Worst-case and numerical analysis of heuristic algorithms for flowshop scheduling problems with a time-dependent learning effect

Research on no-idle permutation flowshop scheduling with time-dependent learning effect and deteriorating jobs

This paper considers the combination of the general sum-of-processing-time effect and position-dependent effect on a single machine. The actual processing time of a job is defined by functions of the sum of the normal processing times of the jobs processed and its position and control parameter in the sequence. We consider two monotonic effect functions: the nondecreasing function and the nonincreasing function. Our focus is the following objective functions, including the makespan, the sum of the completion time, the sum of the weighted completion time, and the maximum lateness. For the nonincreasing effect function, polynomial algorithm is presented for the makespan problem and the sum of completion time problem, respectively. The latter two objective functions can also be solved in polynomial time if the weight or due date and the normal processing time satisfy some agreeable relations. For the nondecreasing effect function, assume that the given parameter is zero. We also show that the makespan problem can remain polynomially solvable. For the sum of the total completion time problem and a 1 is the deteriorating rate of the jobs, there exists an optimal solution for a 1 ≥ M ; a V-shaped property with respect to the normal processing times is obtained for 0 < a 1 ≤ 1 . Finally, we show that the sum of the weighted completion problem and the maximum lateness problem have polynomial-time solutions for a 1 > M under some agreeable conditions, respectively.

This paper presents a predictive robust and stable approach for a two-machine flow shop scheduling problem with machine disruption and uncertain job processing time. Indeed, a general approach is proposed that can be used for robustness and stability optimization in an m-machine flow shop or job shop scheduling problem. The robustness measure is the total expected realized completion time. The expected sum of squared aberration between each jobs’ completion time in the realized and initial schedules is the stability measure. We proposed and compared two methods to deal with such an NP-hard problem; a method based on decomposing the problem into sub-problem and solving each sub-problem, and a theorem-based method. The extensive computational results indicated that the second method has a better performance in terms of robustness and stability, especially in large-sized problems. In other words, the second method is preferable because of the better manufacturer responsiveness to the customer and the production staff satisfaction enhancement.

Over the last two decades, various software reliability growth models (SRGM) have been proposed, and there has been a gradual but marked shift in the balance between software reliability and software testing cost in recent years. Chiu and Huang (2008) provided a Software Reliability Growth Model from the Perspective of Learning Effects, which is able to reasonably describe the S-shaped and exponential-shaped types of behaviors simultaneously, and offers better performance when fitting different data with consideration of the learning effects. However, this earlier model assumes that the learning effects are constant. In contrast, this paper discusses a software reliability growth model with time-dependent learning effects.

Hybrid monkey search algorithm for flow shop scheduling problem under makespan and total flow time

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.

This paper introduces the parallel machine scheduling problems with work related musculoskeletal disorder (WMSD) risk considerations. By the WMSD consideration, we mean that job processing times are an increasing function of occupational repetitive technical actions (OCRA) risk factor. The OCRA index was recruited for risk assessment of occupational repetitive technical actions. WMSD risks were modeled with cumulative mean value of OCRA index. Due to NP-Hard structure of parallel machine scheduling problems with WMSD considerations and learning rate, the solution cannot be found always. However, problem can be solved by transforming assignment problem. In spite of the fact that the computational effort remains O (n 4 ), problem is solved within more efficient time. In this study, a model that includes learning effect and WMSD risk was proposed. WMSD risk was considered as cumulative mean of risk value throughout shift. In order to the balance between productivity and WMSD risk, jobs’ foreseeable cycle time (FCT) value was changed. It is aimed to decrease mean of risk along schedule without increasing total basic process time. The value of sacrifice from the FCT was compensating from job which have optimal, acceptable, borderline or slight risk level. Process time and risk values were recalculated by using new FCT value. Thus, balanced process times and risk values obtained. Proposed model was solved with Lingo software and sequence of jobs was obtained. Total flow time and mean of risk were compared for balanced and none balanced schedules. Total flow time and mean of risk belong to balanced schedule is smaller than none balanced schedule. It was shown that handled problem is solvable at the polynomial time and total flow time can be improved by bringing balance between WMSD risks and productivity.

We consider the problem of optimizing the total flow time of a stream of jobs that are released over time in a multiprocessor setting. This problem is NP-hard even when there are only two machines and preemption is allowed. Although the total (or average) flow time is widely accepted as a good measurement of the overall quality of service, no approximation algorithms were known for this basic scheduling problem. This paper contains two main results. We first prove that when preemption is allowed, Shortest Remaining Processing Time (SRPT) is an O(log(min{nm,P})) approximation algorithm for the total flow time, where n is the number of jobs, m is the number of machines, and P is the ratio between the maximum and the minimum processing time of a job. We also provide an @W(log(nm+P)) lower bound on the (worst case) competitive ratio of any randomized algorithm for the on-line problem in which jobs are known at their release times. Thus, we show that up to a constant factor SRPT is an optimal on-line algorithm. Our second main result addresses the non-preemptive case. We present a general technique that allows to transform any preemptive solution into a non-preemptive solution at the expense of an O(nm) factor in the approximation ratio of the total flow time. Combining this technique with our previous result yields an O(nmlognm) approximation algorithm for this case. We also show an @W(n^1^3^-^@e) lower bound on the approximability of this problem (assuming P NP).

PurposeThe purpose of this paper is to describe the introduction of simple assembly line balancing problems (SALBPs) under four joint combinations of two learning effects and two deterioration effects.Design/methodology/approachIn this paper, effects of learning and deterioration are considered simultaneously. By the effects of learning and deterioration, it is meant that the task time of a task is defined by increasing function of its execution start time and position in the sequence.FindingsIt was shown that polynomial solutions can be obtained for SALBP under four joint combinations of two learning effects and two deterioration effects. Furthermore, this paper also discusses the adaptations of the proposed models by using known ALB problem.Originality/valueIn this paper, SALBPs were introduced under four joint combinations of two learning effects and two deterioration effects. Position dependent learning effect and time dependent learning effect were considered for learning effect when linear deterioration effect and non‐linear deterioration effect were taken up.

Scheduling jobs under decreasing linear deterioration

In traditional flow shop scheduling problems (FSSPs), the processing times are assumed to be pre-known and fixed parameters while in many practical environments, the processing times can be controlled by consumption of extra resources. In this paper, we propose resource-dependent processing times (RDPT) for permutation FSSP in which the processing time of a job depends on the amount of additional resources assigned to that job. To make a trade-off between makespan and required amount of resources, two conflict objective functions are considered: the minimisation of maximum completion time and the minimisation of total cost of resources. In order to solve the problem considered in this paper, a decomposition approach is suggested that strives to deal with the original model via two sub-problems: (i) sequencing problem; and (ii) resource allocation problem. A hybrid discrete differential evolution (HDDE) algorithm with an effective coordinate directions search and a variable neighbourhood search (VNS) are combined to solve two sub-problems. Furthermore, a statistical procedure is employed to adjust the significant parameters of the proposed HDDE and VNS algorithms. This procedure is based on the stepwise regression (SR) technique. The effectiveness of the suggested hybrid algorithm is investigated through a computational study and obtained results show the good performance of our approach with regard to the other algorithms.

This article addresses a permutation flowshop scheduling problem with rework activities. The concept of a reworkable job here means that a job on a machine may need more than one operation to reach a predefined quality level, stochastically. Therefore in this configuration, processing times become random variables with a known probability distribution. The objective function is the minimization of the expected makespan. The solution mechanism is based on using mathematical expectations of processing times in order to find a job sequence by solving a mixed integer mathematical model, then assessing the makespan of the obtained sequence by running several simulated trials and reporting the mean value. In other words, a flowshop scheduling problem with stochastic processing times on machines is considered in this article, and the solution approach merges a mixed integer programming model and simulation. Finally a comprehensive, randomly generated example is presented for verifying the proposed problem. According to the results, the existence of reworkable jobs in a flowshop scheduling problem can change the optimum job sequence when minimization of the makespan is assumed.

Objectives: In this paper, we consider the Flexible Flowshop Scheduling (FFS) problem with parallel machines. The main objective of this paper is to obtain a good schedule of jobs to minimize the makespan of FFS problem. Methods/Statistical analysis: In this study, two heuristic algorithms have been developed of FFS to reduce the makespan. First, we constructed the new heuristic algorithm based on Minimum Processing Time Selective Approach (MPTSA) and Longest Processing Times (LPT) approach to find the optimal or near optimal sequence for minimization of makespan of FFS problem with parallel machines. Next, we developed the heuristic algorithm using PALMER approach. In the PALMER approach we sequence the jobs based on Longest Slope Value (LSV) and obtained the value of objective function. Findings: We compared both the heuristic algorithms with the help of numerical illustrations. We solved the same numerical by both the heuristic algorithm and result show that our constructed heuristic algorithm has resulted in a better industrial production makespan. The percentage improvement of our constructive heuristic algorithm is also calculated. Gantt chart is also generated to verify the effectiveness of constructed heuristic algorithm. Application/Improvements: Our constructed heuristic algorithm is more effective to reduced the makespan of FFS problems as compare to classic heuristic algorithm as Palmer approach and provide an important tool for decision makers in production management. Keywords: Flexible Flowshop Scheduling, Gantt Chart, LPT Approach, Makespan, MPTSA Approach, Parallel Machines, Percentage Improvement

As an emerging novel evolutionary technique, the immune algorithm has gained a lot of attention and wide applications in various fields of engineering and management. To our knowledge, this paper first considers the application of immune algorithm for the classic permutation flow shop scheduling problem. We present a hybrid heuristic combining immune algorithm and simulated annealing for the n-job, m-machine permutation flow shop scheduling problem to minimize makespan and total flow time. A heuristically directed population-based construction approach in the immune algorithm and a forward/backward shift neighborhood search heuristic in the simulated annealing of the proposed method is utilized to explore the search process for better schedules of jobs as well to speed up the convergence speed of the proposed algorithm. The proposed method is tested with Taillard’s flow shop scheduling benchmark instances for different problems with job sizes varying from 20 to 500. The computational results demonstrate that the proposed heuristic is very competitive with the state-of-the-art procedures in terms of both solution quality and computational times.

Clinical Impact of a Radiologic Quality Initiative Promoting More Timely Communication of Critical Pulmonary Embolus Results