Family scheduling with batch availability in flow shops to minimize makespan

This paper addresses a batch scheduling problem in flow shop production systems, where job families are formed based on setup similarities. In order to improve setup efficiency, we consider batching decisions in our solution procedure. Due to its high practical relevance, the batch availability assumption is also adopted in this study. In the presence of sequence-dependent setup times, it is proved that a permutation flow shop is generally not optimal. Therefore, our objective is to determine solutions with inconsistent batches, which essentially lead to non-permutation schedules, to minimize makespan. After examining structural properties, we develop a tabu search algorithm with multiple neighbourhood functions. Computational results confirm the remarkable benefits of batching decisions. Our algorithm also outperforms some well-known and well-performing approaches.     

Scatter search with path relinking for the job shop with time lags and setup times

This paper addresses the job shop scheduling problem with time lags and sequence-dependent setup times. This is an extension of the job shop scheduling problem with many applications in real production environments. We propose a scatter search algorithm which uses path relinking and tabu search in its core. We consider both feasible and unfeasible schedules in the execution, and we propose effective neighborhood structures with the objectives of reducing the makespan and regain feasibility. We also define new procedures for estimating the quality of the neighbors. We conducted an experimental study to compare the proposed algorithm with the state-of-the-art, in benchmarks both with and without setups. In this study, our algorithm has obtained very competitive results in a reduced run time.     

Metaheuristics for scheduling a non-permutation flowline manufacturing cell with sequence dependent family setup times

The broad applications of cellular manufacturing make flowline manufacturing cell scheduling problems with sequence dependent family setup times a core topic in the field of scheduling. Due to computational complexity, almost all published studies focus on using permutation schedules to deal with this problem. To explore the potential effectiveness of treating this argument using non-permutation schedules, three prominent types of metaheuristics—a simulated annealing, a genetic algorithm and a tabu search—are proposed and empirically evaluated. The experimental results demonstrate that in general, the improvement made by non-permutation schedules over permutation schedules for the due-date-based performance criteria were significantly better than that for the completion-time-based criteria. The results of this study will provide practitioners a guideline as to when to adopt a non-permutation schedule, which may exhibit better performance with additional computational efforts.     

Two simple and effective heuristics for minimizing the makespan in non-permutation flow shops

We propose a constructive and an iterated local search heuristic for minimizing the makespan in the non-permutation flow shop scheduling problem. Both heuristics are based on the observation that optimal non-permutation schedules often exhibit a permutation structure with a few local job inversions. In computational experiments we compare our heuristics to the best heuristics for finding non-permutation and permutation flow shop schedules, and evaluate the reduction in makespan and buffer size that can be achieved by non-permutation schedules.     

Tabu search and lower bound for an industrial complex shop scheduling problem

This paper deals with an industrial shop scheduling problem that arises in a metal goods production group. The scheduling problem can be seen as a multi-mode job shop with assembly. Jobs have additional constraints such as release date, due date and sequence-dependent setup times. The aim of the decision-makers is to minimize the maximum lateness. This article introduces a tabu search procedure to solve the whole problem and a valid lower bound used to evaluate the tabu search procedure.     

An Enhanced tabu search algorithm to minimize a bi-criteria objective in batching and scheduling problems on unrelated-parallel machines with desired lower bounds on batch sizes

This paper addresses a sequence- and machine-dependent batch scheduling problem on a set of unrelated-parallel machines where the objective is to minimize a linear combination of total weighted completion time and total weighted tardiness. In particular, batch scheduling disregards the group technology assumptions by allowing for the possibility of splitting pre-determined groups of jobs into batches with respect to desired lower bounds on batch sizes. With regard to bounds on batch sizes, the MILP model is developed as two integrated batching and scheduling phases to present the problem. A benchmark of small-size instances on group scheduling shows the superior performance of batch scheduling up to 37% reduction in the objective function value. An efficient meta-heuristic algorithm based on tabu search with multi-level diversification and multi-tabu structure is developed at three levels, which moves back and forth between batching and scheduling phases. To eliminate searching in ineffective neighborhoods and thus enhance computational efficiency of search algorithms, several lemmas are proposed and proven. The results of applying lemmas reflect up to 40% reduction in computational times. Comparing the optimal solutions found by CPLEX and tabu search shows that the tabu search algorithm could find solutions, at least as good as CPLEX but in incredibly shorter computational time. In order to trigger the search algorithm, two different initial solution finding mechanisms have been developed and implemented. Also, due to lack of a qualified benchmark for unrelated-parallel machines, a comprehensive data generation mechanism has been developed in a way that it fairly reflects the real world situations encountered in practice. The machine availability times and job release times are considered to be dynamic and the run time of each job differs on different machines based upon the capability of the machines.     

An efficient hybrid evolutionary algorithm for scheduling with setup times and weighted tardiness minimization

We confront the job shop scheduling problem with sequence-dependent setup times and weighted tardiness minimization. To solve this problem, we propose a hybrid metaheuristic that combines the intensification capability of tabu search with the diversification capability of a genetic algorithm which plays the role of long term memory for tabu search in the combined approach. We define and analyze a new neighborhood structure for this problem which is embedded in the tabu search algorithm. The efficiency of the proposed algorithm relies on some elements such as neighbors filtering and a proper balance between intensification and diversification of the search. We report results from an experimental study across conventional benchmarks, where we analyze our approach and demonstrate that it compares favorably to the state-of-the-art methods.     

A hybrid shifting bottleneck-tabu search heuristic for the job shop total weighted tardiness problem

In this paper, we study the job shop scheduling problem with the objective of minimizing the total weighted tardiness. We propose a hybrid shifting bottleneck-tabu search (SB-TS) algorithm by replacing the re-optimization step in the shifting bottleneck (SB) algorithm by a tabu search (TS). In terms of the shifting bottleneck heuristic, the proposed tabu search optimizes the total weighted tardiness for partial schedules in which some machines are currently assumed to have infinite capacity. In the context of tabu search, the shifting bottleneck heuristic features a long-term memory which helps to diversify the local search. We exploit this synergy to develop a state-of-the-art algorithm for the job shop total weighted tardiness problem (JS-TWT). The computational effectiveness of the algorithm is demonstrated on standard benchmark instances from the literature.     

求解无等待流水调度的基于禁忌搜索的混合算法

本文提出了解决最小完工时间的无等待流水调度问题的基于禁忌搜索的混合算法。算法结合了调度规则和禁忌搜索算法的优点,首先利用调度规则构造较好的初始解,既可以加快禁忌搜索算法的收敛速度,也可以降低整个算法的运算量,使算法有更好的工程实用性;然后使用变邻域结构的禁忌搜索算法改进当前解。在保持可达性的基础上,该算法缩小了邻域规模和减少了计算时间。数值仿真实验表明,该算法是有效的。     

Lateness minimization with Tabu search for job shop scheduling problem with sequence dependent setup times

We tackle the job shop scheduling problem with sequence dependent setup times and maximum lateness minimization by means of a tabu search algorithm. We start by defining a disjunctive model for this problem, which allows us to study some properties of the problem. Using these properties we define a new local search neighborhood structure, which is then incorporated into the proposed tabu search algorithm. To assess the performance of this algorithm, we present the results of an extensive experimental study, including an analysis of the tabu search algorithm under different running conditions and a comparison with the state-of-the-art algorithms. The experiments are performed across two sets of conventional benchmarks with 960 and 17 instances respectively. The results demonstrate that the proposed tabu search algorithm is superior to the state-of-the-art methods both in quality and stability. In particular, our algorithm establishes new best solutions for 817 of the 960 instances of the first set and reaches the best known solutions in 16 of the 17 instances of the second set.     

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.     

一种用于PFSP节能优化的混合禁忌搜索算法

为了追求节能减排与净利润最大化,建立一种置换流水车间订单接受与调度模型。禁忌搜索是一类启发式全局搜索算法,传统禁忌搜索对初始解依赖较大,没有对考虑能效的置换流水车间调度问题进行更深入的优化。鉴于问题的复杂性,提出了一种节能混合禁忌搜索算法,结合了NEH构造启发式算法的优势,并在该算法中设计了订单接受与拒绝编码方式、能耗调整与交货期配置策略。最后采用大量随机实例对性能进行分析。实验结果表明,通过上述改进,改善了算法的全局搜索能力与解决复杂模型的寻优能力,节能混合禁忌搜索较单一算法而言性能更优,可以有效增加企业总净利润,降低能源消耗。     

Minimizing Total Weighted Tardiness in a Generalized Job Shop

We consider a generalization of the classical job shop scheduling problem with release times, positive end–start time lags, and a general precedence graph. As objective we consider the total weighted tardiness. We use a tabu search algorithm to search for the order in which the operations are processed on each machine. Given a sequence of operations on each machine, we determine optimal starting times by solving a maximum cost flow problem. This solution is used to determine the neighborhood for our tabu search algorithm. All sequences in our neighborhood are obtained by swapping certain pairs of adjacent operations. We show that only swaps that possess a certain property can improve the current solution; if no such swap is available in the neighborhood, then the current solution is globally optimal. In the computational results we compare our method with other procedures proposed in literature. Our tabu search algorithm seems to be effective both with respect to time and solution quality. The research was carried out at the Technische Universiteit Eindhoven and the Universiteit Utrecht with support of Baan and the Future and Emerging Technologies programme of the EU under contract number IST-1999-14186 (ALCOM-FT).     

Non-permutation flowshop scheduling with dual resources

Typically, in order to process jobs in a flowshop both machines and labor are required. However, in traditional scheduling problems, labor is assumed to be plentiful and only machine is considered to be a constraint. This assumption could be due to the lower cost of labor compared to machines or the complexity of dual-resource constrained problems. In this paper a mathematical model is developed to minimize the work-in-process inventory while maximizing the service level in a flowshop with dual resources. The model focuses on optimizing a non-permutation flowshop. There are different skill levels considered for labor and the setup times on machines are sequence-dependent. Jobs are allowed to skip one or more stages in the flowshop. Job release and machine availability times are considered to be dynamic. The problem is solved in two layers. The outer layer is a search algorithm to find the schedule of jobs on the machine (traditional flowshop scheduling problem) and the inner layer is a three-step heuristic to find a schedule of jobs on labor in accordance to the machine schedule. Three different search algorithms are developed to solve the proposed NP-hard problem. First algorithm can solve a permutation flowshop while the other two are developed to solve a non-permutation flowshop. The comparison between the optimal solution and the search algorithms in small examples shows a good performance of the algorithms with an average deviation of only 2.00%. An experimental design analyzes the effectiveness and efficiency of the algorithms statistically. The results show that non-permutation algorithms perform better than the permutation algorithm, although the former are less efficient. The effectiveness and efficiency in all three algorithms have an inverse relation. To the best of our knowledge, this research is the first of its kind to provide a comprehensive mathematical model for dual resource flowshop scheduling problem.     

Greedy randomized adaptive search for dynamic flexible job-shop scheduling

Dynamic flexible job shop scheduling problem is studied under the events such as new order arrivals, changes in due dates, machine breakdowns, order cancellations, and appearance of urgent orders. This paper presents a constructive algorithm which can solve FJSP and DFJSP with machine capacity constraints and sequence-dependent setup times, and employs greedy randomized adaptive search procedure (GRASP). Besides, Order Review Release (ORR) mechanism and order acceptance/rejection decisions are also incorporated into the proposed method in order to adjust capacity execution considering customer due date requirements. The lexicographic method is utilized to assess the objectives: schedule instability, makespan, mean tardiness and mean flow time. A group of experiments is also carried out in order to verify the suitability of the GRASP in solving the flexible job shop scheduling problem. Benchmark problems are formed for different problem scales with dynamic events. The event-driven rescheduling strategy is also compared with periodical rescheduling strategy. Results of the extensive computational experiment presents that proposed approach is very effective and can provide reasonable schedules under event-driven and periodic scheduling scenarios.     

The economic lot scheduling problem in limited-buffer flexible flow shops: Mathematical models and a discrete fruit fly algorithm

This paper considers the lot scheduling problem in the flexible flow shop with limited intermediate buffers to minimize total cost which includes the inventory holding and setup costs. The single available mathematical model by Akrami et al. (2006) for this problem suffers from not only being non-linear but also high size-complexity. In this paper, two new mixed integer linear programming models are developed for the problem. Moreover, a fruit fly optimization algorithm is developed to effectively solve the large problems. For model’s evaluation, this paper experimentally compares the proposed models with the available model. Moreover, the proposed algorithm is also evaluated by comparing with two well-known algorithms (tabu search and genetic algorithm) in the literature and adaption of three recent algorithms for the flexible flow shop problem. All the results and analyses show the high performance of the proposed mathematical models as well as fruit fly optimization algorithm.     

A tabu search algorithm for order acceptance and scheduling

We consider a make-to-order production system, where limited production capacity and order delivery requirements necessitate selective acceptance of the orders. Since tardiness penalties cause loss of revenue, scheduling and order acceptance decisions must be taken jointly to maximize total revenue. We present a tabu search algorithm that solves the order acceptance and scheduling problem on a single machine with release dates and sequence dependent setup times. We analyze the performance of the tabu search algorithm on an extensive set of test instances with up to 100 orders and compare it with two heuristics from the literature. In the comparison, we report optimality gaps which are calculated with respect to bounds generated from a mixed integer programming formulation. The results show that the tabu search algorithm gives near optimal solutions that are significantly better compared to the solutions given by the two heuristics. Furthermore, the run time of the tabu search algorithm is very small, even for 100 orders. The success of the proposed heuristic largely depends on its capability to incorporate in its search acceptance and scheduling decisions simultaneously.     

A tabu search algorithm for the job shop problem with sequence dependent setup times

This paper addresses the classic job shop scheduling problem where sequence dependent setup times are present. Based on a modified disjunctive graph, we further investigate and generalize structural properties for the problem under study. A tabu search algorithm with a sophisticated neighbourhood structure is then developed. Compared to most studies in this research area, we are interested in moving internal critical operations rather than merely focusing on non-internal ones. Moreover, neighbourhood functions are defined using insertion techniques instead of simple swaps. Test results show that our algorithm outperforms a simulated annealing algorithm which is recently published. We have also conducted experiments considering the efficiency of developed propositions.     

A GES/TS algorithm for the job shop scheduling

The job shop scheduling problem is a difficult combinatorial optimization problem. This paper presents a hybrid algorithm which combines global equilibrium search, path relinking and tabu search to solve the job shop scheduling problem. The proposed algorithm used biased random sampling to have a better covering of the solution space. In addition, a new version of N6 neighborhood is applied in a tabu search framework. In order to evaluate the algorithm, comprehensive tests are applied to it using various standard benchmark sets. Computational results confirm the effectiveness of the algorithm and its high speed. Besides, 19 new upper bounds among the unsolved problems are found.     

A tabu search algorithm for parallel machine total tardiness problem

In this study, we consider the problem of scheduling a set of independent jobs with sequence dependent setups on a set of uniform parallel machines such that total tardiness is minimized. Jobs have non-identical due dates and arrival times. A tabu search (TS) approach is employed to attack this complex problem. In order to obtain a robust search mechanism, several key components of TS such as candidate list strategies, tabu classifications, tabu tenure and intensification/diversification strategies are investigated. Alternative approaches to each of these issues are developed and extensively tested on a set of problems obtained from the literature. The results obtained are considerably better than those reported previously and constitute the best solutions known for the benchmark problems as to date. Scope and purposeSeveral surveys on parallel machine scheduling with due date related objectives (Oper. Res. 38(1) (1990) 22; EJOR 38 (1989) 156; Oper. Res. 42 (1994) 1025) reveal that the NP-hard nature of the problem renders it a challenging area for many researchers who studied various versions. However, most of these studies make the assumption that jobs are available at the beginning of the scheduling period, which is an important deviation form reality. In this study, as well as distinct due dates and ready times, features such as sequence dependent setup times and different processing rates for machines are incorporated into the classical model. These enhancements approach the model to the actual practice at the expense of complicating the problem further. For this complex problem, we present a tabu search (TS) algorithm to minimize total tardiness and provide the best solutions known for a set of benchmark problems.