Position-based Learning Effect Research Articles

Scheduling Jobs with Truncated Exponential Sum-of-Logarithm-Processing-Times Based and Position-based Learning Effects

In this study, we consider a scheduling problem with truncated exponential sum-of-logarithm-processing-times based and position-based learning effects on a single machine. We prove that the shortest processing time (SPT) rule is optimal for the makespan minimization problem, the sum of the θth power of job completion times minimization problem, and the total lateness minimization problem, respectively. For the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, we present heuristic algorithms (the worst-case bound of these heuristic algorithms are also given) according to the corresponding single machine scheduling problems without learning considerations. It also shows that the problems of minimizing the total tardiness, the total weighted completion time and the discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.

A Note on Scheduling Jobs with Extended Sum-of-Processing-Times-Based and Position-Based Learning Effect

The note deals with machine scheduling problems with a more general learning effect model, i.e., the actual job processing time is a function of the sum of the function of the processing times of the jobs already processed and job position. We show that some single machine scheduling problems are still polynomially solvable under the proposed model. We also show that some special cases of the flow shop scheduling problems can be solved in polynomial time.

Using a branch-and-bound and a genetic algorithm for a single-machine total late work scheduling problem

Scheduling with learning effects has received a lot of research attention lately. On the other hand, it is commonly seen that time restrictions are usually modeled by due dates or deadlines and the quality of schedules is estimated with reference to these parameters. One of the performance measures involving due dates is the late work criterion, which is relatively unexplored. Thus, we study a single-machine scheduling problem with a position-based learning effect. The objective is to minimize the total late work, where the late work for a job is the amount of processing of this job that is performed after its due date. We attempt to develop a branch-and-bound algorithm incorporating with some dominance rules and a lower bound for the optimal solution. For saving computational time, we also propose three heuristic-based genetic algorithms for the near-optimal solution. Finally, the computational results of proposed algorithms are also provided.

Multiple-Machine Scheduling with Learning Effects and Cooperative Games

Multiple-machine scheduling problems with position-based learning effects are studied in this paper. There is an initial schedule in this scheduling problem. The optimal schedule minimizes the sum of the weighted completion times; the difference between the initial total weighted completion time and the minimal total weighted completion time is the cost savings. A multiple-machine sequencing game is introduced to allocate the cost savings. The game is balanced if the normal processing times of jobs that are on the same machine are equal and an equal number of jobs are scheduled on each machine initially.

A new mathematical model for single machine scheduling with learning effect: continuous approach

In the literature of scheduling, many studies have been devoted to schedule single machine activities. Despite numerous studies done to bridge the gap between the mathematical models and real-life scheduling problems, there is still gap remained to be covered. In this study, position-based, time-based and experience-based learning effect calculations are employed simultaneously in order to extend applicability of the proposed model. At first, the modified single machine scheduling problem is formulated as a mixed integer mathematical model with non-linear terms. Finally, a hybrid imperialistic competitive algorithm and genetic algorithm is designed to solve this complex problem. The hybrid ICA-GA algorithm is modified in order to take advantage of ICAs intelligence and GAs operators such as crossover and mutation simultaneously.

Scheduling with job-dependent past-sequence-dependent setup times and job-dependent position-based learning effects on a single processor

Scheduling with setup time and learning is of importance in today's manufacturing and service organisations where reliable and low cost products/services should be delivered on time. This paper addresses the problem of scheduling jobs on a single processor (or machine) where the setup times are job-dependent and past-sequence-dependent (psd), and the learning effects are job-dependent and position-based. The goal is to minimise each of the objective functions: the sum of the ρth (ρ ≥ 0) powers of completion times, the maximum lateness, the maximum tardiness, the total tardiness, the total weighted completion time when the weights are non-linear functions of job positions, and the total absolute differences in waiting times. Special cases of the resulting problems are solvable polynomially. For the general cases, we introduce heuristic approaches to approximate the solutions with respect to the first four objectives, and extend the branch-and-bound (B&B) methods of Soroush (2012) to derive the optimal sequences with respect to the last two objectives. Computational results show that the proposed heuristics perform well and the solution times of B&Bs are reasonable. [Received 13 July 2013; Revised 30 December 2013; Accepted 21 February 2014]

Scheduling Identical Jobs on Uniform Parallel Machines Under Position-Based Learning Effects

This research considers the problem of scheduling identical jobs on uniform parallel machines for the individual minimization of several different performance measures under position-based learning effects. The performance measures include total weighted completion time, total tardiness, total weighted tardiness, and maximum lateness. We formulate these problems as assignment problems with nonlinear or linear objectives. The n earliest completion times can be used in non-decreasing order to reduce the number of variables significantly and to find optimal solutions efficiently. Our computational results show that it is more efficient to formulate these problems as assignment problems with nonlinear objectives and a few variables and constraints than it is to formulate them as linear programming models with many variables and constraints.

Scheduling in bicriteria single machine systems with past-sequence-dependent setup times and learning effects

Scheduling with setup times and learning plays a crucial role in today's manufacturing and service environments where scheduling decisions are made with respect to multiple performance criteria rather than a single criterion. In this paper, we address a bicriteria single machine scheduling problem with job-dependent past-sequence-dependent setup times and job-dependent position-based learning effects. The setup time and actual processing time of a job are respectively unique functions of the actual processing times of the already processed jobs and the position of the job in a schedule. The objective is to derive the schedule that minimizes a linear composite function of a pair of performance criteria consisting of the makespan, the total completion time, the total lateness, the total absolute differences in completion times, and the sum of earliness, tardiness, and common due date penalty. We show that the resulting problems cannot be solved in polynomial time; thus, branch-and-bound (B&B) methods are proposed to obtain the optimal schedules. Our computational results demonstrate that the B&B can solve instances of various size problems with attractive times.

A general flow shop scheduling problem with consideration of position-based learning effect and multiple availability constraints

In this paper, a more general version of the flow shop scheduling problem with the objective of minimizing the total flow time is investigated. In order to get closer to the actual conditions of the problem, some realistic assumptions including non-permutation scheduling, learning effect, multiple availability constraints, and release times are considered. It is assumed that the real processing time of each job on a machine depends on the position of that job in the sequence, and after processing a specified number of jobs at each machine, an unavailability period is occurring because of maintenance activities. Moreover, it is supposed that each job may not be ready for processing at time zero and may have a release time. According to these assumptions, a new mixed integer linear programming (MILP) model is proposed to formulate the problem. Due to the high complexity of the problem, a heuristic method and a simulated annealing algorithm are presented to find the nearly optimal solutions for medium- and large-sized problems. To obtain better and more robust solutions, the Taguchi method is used in order to calibrate the simulated annealing algorithm parameters. Finally, the computational results are provided for evaluating the performance and effectiveness of the proposed solution methods.

Single-machine rescheduling with deterioration and learning effects against the maximum sequence disruption

In this paper, we study the issue of single-machine rescheduling with linear deteriorating jobs and position-based learning effects simultaneously in response to an unexpected arrival of new jobs. The scheduling efficiency is measured in terms of the makespan, while the cost of disruption is measured in terms of the maximum difference in processing orders of the original jobs before and after disruption. By introducing the effects of deterioration and learning, the job actual processing time is defined by an increasing function of its starting time, meanwhile a decreasing function of its position. Two types of problems are considered. For the first one, the makespan is minimised subject to a limit on the maximum sequence disruption; while in the second one, a linear combination of the makespan and the maximum sequence disruption is minimised. For each problem, the polynomial solvability is demonstrated, and an efficient algorithm is then developed. Finally, extensive computational experiments are conducted to show the efficiency and running behaviours of the proposed algorithms.

Cross-docking truck scheduling with the arrival times for inbound trucks and the learning effect for unloading/loading processes

Cross-docking is a technique firstly proposed to reduce the storage space and flow time, simultaneously. This paper addresses a truck scheduling problem, in which a position-based learning effect is taken into consideration for unloading and loading tasks done by human labors in many related environments. The goal of the given problem is to minimize the mean completion time of outbound trucks. Therefore, a mathematical model is proposed inspired by an available model in the literature of this field. Furthermore, four heuristic algorithms are developed along with a simulated annealing (SA) algorithm in order to overwhelm the complexity of large-sized problems. The performance of the proposed algorithms is compared with the optimal solutions obtained by a complete enumeration method.

Several flow shop scheduling problems with truncated position-based learning effect

The concept of truncated position-based learning process plays a key role in production environments. However, it is relatively unexplored in the flow shop setting. In this paper, we consider the flow shop scheduling with truncated position-based learning effect, i.e., the actual processing time of a job is a function of its position and a control parameter in a processing permutation. The objective is to minimize one of the six regular performance criteria, namely, the total completion time, the makespan, the total weighted completion time, the discounted total weighted completion time, the sum of the quadratic job completion times, and the maximum lateness. We present heuristic algorithms and analyze the worst-case bound of these heuristic algorithms. We also provide the computational results to evaluate the performance of the heuristics.

Stochastic scheduling problems with general position-based learning effects and stochastic breakdowns

The focus of this study is to analyze position-based learning effects in single-machine stochastic scheduling problems. The optimal permutation policies for the stochastic scheduling problems with and without machine breakdowns are examined, where the performance measures are the expectation and variance of the makespan, the expected total completion time, the expected total weighted completion time, the expected weighted sum of the discounted completion times, the maximum lateness and the maximum tardiness.

Single machine scheduling with sum-of-logarithm-processing-times based and position based learning effects

In this paper we consider the single machine scheduling problems with sum-of-logarithm-processing-times based and position based learning effects, i.e., the actual job processing time of a job is a function of the sum of the logarithms of the processing times of the jobs already processed and its position in a sequence. The logarithm function is used to model the phenomenon that learning as a human activity is subject to the law of diminishing return. We show that even with the introduction of the proposed model to job processing times, several single machine problems remain polynomially solvable.

Minimizing makespan in a single-machine scheduling problem with a learning effect and fuzzy processing times

In scheduling problems with learning effects, most research assumes that processing times are deterministic. This paper studies a single-machine scheduling problem with a position-based learning effect and fuzzy processing times where the objective is to minimize the makespan. The position-based learning effect of a job is assumed to be a function of its position. The processing times are considered to be triangular fuzzy numbers. Two different polynomial-time algorithms are developed for the problem. The first solution methodology is based on the fuzzy chance-constrained programming, whereas the second is based on a method to rank fuzzy numbers. Computational experiments are then conducted in order to evaluate the performance of the algorithms.

A note on machine scheduling with sum-of-logarithm-processing-time-based and position-based learning effects

Recently, Biskup [2] classifies the learning effect models in scheduling environments into two types: position-based and sum-of-processing-time-based. In this paper, we study scheduling problem with sum-of-logarithm-processing-time-based and position-based learning effects. We show that the single machine scheduling problems to minimize the makespan and the total completion time can both be solved by the smallest (normal) processing time first (SPT) rule. We also show that the problems to minimize the maximum lateness, the total weighted completion times and the total tardiness have polynomial-time solutions under agreeable WSPT rule and agreeable EDD rule. In addition, we show that m-machine permutation flowshop problems are still polynomially solvable under the proposed learning model.

The single-machine total weighted tardiness scheduling problem with position-based learning effects

This study addresses the problem of minimizing the total weighted tardiness on a single-machine with a position-based learning effect. Several dominance properties are established to develop branch and bound algorithm and a lower bound is provided to derive the optimal solution. In addition, three heuristic procedures are developed for near-optimal solutions. Computational results are also presented to evaluate the performance of the proposed algorithms.

Single-machine scheduling with a position-based learning effect and fuzzy processing times

In scheduling problems with learning effects, most researches assume that processing times are deterministic. This paper considers a single-machine scheduling problem with a position-based learning effect and fuzzy processing times, simultaneously. The position-based learning effect of a job is assumed to be a function of its position. The processing times are considered to be triangular fuzzy numbers. A polynomial time algorithm is proposed for the problem where the objective is to minimize the total completion time. The solution procedure is based on applying the shortest processing time rule to triangular fuzzy processing times. Computational results show that our model gives better results than the model ignoring the uncertainty.

Multi-objective group scheduling with learning effect in the cellular manufacturing system

Article history: Received 18 December 2010 Received in revised form 14 February 2011 Accepted 15 February 2011 Available online 15 February 2011 Group scheduling problem in cellular manufacturing systems consists of two major steps. Sequence of parts in each part-family and the sequence of part-family to enter the cell to be processed. This paper presents a new method for group scheduling problems in flow shop systems where it minimizes makespan (Cmax) and total tardiness. In this paper, a position-based learning model in cellular manufacturing system is utilized where processing time for each part-family depends on the entrance sequence of that part. The problem of group scheduling is modeled by minimizing two objectives of position-based learning effect as well as the assumption of setup time depending on the sequence of parts-family. Since the proposed problem is NP-hard, two meta heuristic algorithms are presented based on genetic algorithm, namely: Non-dominated sorting genetic algorithm (NSGA-II) and non-dominated rank genetic algorithm (NRGA). The algorithms are tested using randomly generated problems. The results include a set of Pareto solutions and three different evaluation criteria are used to compare the results. The results indicate that the proposed algorithms are quite efficient to solve the problem in a short computational time. © 2011 Growing Science Ltd. All rights reserved

Single-machine scheduling with general sum-of-processing-time-based and position-based learning effects

In this paper, we propose a new learning effect model in which the actual job processing time is a general function of the normal processing time of jobs already processed and its scheduled position. This model has the advantage that different learning curves can be constructed easily, such as the plateau function. It is found that most of the models in the literature are special cases of our proposed model. The optimal sequences for some single-machine problems are then provided.