Actual Processing Time Of Job Research Articles

Online Parallel-Batch Scheduling of Learning Effect Jobs with Incompatible Job Families for Prefabricated Components

In the production scheduling of prefabricated components, we study an online [Formula: see text] parallel-batch machines scheduling model considering learning effect jobs with [Formula: see text] incompatible job families to minimize the makespan in this paper, where the capacity of batch is unbounded. Job families indicate that a job must belong to some job family and jobs of distinct job families are incapable to be executed in the same batch. The information of each job including its basic processing time [Formula: see text] and release time [Formula: see text] is unknown in advance and is revealed at the instant of its arrival. Moreover, the actual processing time of job [Formula: see text] with learning effect is [Formula: see text], where [Formula: see text] and [Formula: see text] are non-negative parameters and [Formula: see text] denotes the starting time of prefabricated job [Formula: see text], respectively. When [Formula: see text], we propose an online algorithm with a competitive ratio of [Formula: see text]. Furthermore, the performance of the online algorithm is demonstrated by numerical experiments.

Solving a stochastic hierarchical scheduling problem by VNS-based metaheuristic with locally assisted algorithms

High-end equipment manufacture has features of intensive technology, uncertain process, and large scale. Hence, the scheduling of the High-end equipment manufacture is challenging. Large ships are a type of High-end equipment that is tied to national maritime security. In this paper, we study a stochastic hierarchical scheduling problem with serial-batch processing machines and the deterioration effect in ship manufacture. In the studied problem, the job processing time is uncertain and follows a normal probability distribution. Under the deterioration effect, the actual processing time of jobs is formulated as a function of the start time. The first objective is to maximize the robustness of the manufacturing system. The second objective is to minimize the total inventory cost subjected to the optimization of the first objective. The robustness of the manufacturing system is measured by the worst level of completion probability. The total inventory cost is measured by the difference between the job delivery time and the job completion time. The mathematical model for the studied problem is formulated. Some structural properties are derived to solve the problem. Based on the properties, the optimal sequence for the first objective can be obtained and a heuristic algorithm is designed to optimize the second objective. The considered problem is NP-hard involving several non-linearities. Hence, a variable neighborhood search (VNS) algorithm is developed to solve the problem in a reasonable time, which is integrated with three local search strategies and a heuristic algorithm. Various problem instances are generated and extensive computational experiments verify that the proposed VNS algorithm outperforms other compared algorithms and has strong robustness.

Comparing linear and non-linear modelling approaches of learning effects in 2-stage flow-shop scheduling problems

Scheduling problems deal with the allocation and sequencing of a set of jobs to a set of production resources (machines, workers) to optimize one or more objective functions. In the literature, traditional deterministic approaches consider that processing times of jobs are fixed, constant and known at the initial time of scheduling. However, this assumption is not realistic particularly in hand-intensive manufacturing, where processing times may vary according to workers’ learning about the production process. To deal with this, this paper considers the problem of jobs scheduling with learning effect in the processing times. In contrast with previous works in the literature, it is not the processing time that changes per se, but the resource (worker) that improves his/her productivity by decreasing the actual job processing time. This paper considers the flow-shop configuration in which all jobs are processed by a set of different workers following the same production routing. It reviews linear and non-linear modelling approaches of the learning effect in processing times, in order to gain insights about the actual impact of such different modelling approaches. A computational comparison of exact solutions based on mathematical modelling of the flow-shop problem is presented for the case of two workers. Experiments were run using random-generated instances. Several insights are drawn regarding the behavior of the different models.

A Chance Constrained Programming Approach for No-Wait Flow Shop Scheduling Problem under the Interval-Valued Fuzzy Processing Time

This work focuses on the study of robust no-wait flow shop scheduling problem (R-NWFSP) under the interval-valued fuzzy processing time, which aims to minimize the makespan within an upper bound on total completion time. As the uncertainty of actual job processing times may cause significant differences in processing costs, a R-NWFSP model whose objective function involves interval-valued fuzzy sets (IVFSs) is proposed, and an improved SAA is designed for its efficient solution. Firstly, based on the credibility measure, chance constrained programming (CCP) is utilized to make the deterministic transformation of constraints. The uncertain NWFSP is transformed into an equivalent deterministic linear programming model. Then, in order to tackle the deterministic model efficiently, a simulated annealing algorithm (SAA) is specially designed. A powerful neighborhood search method and new acceptance criterion are applied to find better solutions. Numerical computations demonstrate the high efficiency of the SAA. In addition, a sensitivity analysis convincingly shows that the applicability of the proposed model and its solution strategy under interval-valued fuzzy sets.

A dynamic optimisation approach for a single machine scheduling problem with machine conditions and maintenance decisions

In modern production systems, considering machine conditions is becoming essential to achieving an overall optimisation of the production schedule. This paper studies a single machine scheduling problem, where the actual processing times of jobs depend on their position in the production sequence and maintenance is considered. Moreover, the machine is subject to an uncertain condition variation. There is a trade-off between rejecting a maintenance action, resulting in longer processing times, and accepting a maintenance action, leading to higher processing efficiency for future jobs. The problem is formulated as a finite-horizon Markov Decision Process. The objective is to minimise the makespan. Optimality properties are analysed, based on which a dynamic optimisation approach is developed. Computational experiments demonstrate the effectiveness of the proposed approach.

Multitasking scheduling and due date assignment with deterioration effect and efficiency promotion

We investigate a multitasking scheduling and due date assignment problem with position-dependent deterioration effect and efficiency promotion. Multitasking scheduling allows the processing of a primary job being interrupted by the waiting jobs that are available but unfinished. The duration of processing a primary job is comprised of three parts: the processing time of the remaining part of the primary job, the interruption time denoting the time of the partial processing of the waiting jobs, and the switching time denoting the time during which no jobs are processed when the primary job being scheduled. We consider two behavioral factors which may affect the production efficiency. One is the position-dependent deterioration effect on primary jobs, and the other is the linear efficiency promotion on waiting jobs. The position-dependent deterioration effect means that the productivity deteriorates over time due to personnel fatigue, thereby increasing the actual processing times of primary jobs depending on their scheduled positions. The efficiency promotion indicates that switching between different jobs can keep them from being bored, thereby leading to an increase in productivity when operators tackle the interruption parts of waiting jobs. The due dates of jobs are decision variables in two well-known due date assignment models, i.e., the common and unrestricted due date assignment models. We study several scheduling criteria including the makespan, the total completion time, and two due date-related criteria. For each considered problem, we design an efficient polynomial time algorithm, and present the structural properties of the optimal schedules under different conditions considering the relationships between deterioration effect and efficiency promotion.

Refined conditions for V-shaped optimal sequencing on a single machine to minimize total completion time under combined effects

We address single-machine scheduling problems for which the actual processing times of jobs are subject to various effects, including a positional effect, a cumulative effect and their combination. We review the known results on the problems to minimize the makespan, the sum of the completion times and their combinations and identify the problems for which an optimal sequence cannot be found by simple priority rules such as Shortest Processing Time (SPT) and/or Longest Processing Time (LPT). Typically, these are problems to minimize the sum of the completion times under a deterioration effect, and we verify under which conditions for these problems an optimal permutation is V-shaped (an LPT subsequence followed by an SPT subsequence). We demonstrate that previously used techniques for proving that an optimal sequence is V-shaped are not properly justified. We use the corrected method to describe a wide range of problems with a pure positional effect and a combination of a cumulative effect with a positional effect for which an optimal sequence is V-shaped. On the other hand, we show that even the refined approach has its limitations.

Solution algorithms for single-machine resource allocation scheduling with deteriorating jobs and group technology

ABSTRACTThis article deals with a single-machine resource allocation scheduling problem with deteriorating jobs. Under a group technology environment, the actual processing times of jobs are a convex resource allocation function of their starting time and the amount of resource allocation. The objective is to minimize the weighted sum of makespan and resource allocation cost. For two special cases, it is proved that the problem can be solved in polynomial time. For the general case of the problem, heuristic and branch-and-bound procedures are developed to solve the problem. Computational experiments are also performed to examine the effectiveness and the efficiency of the algorithms.

Scheduling parallel machine problem under general effects of deterioration and learning with past-sequence-dependent setup time: heuristic and meta-heuristic approaches

This study investigates an identical parallel machine scheduling problem with past-sequence-dependent setup times and general effects of deteriorating and learning. The actual job processing time on each machine is defined by a two-element function of the normal processing times of the preprocessed jobs and its scheduled position on the same machine. Moreover, the job setup time on each machine is a function of the actual processing times of the preprocessed jobs on the same machine. A novel mixed-integer programming model is developed to satisfy the goal of minimizing total completion time. Due to the NP-hard characteristic and intractability of the problem, three efficient methodologies including a heuristic algorithm (HA), a genetic algorithm (GA) with an enhanced exploration ability and an ant colony optimization (ACO) combined with a new stochastic elitism strategy are designed to find optimal/near-optimal solutions within an appropriate period of time. The effectiveness and efficiency of the presented model and the proposed algorithms are verified by computational experiments. The computational results indicate that the suggested algorithms are effective and executable approaches to generate solutions as good as optimal solution in the small-sized problems. Also, the ACO statistically outperformed the HA and GA in the medium- and large-sized problems.

Dominance rule and opposition-based particle swarm optimization for two-stage assembly scheduling with time cumulated learning effect

This paper introduces a two-stage assembly flowshop scheduling model with time cumulated learning effect, which exists in many realistic scheduling settings. By the time cumulated learning effect, we mean that the actual job processing time of a job depends on its scheduled position as well as the processing times of the jobs already processed. The first stage consists of two independently working machines where each machine produces its own component. The second stage consists of a single assembly machine. The objective is to identify a schedule that minimizes the total completion time of all jobs. With analysis on the discussed problem, some dominance rules are developed to optimize the solving procedure. Incorporating with the developed dominance rules, a dominance rule and opposition-based particle swarm optimization algorithm (DR-OPSO) and branch-and-bound are devised. Computational experiments have been conducted to compare the performances of the proposed DR-OPSO and branch-and-bound through comparing with the standard O-PSO and PSO. The results fully demonstrate the efficiency and effectiveness of the proposed DR-OPSO algorithm, providing references to the relevant decision-makers in practice.

Two-agent stochastic flow shop deteriorating scheduling via a hybrid multi-objective evolutionary algorithm

Multi-agent and deteriorating scheduling has gained an increasing concern from academic and industrial communities in recent years. This study addresses a two-agent stochastic flow shop deteriorating scheduling problem with the objectives of minimizing the makespan of the first agent and the total tardiness of the second agent. In the investigated problem, the normal processing time of jobs is a random variable, and the actual processing time of jobs is a linear function of their normal processing time and starting time. To solve this problem efficiently, this study proposes a hybrid multi-objective evolutionary algorithm which is a combination of an evolutionary algorithm and a local search method. It maintains two populations and one archive. The two populations are utilized to execute the global and local searches, where one population employs an evolutionary algorithm to explore the whole solution space, and the other applies a local search method to exploit the promising regions. The archive is used to guide the computation resource allocation in the search process. Some special techniques, i.e., evolutionary methods, local search methods and information exchange strategies between two populations, are designed to enhance the exploration and exploitation ability. Comparing with the classical and popular multi-objective evolutionary algorithms on some test instances, the experimental results show that the proposed algorithm can produce satisfactory solution for the investigated problem.

Minimizing the Makespan for a Two-Stage Three-Machine Assembly Flow Shop Problem with the Sum-of-Processing-Time Based Learning Effect

Two-stage production process and its applications appear in many production environments. Job processing times are usually assumed to be constant throughout the process. In fact, the learning effect accrued from repetitive work experiences, which leads to the reduction of actual job processing times, indeed exists in many production environments. However, the issue of learning effect is rarely addressed in solving a two-stage assembly scheduling problem. Motivated by this observation, the author studies a two-stage three-machine assembly flow shop problem with a learning effect based on sum of the processing times of already processed jobs to minimize the makespan criterion. Because this problem is proved to be NP-hard, a branch-and-bound method embedded with some developed dominance propositions and a lower bound is employed to search for optimal solutions. A cloud theory-based simulated annealing (CSA) algorithm and an iterated greedy (IG) algorithm with four different local search methods are used to find near-optimal solutions for small and large number of jobs. The performances of adopted algorithms are subsequently compared through computational experiments and nonparametric statistical analyses, including the Kruskal–Wallis test and a multiple comparison procedure.

A blocking flow shop deteriorating scheduling problem via a hybrid chemical reaction optimization

This study presents a blocking flow shop deteriorating scheduling problem which has a widespread application in manufacturing and service systems. In the investigated problem, there is no buffer between machines, and the actual processing time of jobs on each machine is described as a linear function of their starting time and normal processing time. In order to deal with this problem more efficiently, this study develops a hybrid chemical reaction optimization algorithm, where some special strategies are developed based on the problem characteristics, for example, solution representation, on-wall ineffective collision, decomposition, inter-molecule ineffective collision, and synthesis reactions. In addition, a variable neighborhood search is designed to strengthen the search ability of the chemical reaction optimization algorithm. Computational simulation experiments on a set of instances and performance comparisons are provided. They show that the proposed algorithm is superior to the standard chemical ...

A rule-based genetic algorithm with an improvement heuristic for unrelated parallel machine scheduling problem with time-dependent deterioration and multiple rate-modifying activities

In this article, we consider an unrelated parallel machine scheduling (UPMS) problem with time-dependent deterioration and multiple rate-modifying activities (RMAs). The actual processing time of a job is defined by a linear function of a gap between starting time of the job and ending time of the recent RMA. The starting rate of the actual processing time of jobs is restored to the original processing time through the application of RMAs. In the UPMS problem, we simultaneously determine the schedule of jobs and the number and positions of RMAs to minimize the makespan. To solve the problem, a mixed integer linear programming (MILP) model for the problem is developed to find the optimal solution. Then, we propose a novel rule-based genetic algorithm (GA) with a chromosome representing job assigning sequence to one of the machines and the schedule of jobs and the number and positions of RMAs in each machine are determined by a completion time rule-based dispatching heuristic during the decoding process of the chromosome. To enhance the solution effectiveness, an improvement heuristic is implemented to the GA. Extensive computational experiments are conducted through randomly generated examples to evaluate the performance of the proposed algorithms.

Single-machine and parallel-machine serial-batching scheduling problems with position-based learning effect and linear setup time

This paper introduces the serial batching scheduling problems with position-based learning effect, where the actual job processing time is a function of its position. Two scheduling problems respectively for single-machine and parallel-machine are studied, and in each problem the objectives of minimizing maximum earliness and total number of tardy jobs are both considered respectively. In the proposed scheduling models, all jobs are first partitioned into serial batches, and then all batches are processed on the serial-batching machine. We take some practical production features into consideration, i.e., setup time before processing each batch increases with the time, regarded as time-dependent setup time, and we formalize it as a linear function of its starting time. Under the single-machine scheduling setting, structural properties are derived for the problems with the objectives of minimizing maximum earliness and number of tardy jobs respectively, based on which optimization algorithms are developed to solve them. Under the parallel-machine scheduling setting, a hybrid VNS–GSA algorithm combining variable neighborhood search (VNS) and gravitational search algorithm (GSA) is proposed to solve the problems with these two objectives respectively, and the effectiveness and efficiency of the proposed VNS–GSA are demonstrated and compared with the algorithms of GSA, VNS, and simulated annealing (SA). This paper demonstrates that the consideration of different objectives leads to various optimal decisions on jobs assignment, jobs batching, and batches sequencing, which generates a new insight to investigate batching scheduling problems with learning effect under single-machine and parallel-machine settings.

Single-machine past-sequence-dependent setup times scheduling with resource allocation and learning effect

This paper addresses single-machine scheduling problem with resource allocation and learning effect in the background of past-sequence-dependent (p-s-d) setup times. In the proposed model of this paper, the actual job processing times are dependent on learning effect and the amount of resource allocated, and the setup times are proportional to the length of the already processed jobs. The resource function used here is a general convex one. The optimal job sequence and the optimal amount of resource allocated to each job are determined jointly for the objective function yielded by a combination of the total completion time, total absolute differences in completion times, and the total resource consumption. Besides, we also discuss some extension and special cases of this problem. It is shown that all the problems under study are polynomially solvable while the complexity results are different.

Hybrid Pareto artificial bee colony algorithm for multi-objective single machine group scheduling problem with sequence-dependent setup times and learning effects.

Group scheduling is significant for efficient and cost effective production system. However, there exist setup times between the groups, which require to decrease it by sequencing groups in an efficient way. Current research is focused on a sequence dependent group scheduling problem with an aim to minimize the makespan in addition to minimize the total weighted tardiness simultaneously. In most of the production scheduling problems, the processing time of jobs is assumed as fixed. However, the actual processing time of jobs may be reduced due to “learning effect”. The integration of sequence dependent group scheduling problem with learning effects has been rarely considered in literature. Therefore, current research considers a single machine group scheduling problem with sequence dependent setup times and learning effects simultaneously. A novel hybrid Pareto artificial bee colony algorithm (HPABC) with some steps of genetic algorithm is proposed for current problem to get Pareto solutions. Furthermore, five different sizes of test problems (small, small medium, medium, large medium, large) are tested using proposed HPABC. Taguchi method is used to tune the effective parameters of the proposed HPABC for each problem category. The performance of HPABC is compared with three famous multi objective optimization algorithms, improved strength Pareto evolutionary algorithm (SPEA2), non-dominated sorting genetic algorithm II (NSGAII) and particle swarm optimization algorithm (PSO). Results indicate that HPABC outperforms SPEA2, NSGAII and PSO and gives better Pareto optimal solutions in terms of diversity and quality for almost all the instances of the different sizes of problems.

Minimizing Makespan with Start Time-Dependent Jobs in a Two-Machine Flow Shop

[if gte mso 9]> The purpose of this paper is to consider the problem of scheduling a set of start time-dependent jobs in a two-machine flow shop, in which the actual processing times of jobs increase linearly according to their starting time. The objective of this problem is to minimize the makespan. The problem is known to be NP-hardness[ah1] ; therefore, there is no polynomial-time algorithm to solve it optimally in a reasonable time. So, a branch-and-bound algorithm is proposed to find the optimal solution by means of dominance rules, upper and lower bounds. Several easy heuristic procedures are also proposed to derive near-optimal solutions. To evaluate the performance of the proposed algorithms, the computational experiments are extracted based on the recent literature. Deteriorating jobs lead to an increase in the makespan of the problems; therefore, it is important to obtain the optimal or near-optimal solution. Considering the complexity of the problem, the branch-and-bound algorithm is capable of solving problems of up to 26 jobs. Additionally, the average error percentage of heuristic algorithms is less than 1.37%; therefore, the best one is recommended to obtain a near-optimal solution for large-scale problems.

A hybrid genetic algorithm with two-stage dispatching heuristic for a machine scheduling problem with step-deteriorating jobs and rate-modifying activities

This article is concerned with a single machine scheduling problems that integrate by step-deterioration along with multiple rate-modifying activities (RMAs). The actual processing time of a job is defined by a step function of its starting time and a specific deterioration threshold. The starting rate of the actual processing time of jobs is restored through the application of RMAs, which recover the original processing time. In this scheduling environment, we simultaneously determine the schedule of step-deteriorating jobs and the number and positions of RMAs to minimize the makespan. We derive a mixed integer programming model to obtain the optimal solution and propose a hybrid genetic algorithm with a two-stage dispatching heuristic represented by a simple chromosome. The performance of the proposed genetic algorithm (GA) is compared with GAs with two types of chromosome representations using randomly generated test instances.

기대 평균흐름시간 최소화를 위한 단일설비 일정계획의 성능변동 분석

A single machine scheduling problem for jobs with stochastic processing time is considered in this study. Shortest processing time (SPT) sequencing according to the expected processing times of jobs is optimal for schedules with minimal expected mean flow time when all the jobs arrive to be scheduled and their expected processing times are known. However, SPT sequencing according to the expected processing time may not be optimal for the minimization of the mean flow time when the actual processing times of jobs are known. This study evaluates the complexity of SPT sequencing through a comparison of the mean flow times of schedules based on the expected processing times and actual processing times of randomly generated jobs. Evaluation results show that SPT sequencing according to the expected flow time exhibits chaotic variation to the optimal mean flow time. The relative deviation from the optimal mean flow time increases as the number of jobs, processing time, or coefficient of variation increases.