Position-based Learning Effect Research Articles

Single-machine scheduling with periodic maintenance and learning effect

This paper discusses a single-machine scheduling problem with periodic maintenance activities and position-based learning effect to minimize the makespan. To obtain exact solutions of small-scale problems, one new two-stage binary integer programming model is formulated. In addition, a branch and bound algorithm combining boundary method and pruning rules is also proposed. According to the property of the optimal solution, a special search neighborhood is constructed. A hybrid genetic-tabu search algorithm based on genetic mechanism with tabu technique as an operator is proposed to solve medium-scale and large-scale problems. Moreover, to improve the efficiency of genetic algorithm and hybrid genetic-tabu search algorithm, Taguchi method is used for parameter tuning. Furthermore, computational experiments are carried out to compare the efficiency and performance of these algorithms.

Single-Machine Scheduling with a Deteriorating Maintenance Activity and DeJong’s Learning Effect

In this paper, we study the single-machine scheduling problems with DeJong’s learning effect and deteriorating maintenance activity, where DeJong’s learning effect is a special position-based learning effect and the duration of the deteriorating maintenance activity is a linear increasing function of its starting time. Our goal is to determine the job sequence of all jobs and the position of the maintenance activity to minimize some performance measures. When the performance measures are the makespan and the total completion time, we show that both of them can be solved in polynomial time. When the performance measure is the total weighted completion time, we develop a pseudo-polynomial time dynamic programming algorithm under a special case. When the performance measure is the maximum lateness, we show that the earliest due date first (EDD) order is a bad algorithm for the general case, and develop a polynomial time algorithm under a special case.

An optimal online algorithm for single-processor scheduling problem with learning effect

This paper deals with the canonical single-processor online scheduling problem with the position-based learning effect. Specially speaking, a round of jobs arriving online over time will be processed on a single processor. Noticeably, in this model, for each job Jk, the actual processing time pkl is defined as a power function of its position l, i.e., pkl=pklβ, where pk indicates its normal processing time and β≤0 is the learning index. Our goal is to make the sum of completion times as small as possible. For this problem, we testify that there is no online algorithm with a competitive ratio of less than 2. Most notably, we design an online algorithm entitled as Delayed Shortest Normal Processing Time (DSNPT), matching the lower bound proposed by us, and hence DSNPT is optimal.

Permutation flow shop energy-efficient scheduling with a position-based learning effect

Severe environmental problems have made green scheduling an emerging research hotspot. In this paper, a permutation flow shop energy-efficient scheduling problem that considers multiple criteria is investigated. The aim is to find the optimal job processing sequence and conveyor speed that minimise both the makespan and total energy consumption. In addition to two types of common criteria, namely, machine-based criterion (i.e. sequence-dependent setup time) and energy-based criteria (including both the transportation time control strategy and machine shutdown strategy), a human-based criterion (i.e. a position-based learning effect) is introduced. A bi-objective programming model is developed, and a multi-objective iterated greedy (MOIG) is designed to reach the Pareto front of the model. Considering that there are two types of decisions in the model (i.e. job sequence and conveyor speed), two algorithm alternatives are designed based on the job sequence and conveyor speed, respectively. Meanwhile, an acceptance criterion with advantages in terms of the convergence speed and solution diversity is proposed. Existing algorithms, including NSGA-II and MOEA/D, are introduced to evaluate the performance of the MOIG. The results emphasise the efficiency of the MOIG. Overall, the model and MOIG effectively improve the green efficiency of enterprises and can reasonably control operating costs.

Uniform Parallel Machines Scheduling with Setup Time, Learning Effect, Machine Idle Time, and Processing Set Restrictions to Minimize Earliness/Tardiness Costs

Inspired by a real industrial case, this study deals with the problem of scheduling jobs on uniform parallel machines with past-sequence-dependent setup times to minimize the total earliness and tardiness costs. The paper contributes to the existing literature of uniform parallel machines problems by the novel idea of considering position-based learning effects along with processing set restrictions. The presented problem is formulated as a Mixed Integer linear programming (MILP) model. Then, an exact method is introduced to calculate the accurate objective function in the just-in-time (JIT) environments for a given sequence of jobs. Furthermore, three meta-heuristic approaches, (1) a genetic algorithm (GA), (2) a simulated annealing algorithm (SA), and (3) a particle swarm optimization algorithm (PSO) are proposed to solve large size problems in reasonable computational time. Finally, computational results of the proposed meta-heuristic algorithms are evaluated through extensive experiments and tested using ANOVA followed by t-tests to identify the most effective meta-heuristic.

Minimization of the total weighted tardiness on a single machine scheduling problem with a position based learning effect and unequal release dates

This paper concerns with the total weighted tardiness on a single machine scheduling problem with the concept of learning effect and unequal release dates. A mathematical model is proposed with binary variables and only small size problems can be solved efficiently due to its NP-hardness. Therefore, four heuristic methods are developed to solve real size applications including the size of 1000 jobs. Proposed heuristics are: genetic, genetic with solution combination, kangaroo and genetic-kangaroo hybrid algorithms. Results denote that developed heuristics are efficient for the considered problem. Research on this topic shows that no study exists on the total weighted tardiness problem with learning effect and unequal release dates simultaneously tackled in this paper.

A novel bi-objective model for a job shop scheduling problem with consideration of Fuzzy parameters, modified learning effects and multiple preventive maintenance activities

This paper aims at introducing a novel bi-objective model for a Job Shop Scheduling Problem (JSSP) in order to minimize makespan and maximum tardiness simultaneously. Some realistic assumptions, i.e. Fuzzy processing times and due dates involving triangular possibility distributions, transportation times, availability constraints, modified position-based learning effects on processing times, and sum-of-processing-time based learning effects on duration of maintenance activities have been considered, to provide a more general and practical model for the JSSP. Based on the learning effects, Processing times decrease as a machine performs an operation frequently, and workers gain working skills and experiences. In this paper based on DeJong’s learning effect a novel and modified formulation has been proposed for this effect. According to the above-mentioned assumptions, a novel mixed-integer linear programming (MILP) model for the JSSP is suggested. The proposed model is first converted to an auxiliary crisp model, given that model is a possibilistic programming, it is then solved by the TH and ε-constraint methods for small instances, and the results are compared. For medium and large instances, five metaheuristic algorithms, including NSGA-ΙΙΙ, PESA-ΙΙ, SPEA-ΙΙ, NSGA-ΙΙ, and MOEA/D are utilized, and the results are finally compared on the basis of three performance metrics.

A hybrid heuristic for agent-based scheduling problem with an ordinal scale objective criterion

Scheduling with multiple agents and learning effects has attracted growing attention of the scheduling research community. However, scheduling research together with learning, multiple agents and release times considerations is few. This paper considers two-agent single-machine scheduling with a position-based learning effect. The criterion measurement is to minimize the number of the tardy jobs of the first agent subject to the condition that the second agent has no tardy job. A branch-and-bound and a hybrid heuristic are proposed to solve the problem.

A two-stage three-machine assembly scheduling problem with a truncation position-based learning effect

The two-stage assembly scheduling problem has a lot of applications in industrial and service sectors. Furthermore, truncation-based learning effects have received growing attention in connection with scheduling problems. However, it is relatively unexplored in the two-stage assembly scheduling problem. Therefore, we addressed the two-stage assembly with truncation learning effects with two machines in the first stage and an assembly machine in the second stage. The objective function was to complete all jobs as soon as possible (or to minimize the makespan). Due to the NP-hardness of the considered problem, we proposed several dominance relations and a lower bound for the branch-and-bound method for finding the optimal solution. Moreover, we proposed six versions of hybrids greedy iterative algorithm, where three versions of the local searches algorithm with and without a probability scheme are embedded. They include extraction and backward-shifted reinsertion, pairwise interchange and extraction and forward-shifted reinsertion for searching good-quality solutions. The experimental results of all proposed algorithms are presented on small-size and big-size jobs.

Due-date assignment scheduling involving job-dependent learning effects and convex resource allocation

ABSTRACTThis article addresses single machine resource allocation scheduling problems with learning effects, where learning effects mean job-dependent position-based learning effects. For the common due-date assignment (CON) and slack due-date assignment (SLK) methods, a bi-cost analysis of the scheduling cost and the total weighted resource consumption cost is provided. The objective is to determine the optimal job sequence and the resource allocation simultaneously, such that the scheduling cost (the total weighted resource consumption cost) is minimized subject to the total weighted resource consumption cost (the scheduling cost) being limited. Solution procedures are provided for the problems under consideration.

Single machine scheduling with stochastically dependent times

This paper examines the behavior of several single machine scheduling problems when presented with times that are random and potentially dependent. A position-based learning effect model is revisited and optimal schedules are derived under several typical performance measures. A sum-of-processing-time based model is proposed to incorporate the learning effects and deteriorations in one unified framework. Optimal schedules are derived to minimize the maximum lateness or jointly minimize the completion times under the proposed model, and the model is used to solve the optimal issuing problem.

The single machine scheduling problem with sequence-dependent setup times and a learning effect on processing times

For the past few years, learning effect has been receiving wide attention in the scheduling problems. There are many studies that take into account the learning effect with several structural constraints and some specific conditions of machine scheduling problems. However, very few studies have explored the scheduling problem including learning effect and sequence-dependent setup times simultaneously, although both are found in the scheduling literature. Therefore, this study addresses an NP-Hard problem of minimizing the total tardiness on a single machine with sequence-dependent setup times and a position-based learning effect on processing times. Several dominance properties are verified and a lower bound is provided to develop a branch and bound algorithm for solving the problem. In addition, four heuristic algorithms (two genetic algorithms and two variable neighborhood search algorithms) are developed in order to obtain near optimal solutions in reasonable time limits. Furthermore, some computational experiments are performed on randomly generated test problems to evaluate the performance of the algorithms.

A two-stage three-machine assembly scheduling problem with a position-based learning effect

The two-stage assembly scheduling problem has attracted increasing research attention. In many such problems, job processing times are commonly assumed to be fixed. However, this assumption does not hold in many real production situations. In fact, processing times usually decrease steadily when the same task is performed repeatedly. Therefore, in this study, we investigated a two-stage assembly position-based learning scheduling problem with two machines in the first stage and an assembly machine in the second stage. The objective was to complete all jobs as soon as possible (or to minimise the makespan, implying that the system can perform better and efficient task planning with limited resources). Because this problem is NP-hard, we derived some dominance relations and a lower bound for the branch-and-bound method for finding the optimal solution. We also propose three heuristics, three versions of the simulated annealing (SA) algorithm, and three versions of cloud theory-based simulated annealing algorithm for determining near-optimal solutions. Finally, we report the performance levels of the proposed algorithms.

An Exact Algorithm for the Shortest Path Problem With Position-Based Learning Effects

The shortest path problems (SPPs) with learning effects (SPLEs) have many potential and interesting applications. However, at the same time they are very complex and have not been studied much in the literature. In this paper, we show that learning effects make SPLEs completely different from SPPs. An adapted A* (AA*) is proposed for the SPLE problem under study. Though global optimality implies local optimality in SPPs, it is not the case for SPLEs. As all subpaths of potential shortest solution paths need to be stored during the search process, a search graph is adopted by AA* rather than a search tree used by A*. Admissibility of AA* is proven. Monotonicity and consistency of the heuristic functions of AA* are redefined and the corresponding properties are analyzed. Consistency/monotonicity relationships between the heuristic functions of AA* and those of A* are explored. Their impacts on efficiency of searching procedures are theoretically analyzed and experimentally evaluated.

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.

An order scheduling problem with position-based learning effect

The order scheduling problem is receiving increasing attention in the relatively new but creative area of scheduling research. In order scheduling, several orders are processed on multiple machines, and each order comprises multiple components. The order completion time is defined as the time at which all components in an order are completed. In previous studies, the processing times of all components were fixed in order scheduling problems. This is unreasonable because a steady decline in processing time usually occurs when the same task is performed repeatedly in practical situations. Therefore, we propose a multiple-machine order scheduling problem with a learning effect to minimize the total tardiness. We develop a branch-and-bound algorithm incorporating certain dominance rules and three lower bounds for obtaining the optimal solution. Subsequently, we propose simulated annealing, particle swarm optimization, and order-scheduling MDD algorithms for obtaining a near-optimal solution. In addition, the experimental results of all proposed algorithms are provided.

Heuristic based genetic algorithms for the re-entrant total completion time flowshop scheduling with learning consideration

AbstractRecently, both the learning effect scheduling and re-entrant scheduling have received more attention separately in research community. However, the learning effect concept has not been introduced into re-entrant scheduling in the environment setting. To fill this research gap, we investigate re-entrant permutation flowshop scheduling with a position-based learning effect to minimize the total completion time. Because the same problem without learning or re-entrant has been proved NP-hard, we thus develop some heuristics and a genetic algorithm (GA) to search for approximate solutions. To solve this problem, we first adopt four existed heuristics for the problem; we then apply the same four methods combined with three local searches to solve the proposed problem; in the last stage we develop a heuristic-based genetic algorithm seeded with four good different initials obtained from the second stage for finding a good quality of solutions. Finally, we conduct experimental tests to evaluate the behavi...

작업별 위치기반 지수학습 효과를 갖는 2-에이전트 스케줄링 문제를 위한 시뮬레이티드 어닐링

In this paper, we consider a two-agent single-machine scheduling problem with exponential job-dependent position-based learning effects. The objective is to minimize the total weighted completion time of one agent with the restriction that the makespan of the other agent cannot exceed an upper bound. First, we propose a branch-andbound algorithm by developing some dominance /feasibility properties and a lower bound to find an optimal solution. Second, we design an efficient simulated annealing (SA) algorithm to search a near optimal solution by considering six different SAs to generate initial solutions. We show the performance superiority of the suggested SA using a numerical experiment. Specifically, we verify that there is no significant difference in the performance of % errors between different considered SAs using the paired t-test. Furthermore, we testify that random generation method is better than the others for agent A, whereas the initial solution method for agent B did not affect the performance of% error.

Permutation flowshop group scheduling with position-based learning effect

For the past few years, scheduling with learning effect has been receiving wide attention. However, learning effect and group technology have not been simultaneously explored in a flowshop setting although group technology plays an important role in a modern manufacturing system. Accordingly, this research formulates several flowshop scheduling problems with position-dependent learning and group effects. In particular, the learning effect of each job on every machine is based not only on its job position but also on its group position. Four objectives, namely, minimizing the makespan, total completion time, total weighted completion time, and maximum lateness, are considered. This research also shows the tight worst case ratios for several heuristics of the respective problems and derives the lower bound estimates to examine the performance of the proposed heuristics and meta-heuristics (genetic algorithm and quantum differential evolutionary algorithm). Finally, this research presents the result of the computational experiments, provides a case study on satellite production, and outlines some future research directions.

Two-Agent Single-Machine Scheduling with Linear Job-Dependent Position-Based Learning Effects

Two-Agent Single-Machine Scheduling with Linear Job-Dependent Position-Based Learning Effects