On the scheduling with past-sequence-dependent setup times and learning effects on a single machine

This paper deals with a single-machine scheduling problem with setup time and learning effects. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are job-independent and past-sequence-dependent, and the learning effects are job-independent and position-dependent. The objective is to minimize the sum of earliness penalties subject to no tardy jobs. Wang, Wang, Gao, and Huang [Int J Adv Manuf Technol 48: 739–746, 2010] showed that an optimal sequence for this problem could be obtained by arranging jobs in non-increasing order of processing times. In this paper, we first demonstrate that this result is incorrect, and then introduce new exact solution strategies that polynomially solve problems whose earliness penalties are strictly increasing functions of job earliness. Polynomial time solutions are also presented for some special cases.     

Scheduling with deteriorating jobs and past-sequence-dependent setup times

In this paper, we presented a scheduling model in which the deteriorating jobs and the setup times are considered at the same time. Under the proposed model, the actual job processing time is a general function of the processing times of jobs already processed and its scheduled position, while the setup time is past-sequence-dependent. We provided the optimal schedules for some single-machine scheduling problems.     

Deteriorating jobs and learning effects on a single-machine scheduling with past-sequence-dependent setup times

In this paper, we consider the single-machine setup times scheduling with the effects of learning and deterioration. By the effects of learning and deterioration, we mean that the actual processing time of a job depends not only on the processing times of the jobs already processed but also on its scheduled position. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We show that the problems to minimize the makespan, the total completion time, and the sum of the $\mathit{\delta}$ th ( ${\mathit{\delta}} \geq 0$ ) power of job completion times are polynomially solvable. We also show that the total weighted completion time minimization problem, the maximum lateness minimization problem, and the number of tardy jobs minimization problem can be solved in polynomial time under certain conditions.     

Single-machine scheduling with past-sequence-dependent setup times and effects of deterioration and learning

The paper deals with some single-machine scheduling problems with setup time considerations where the processing time of a job is given as a function of its starting times and position in a sequence. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We consider the following objective functions: the makespan, the total completion time, the sum of the δth ( $ \delta \geqslant 0 $ ) power of job completion times, the total weighted completion time, the maximum lateness and the number of tardy jobs. We show that the makespan minimization problem, the total completion time minimization problem, and the sum of the δth power of job completion times minimization problem can be solved in polynomial time, respectively. We also show that the total weighted completion time minimization problem, the maximum lateness minimization problem and the number of tardy jobs minimization problem can be solved in polynomial time under certain conditions.     

A note on deteriorating jobs and learning effects on a single-machine scheduling with past-sequence-dependent setup times

A result in a recent paper by Yin et al. (Int J Adv Manuf Technol 46:707–714, (2010) is incorrect because job processing times are variable due to both deteriorating jobs and learning effects, a consideration which was not taken into account by the authors. In this note, we show by a counter-example that the published result is incorrect.     

Note to: Deteriorating jobs and learning effects on a single-machine scheduling with past-sequence-dependent setup times

Some results in a recent paper (Yin et al., Int J Adv Manuf Technol 46:707–714, 2010) are incorrect. In this note, we show by a counterexample that the results are incorrect.     

Some single-machine scheduling problems with past-sequence-dependent setup times and a general learning effect

This paper considers a single-machine scheduling model with past-sequence-dependent setup times and a general learning effect. It develops a general model with setup times and learning effect considerations where the actual processing time of a job is not only a function of the total actual processing time of the jobs already processed, but also a function of the job’s scheduled position. The paper shows that the single-machine scheduling problems to minimize the makespan and the sum of the kth power of completion times are polynomially solvable under the proposed model. It further shows that the problems to minimize the total weighted completion time and the maximum lateness are polynomially solvable under certain conditions.     

Scheduling parallel machines with major and minor setup times

This article discusses the problem of scheduling a large set of parts on an FMS so as to minimize the total completion time. Here, the FMS consists of a set of parallel identical machines. Setup time is incurred whenever a machine switches from one type of part to another. The setup time may be large or small depending on whether or not the two part types belong to the same family. This article describes a fast heuristic for this scheduling problem and derives a lower bound on the optimal solution. In computational tests using random data and data from an IBM card test line, the heuristic archieves nearly optimal schedules.     

Scheduling jobs on dynamic parallel machines with sequence-dependent setup times

Dynamic parallel machine scheduling problems (DPMSPs) with sequence-dependent setup times represent a very important production scheduling problem but remain under-represented in the research literature. In this study, a restricted simulated annealing (RSA) algorithm that incorporates a restricted search strategy with the elimination of non-effect job moves to find the best neighborhood schedule is presented. The proposed RSA algorithm can reduce search efforts significantly while minimizing maximum lateness on DPMSPs. Extensive computational experiments demonstrate that the proposed RSA algorithm is highly effective as compared to the basic simulated annealing and existing algorithms on the same benchmark problem data set.     

双目标函数下需要安装时间的平行多功能机排序问题

讨论了双目标函数下需要安装时间的平行多功能机排序问题。在该问题中,每个工件对应机器集合的一个子集,且每个工件只能在相应子集中的任一台机器上加工,工件分组,不同组中的工件连续加工需要安装时间,目标函数为极小化最大完工时间和安装次数。根据实际应用背景确定双目标排序问题的形式,并证明了该问题是NP—难的。设计了一个求启发式有效解的算法,首先按照特定的规则将所有工件组都整组地安排到各台机器上,然后逐步改进最大完工时间和拆分工件组,从而得到一系列的启发式有效解。实验表明,该算法是实用而有效的。     

Scheduling on unrelated parallel machines with sequence- and machine-dependent setup times and due-date constraints

We consider the unrelated parallel-machine scheduling problem with sequence- and machine-dependent setup times and due-date constraints. There are N jobs, each having a due date and requiring a single operation on one of the M machines. A setup is required if there is a switch from processing one type of job to another. Due to the characteristics of machines, the processing time depends upon the job and machine on which the job is processed, and the setup time is sequence and machine dependent. In addition, certain jobs have strict due-date constraints. An effective heuristic based on a modified apparent-tardiness-cost-with-setup procedure, the simulated annealing method, and designed improvement procedures is proposed to minimize the total tardiness of this scheduling problem. Computational characteristics of the proposed heuristic are evaluated through an extensive experiment using a newly created data set. Computational results show that the proposed heuristic is able to effectively improve the initial solutions, obtained by a modified apparent-tardiness-cost-with-setup procedure, and obtains better results than a random descent heuristic.     

Scheduling hybrid flow shop with sequence-dependent setup times and machines with random breakdowns

Much of the research on operations scheduling problems has either ignored setup times or assumed that setup times on each machine are independent of the job sequence. Furthermore, most scheduling problems which have been discussed in the literature are under the assumption that machines are continuously available. Nevertheless, in most real life industries, a machine can be unavailable for many reasons, such as unanticipated breakdowns, i.e., stochastic unavailability, or due to a scheduled preventive maintenance where the periods of unavailability are known in advance, i.e., deterministic unavailability. This paper deals with the hybrid flow shop scheduling problems in which there are sequence-dependent setup times, commonly known as the SDST, and machines which suffer stochastic breakdown to optimize objectives based on expected makespan. This type of production system is found in industries such as chemical, textile, metallurgical, printed circuit board, and automobile manufacture. With the increase in manufacturing complexity, conventional scheduling techniques for generating a reasonable manufacturing schedule have become ineffective. The genetic algorithm can be used to tackle complex problems and produce a reasonable manufacturing schedule within an acceptable time. This paper describes how we can incorporate simulation into genetic algorithm approach to the scheduling of a SDST hybrid flow shop with machines that suffer stochastic breakdown. An overview of the hybrid flow shops and scheduling under stochastic unavailability of machines are presented. Subsequently, the details of incorporated simulation into genetic algorithm approach are described and implemented. Consequently, the results obtained are analyzed with Taguchi experimental design.     

Hybrid metaheuristics for unrelated parallel machine scheduling with sequence-dependent setup times

This paper proposes several hybrid metaheuristics for the unrelated parallel-machine scheduling problem with sequence-dependent setup times given the objective of minimizing the weighted number of tardy jobs. The metaheuristics begin with effective initial solution generators to generate initial feasible solutions; then, they improve the initial solutions by an approach, which integrates the principles of the variable neighborhood descent approach and tabu search. Four reduced-size neighborhood structures and two search strategies are proposed in the metaheuristics to enhance their effectiveness and efficiency. Five factors are used to design 32 experimental conditions, and ten test problems are generated for each condition. Computational results show that the proposed hybrid metaheuristics are significantly superior to several basic tabu search heuristics under all the experimental conditions.     

Minimizing total weighted tardiness on a single machine with sequence-dependent setup and future ready time

This paper minimizes total weighted tardiness on a single machine with sequence-dependent setup time and future ready time. The sequence-dependent setup is classified into two categories: continuous sequence-dependent setup and separable sequence-dependent setup. The former is the conventional type, which needs a part on a machine to setup, while the latter does not. The weighted shortest processing time (WSPT) term, the slack term, and the ready time term of the apparent tardiness cost (ATC)-based rules are analyzed. Two dispatching rules, ATC with ready time and continuous setup (ATCRCS) and ATC with ready time and separable setup (ATCRSS), are proposed for the problems which setup are the continuous type and the separable type, respectively. These new rules are evaluated by the best-of-the-best measure and the territory measure of the performance.     

Scheduling hybrid flowshops with sequence dependent setup times to minimize makespan and maximum tardiness

This article addresses the problem of scheduling hybrid flowshops where the setup times are sequence dependent to minimize makespan and maximum tardiness. To solve such an NP-hard problem, we introduce a novel simulated annealing (SA) with a new concept, called “Migration mechanism”, and a new operator, called “Giant leap”, to bolster the competitive performance of SA through striking a compromise between the lengths of neighborhood search structures. We hybridize the SA (HSA) with a simple local search to further equip our algorithm with a new strong tool to promote the quality of final solution of our proposed SA. We employ the Taguchi method as an optimization technique to extensively tune different parameters and operators of our algorithm. Taguchi orthogonal array analysis is specifically used to pick the best parameters for the optimum design process with the least number of experiments. We established a benchmark to draw an analogy between the performance of SA with other algorithms. Two basically different objective functions, minimization of makespan and maximum tardiness, are taken into consideration to evaluate the robustness and effectiveness of the proposed HSA. Furthermore, we explore the effects of the increase in the number of jobs on the performance of our algorithm to make sure it is effective in terms of both the acceptability of the solution quality and robustness. The excellence and strength of our HSA are concluded from all the results acquired in various circumstances.     

Scheduling deteriorating jobs to minimize the makespan on a single machine

Machine scheduling problems with deteriorating jobs have received increasing attention in recent years, mostly focusing on the linear deterioration models. However, if certain maintenance procedures fail to be completed prior to a prespecified deadline, jobs will require extra time for successful accomplishment in some situations. Therefore, this paper addresses a single-machine problem where the objective is to minimize the makespan under the piecewise linear deterioration model. A branch-and-bound algorithm and two heuristic algorithms are provided to search for the optimal solution and near-optimal solutions, respectively. Computational results are also presented to evaluate the performance of the proposed algorithms.     

Sequencing of an M machine flow shop with setup, processing and removal times separated

In this research, a flow shop scheduling problem in which setup, processing and removal times are separated, with the objective of minimizing makespan, is considered. A tabu search based heuristic is presented for solving the addressed problem. The proposed heuristic begins with the construction of artificial processing times for each operation; then a modified NEH algorithm is used to generate an initial solution, followed by a designed tabu search procedure applied for further improvement of the solution. The proposed heuristic, as well as the existing one, is evaluated in a large number of randomly generated problems. The results of the experimental investigations of the proposed heuristic algorithm and the existing heuristic in meeting the objective of makespan are also reported. It is found that the solution quality of the proposed tabu search heuristic is better than that of the existing heuristic, but for large size problems more computational efforts are needed; however, the CPU time is still acceptable.     

Scheduling a single machine with multiple preventive maintenance activities and position-based deteriorations using genetic algorithms

In this paper, we study a single machine scheduling problem with deteriorating processing time of jobs and multiple preventive maintenances which reset deteriorated processing time to the original processing time. In this situation, we consider three kinds of problems whose performance measures are makespan, total completion time, and total weighted completion time. First, we formulate integer programming formulations, and using the formulations, one can find optimal solutions for small problems. Since these problems are known to be NP-hard and the size of real problem is very large, we propose a number of heuristics and design genetic algorithms for the problems. Finally, we conduct some computational experiments to evaluate the performance of the proposed algorithms.     

Bicriteria scheduling of a two-machine flowshop with sequence-dependent setup times

A two-machine flowshop scheduling problem is addressed to minimize setups and makespan where each job is characterized by a pair of attributes that entail setups on each machine. The setup times are sequence-dependent on both machines. It is shown that these objectives conflict, so the Pareto optimization approach is considered. The scheduling problems considering either of these objectives are $ \mathcal{N}{\wp } - {\text{hard}} $ , so exact optimization techniques are impractical for large-sized problems. We propose two multi-objective metaheurisctics based on genetic algorithms (MOGA) and simulated annealing (MOSA) to find approximations of Pareto-optimal sets. The performances of these approaches are compared with lower bounds for small problems. In larger problems, performance of the proposed algorithms are compared with each other. Experimentations revealed that both algorithms perform very similar on small problems. Moreover, it was observed that MOGA outperforms MOSA in terms of the quality of solutions on larger problems.