启发式算法求解混合流水车间调度问题

针对以最小化时间表长为目标的复杂混合流水车间调度问题,提出了一种将机器布局和工件加工时间特征紧密结合的启发式算法.首先,充分利用各阶段平均机器负荷一般不相等的特点确定瓶颈阶段,构建初始工件排序.其次,针对在瓶颈阶段前加工时间较短而瓶颈阶段后加工时间相对较长的工件,在第1阶段优先开始加工.同时,在瓶颈阶段前的每一个阶段,每当有工件等待加工或同时完工时,优先选择瓶颈阶段前剩余加工时间最短的工件加工;在瓶颈阶段以及瓶颈阶段之后,则优先选择这台机器后剩余加工时间最长的工件加工.最后,采用工件交换和插入操作改进初始调度.用Carlier和Neron的Benchmark算例测试提出的启发式算法.将计算结果与NEH启发式算法进行了比较,平均偏差降低了0.0555%,表明这个启发式算法是有效的.     

An improved heuristic to minimize total flow time for scheduling in the m-machine no-wait flow shop

In this paper, we present a constructive heuristic to minimize total flow time criterion for the well-known NP-hard no-wait flow shop scheduling problem. It is based on the assumption that the priority of a job in the initial sequence is given by the sum of its processing times on the bottleneck machines. The initial sequence of jobs thus generated is further improved using a new job insertion technique. We show, through computational experimentation, that the proposed method significantly outperforms the best-known heuristics while retaining its time complexity of O(n²). Statistical tests of significance are used to confirm the improvement in solution quality.     

Improvement of constructive heuristics using variable neighbourhood descent for scheduling a flow shop with sequence dependent setup time

This paper deals with the problem of scheduling a flow shop operating in a sequence dependent setup time environment. The objective is to determine the sequence that minimises the makespan. Two efficient neighbourhood search-based heuristics have been developed and tested using 960 problems, and the results obtained reveal their usefulness. The algorithms make use of two existing constructive heuristics. A neighbourhood search known as variable neighbourhood descent is used to improve the two constructive heuristics. Experimentation is carried out on the 96 groups of problems with 10 problem instances in each group. Performance analysis is carried out using the relative performance improvement of each heuristic. The analysis shows a consistently better performance of the neighbourhood-based improvement heuristics. A paired comparison test is used for validating the superiority of the proposed heuristics. The statistical analysis reveals that the performance of the neighbourhood-based heuristics is very much dependent on the initial constructive heuristics used.     

Tsp-based scheduling in a batch-wise hybrid flow-shop

In the past few years, flexible production systems have allowed an extensive exploitation of new technologies, but have also led to new difficulties in production planning management science. The model presented in this paper extends the traditional HFS (hybrid flow-shop) scheduling problem to the case in which jobs are due to follow strict precedence constraints and batch assignment constraints and the parallel machines at a stage are served by a bottleneck machine. A variant of the well-known TSP problem is used to develop an efficient heuristic solution for the problem. The effectiveness of the proposed approach is validated through a comparison with different heuristics traditionally used in HFS scheduling problems. Furthermore, a simple insertion heuristic based on the TSP model of the problem is tested. Finally, a MIP-based approach is also explored to provide the optimum solutions within much larger times for comparison.     

The two-stage assembly scheduling problem to minimize total completion time with setup times

We address the two-stage assembly scheduling problem where there are m machines at the first stage and an assembly machine at the second stage. The objective is to schedule the available n jobs so that total completion time of all n jobs is minimized. Setup times are treated as separate from processing times. This problem is NP-hard, and therefore we present a dominance relation and propose three heuristics. The heuristics are evaluated based on randomly generated data. One of the proposed heuristics is known to be the best heuristic for the case of zero setup times while another heuristic is known to perform well for such problems. A new version of the latter heuristic, which utilizes the dominance relation, is proposed and shown to perform much better than the other two heuristics.     

A comparison of scheduling algorithms for flexible flow shop problems with unrelated parallel machines,setup times,and dual criteria

This paper considers a flexible flow shop scheduling problem, where at least one production stage is made up of unrelated parallel machines. Moreover, sequence- and machine-dependent setup times are given. The objective is to find a schedule that minimizes a convex sum of makespan and the number of tardy jobs in a static flexible flow shop environment. For this problem, a 0–1 mixed integer program is formulated. The problem is, however, a combinatorial optimization problem which is too difficult to be solved optimally for large problem sizes, and hence heuristics are used to obtain good solutions in a reasonable time. The proposed constructive heuristics for sequencing the jobs start with the generation of the representatives of the operating time for each operation. Then some dispatching rules and flow shop makespan heuristics are developed. To improve the solutions obtained by the constructive algorithms, fast polynomial heuristic improvement algorithms based on shift moves and pairwise interchanges of jobs are applied. In addition, metaheuristics are suggested, namely simulated annealing (SA), tabu search (TS) and genetic algorithms. The basic parameters of each metaheuristic are briefly discussed in this paper. The performance of the heuristics is compared relative to each other on a set of test problems with up to 50 jobs and 20 stages and with an optimal solution for small-size problems. We have found that among the constructive algorithms the insertion-based approach is superior to the others, whereas the proposed SA algorithms are better than TS and genetic algorithms among the iterative metaheuristic algorithms.     

A heuristic method for two-stage hybrid flow shop with dedicated machines

This paper considers a two-stage hybrid flow shop scheduling problem with dedicated machines, in which the first stage contains a single common critical machine, and the second stage contains several dedicated machines. Each job must be first processed on the critical machine in stage one and depending on the job type, the job will be further processed on the dedicated machine of its type in stage two. The objective is to minimize the makespan. To solve the problem, a heuristic method based on branch and bound (B&B) algorithm is proposed. Several lower bounds are derived and four constructive heuristics are used to obtain initial upper bounds. Then, three dominance properties are employed to enhance the performance of the proposed heuristic method. Extensive computational experiments on two different problem categories each with various problem configurations are conducted. The results show that the proposed heuristic method can produce very close-to-optimal schedules for problems up to 100 jobs and five dedicated machines within 60 s. The comparisons with solutions of two other meta-heuristic methods also prove the better performance of the proposed heuristic method.     

Single machine scheduling with controllable processing times to minimize total tardiness and earliness

In most deterministic scheduling problems job processing times are considered as invariable and known in advance. Single machine scheduling problem with controllable processing times with no inserted idle time is presented in this study. Job processing times are controllable to some extent that they can be reduced or increased, up to a certain limit, at a cost proportional to the reduction or increase. In this study, our objective is determining a set of compression/expansion of processing times in addition to a sequence of jobs simultaneously, so that total tardiness and earliness are minimized. A mathematical model is proposed firstly and afterward a net benefit compression–net benefit expansion (NBC–NBE) heuristic is presented so as to acquire a set of amounts of compression and expansion of jobs processing times in a given sequence. Three heuristic techniques in small problems and in medium-to-large instances two meta-heuristic approaches, as effective local search methods, as well as these heuristics are employed to solve test examples. The single machine total tardiness problem (SMTTP) is already NP-hard, so the considered problem is NP-hard obviously. The computational experiments demonstrate that our proposed heuristic is efficient approach for such just-in-time (JIT) problem, especially equipped with competent heuristics.     

An artificial neural network based heuristic for flow shop scheduling problems

The objective of this paper is to find a sequence of jobs in the flow shop to minimize makespan. A feed forward back propagation neural network is used to solve the problem. The network is trained with the optimal sequences of completely enumerated five, six and seven jobs, ten machine problem and this trained network is then used to solve the problem with greater number of jobs. The sequence obtained using artificial neural network (ANN) is given as the initial sequence to a heuristic proposed by Suliman and also to genetic algorithm (GA) as one of the sequences of the population for further improvement. The approaches are referred as ANN-Suliman heuristic and ANN-GA heuristic respectively. Makespan of the sequences obtained by these heuristics are compared with the makespan of the sequences obtained using the heuristic proposed by Nawaz, Enscore and Ham (NEH) and Suliman Heuristic initialized with Campbell Dudek and Smith (CDS) heuristic called as CDS-Suliman approach. It is found that the ANN-GA and ANN-Suliman heuristic approaches perform better than NEH and CDS-Suliman heuristics for the problems considered.     

Efficient constructive and composite heuristics for the Permutation Flowshop to minimise total earliness and tardiness

In this paper we address the problem of scheduling jobs in a permutation flowshop with a just-in-time objective, i.e. the minimisation of the sum of total tardiness and total earliness. Since the problem is NP-hard, there are several approximate procedures available for the problem, although their performance largely depends on the due dates of the specific instance to be solved. After an in-depth analysis of the problem, different cases or sub-problems are identified and, by incorporating this knowledge, four heuristics are proposed: a fast constructive heuristic, and three different local search procedures that use the proposed constructive heuristic as initial solution.The proposed Prod. Type: FLPheuristics have been compared on an extensive set of instances with the best-so-far heuristic for the problem, as well as with adaptations of efficient heuristics for similar scheduling problems. The computational results show the excellent performance of the proposed algorithms. Finally, the positive impact of the efficient heuristics is evaluated by including them as seed sequences for one of the best metaheuristic for the problem.     

Unrelated parallel machine scheduling with setup times and a total weighted tardiness objective

This paper presents several search heuristics and their performance in batch scheduling of parallel, unrelated machines. Identical or similar jobs are typically processed in batches in order to decrease setup times and/or processing times. The problem accounts for allotting batched work parts into unrelated parallel machines, where each batch consists of a fixed number of jobs. Some batches may contain different jobs but all jobs within each batch should have an identical processing time and a common due date. Processing time of each job of a batch is determined according to the machine group as well as the batch group to which the job belongs. Major or minor setup times are required between two subsequent batches depending on batch sequence but are independent of machines. The objective of our study is to minimize the total weighted tardiness for the unrelated parallel machine scheduling. Four search heuristics are proposed to address the problem, namely (1) the earliest weighted due date, (2) the shortest weighted processing time, (3) the two-level batch scheduling heuristic, and (4) the simulated annealing method. These proposed local search heuristics are tested through computational experiments with data from dicing operations of a compound semiconductor manufacturing facility.     

Heuristics for scheduling in flowshops and flowline-based manufacturing cells to minimize the sum of weighted flowtime and weighted tardiness of jobs

The problem of scheduling in two different types of flowshops (all jobs available at time zero, different job availability times known a priori) and in flowline-based manufacturing cells is considered with the objective of minimizing the sum of weighted flowtime and weighted tardiness of jobs. First, heuristic preference relations are developed by the consideration of lower bounds on the completion times, operation due-dates, and weights for holding and tardiness of jobs. A heuristic algorithm for scheduling is then proposed by making use of the heuristic preference relations. Two more heuristic algorithms are developed by implementing an improvement scheme to enhance the quality of the solution given by the first heuristic algorithm. The proposed and the existing heuristics are evaluated with respect to the three problem classes under consideration by solving a large number of randomly generated problems. The results of an extensive computational investigation for various problem sizes are presented. It has been observed that all three proposed heuristics perform better than the existing heuristics in giving a solution of superior quality and that the first proposed heuristic yields a good solution by requiring a negligible CPU time. In addition, an experimental investigation is carried out to evaluate the effectiveness of the improvement scheme when implemented in the existing heuristics, and also the effectiveness of heuristics based on simulated annealing. The results are discussed in detail.     

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.     

Evolving priority scheduling heuristics with genetic programming

This paper investigates the use of genetic programming in automated synthesis of scheduling heuristics for an arbitrary performance measure. Genetic programming is used to evolve the priority function, which determines the priority values of certain system elements (jobs, machines). The priority function is used within an appropriate meta-algorithm for a given environment, which forms the priority scheduling heuristic. The evolved solutions are compared with existing scheduling heuristics and found to perform similarly to or better than existing algorithms. We intend to show that this approach is particularly useful for combinations of scheduling environments and performance measures for which no adequate scheduling algorithms exist.     

An efficient stochastic hybrid heuristic for flowshop scheduling

The paper addresses the problem of flowshop scheduling in order to minimize the makespan objective. Three probabilistic hybrid heuristics are presented for solving permutation flowshop scheduling problem. The proposed methodology combines elements from both constructive heuristic search and a stochastic improvement technique. The stochastic method used in this paper is simulated annealing (SA). Experiments have been run on a large number of randomly generated test problems of varying jobs and machine sizes. Our approach is shown to outperform best-known existing heuristics, including the classical NEH technique (OMEGA, 1983) and the SA based on (OMEGA, 1989) of Osman and Potts . Statistical tests of significance are performed to substantiate the claims of improvement.     

Integrating the lot-sizing and sequencing decisions for scheduling a capacitated flow line

In this paper we consider a general problem of scheduling a single flow line consisting of multiple machines and producing a given set of jobs. The manufacturing environment is characterized by sequence dependent set-up times, limited intermediate buffer space, and capacity constraints. In addition, jobs are assigned with due dates that have to be met. The objectives of the scheduling are: (1) to meet the due dates without violating the capacity constraints, (2) to minimize the makespan, and (3) to minimize the inventory holding costs. While most of the approaches in the literature treat the problem of scheduling in flow lines as two independent sub-problems of lot-sizing and sequencing, our approach integrates the lot-sizing and sequencing heuristics. The integrated approach uses the Silver-Meal heuristic (modified to include lot-splitting) for lot-sizing and an improvement procedure applied to Palmer's heuristic for sequencing, which takes into account the actual sequence dependent set-up times and the limited intermedite buffer capacity. We evaluate the performance of the integrated approach and demonstrate its efficacy for scheduling a real world SMT manufacturing environment.     

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.     

Flowshop scheduling with a general exponential learning effect

This paper investigates flowshop scheduling problems with a general exponential learning effect, i.e., the actual processing time of a job is defined by an exponent function of the total weighted normal processing time of the already processed jobs and its position in a sequence, where the weight is a position-dependent weight. The objective is to minimize the makespan, the total (weighted) completion time, the total weighted discounted completion time, and the sum of the quadratic job completion times, respectively. Several simple heuristic algorithms are proposed in this paper by using the optimal schedules for the corresponding single machine problems. The tight worst-case bound of these heuristic algorithms is also given. Two well-known heuristics are also proposed for the flowshop scheduling with a general exponential learning effect.