Normal Processing Time Of Jobs Research Articles

Scheduling Dual-Objective Stochastic Hybrid Flow Shop With Deteriorating Jobs via Bi-Population Evolutionary Algorithm

Hybrid flow shop scheduling problems have gained an increasing attention in recent years because of its wide applications in real-world production systems. Most of the prior studies assume that the processing time of jobs is deterministic and constant. In practice, jobs’ processing time is usually difficult to be exactly known in advance and can be influenced by many factors, e.g., machines’ abrasion and jobs’ feature, thereby leading to their uncertain and variable processing time. In this paper, a dual-objective stochastic hybrid flow shop deteriorating scheduling problem is presented with the goal to minimize makespan and total tardiness. In the formulated problem, the normal processing time of jobs follows a known stochastic distribution, and their actual processing time is a linear function of their start time. In order to solve it effectively, this paper develops a hybrid multiobjective optimization algorithm that maintains two populations executing the global search in the whole solution space and the local search in promising regions, respectively. An information sharing mechanism and resource allocating method are designed to enhance its exploration and exploitation ability. The simulation experiments are carried out on a set of instances, and several classical algorithms are chosen as its peers for comparison. The results demonstrate that the proposed algorithm has a great advantage in dealing with the investigated problem.

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.

The single machine total weighted completion time scheduling problem with the sum-of-processing time based models: Strongly NP-hard

• We analyse the single machine total weighted completion time scheduling with learning and aging effects. • The job processing times depend on the sum of the normal job processing times. • The considered problem with the learning effect is proved to be strongly NP-hard. • The considered problem with the aging effect is proved to be strongly NP-hard. • A parallel branch and bound algorithm is constructed for the general version of the problem. Although the single machine scheduling problem to minimize the total weighted completion times with the sum-of-processing time based learning or aging effects have been known for a decade, it is still an open question whether these problems are strongly NP-hard. We resolve this issue and prove them to be strongly NP-hard with the learning effect as well as with the aging effect. Furthermore, we construct an exact parallel branch and bound algorithm for the problem with general sum-of-processing time based models, which can solve optimally moderate problem instances in reasonable time.

Single machine scheduling with a generalized job-dependent cumulative effect

We consider a single machine scheduling problem with changing processing times. The processing conditions are subject to a general cumulative effect, in which the processing time of a job depends on the sum of certain parameters associated with previously scheduled jobs. In previous papers, these parameters are assumed to be equal to the normal processing times of jobs, which seriously limits the practical application of this model. We further generalize this model by allowing every job to respond differently to these cumulative effects. For the introduced model, we solve the problem of minimizing the makespan, with and without precedence constraints. For the problem without precedence constraints, we also consider a situation in which a maintenance activity is included in the schedule, which can improve the processing conditions of the machine, not necessarily to its original state. The resulting problem is reformulated as a variant of a Boolean programming problem with a quadratic objective, known as a half-product, which allows us to develop a fully polynomial-time approximation scheme with the best possible running time.

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.

Single machine scheduling problems with exponentially time-dependent learning effects

In this paper, we introduce a single-machine scheduling problem with an exponentially time-dependent learning effect. The processing time of a job is assumed to be an exponential function of the total normal processing time of jobs already processed before it. For such a scheduling problem, we first provide the upper bound for the maximum lateness and for the total weighted completion time. Next, we show that problems with the following criteria: makespan, the total completion time, the total weighted completion time, the total earliness/tardiness penalties and the maximum lateness under some agreeable conditions, are polynomially solvable.

Some single-machine scheduling with sum-of-processing-time-based and job-position-based processing times

The single-machine scheduling problems with position and sum-of-processing-time based processing times are considered. The actual processing time of a job is defined by function of its scheduled position and total normal processing time of jobs in front of it in the sequence. We provide optimal solutions in polynomial time for some special cases of the makespan minimization and the total completion time minimization. We also show that an optimal schedule to be a V-shaped schedule in terms of the normal processing times of jobs for the total completion time minimization problem and the makespan minimization problem.

Due-Date Assignment on a Single Machine Scheduling Problem with Nonlinear Deterioration Function

The paper considers the due-date assignment problem with a non-linear deterioration in which the due dates are determined by the equal slack method. Here, the processing time of a job is defined by a non-linear function of total normal processing time of jobs in front of it in the sequence. The objective is to minimize the total tardiness penalties. According to the needs from the real world, the problem is divided into two cases, i.e., allowing with early jobs and no early jobs respectively. The related lemma, corollary and theorems for the problems are proposed and proved. At the same time, it shows that the problems in this paper can be solved in the polynomial times.

Single-machine scheduling with past-sequence-dependent delivery times and a linear deterioration

In many real-life scheduling environments, the jobs deteriorate at a certain rate while waiting to be processed. This paper addresses some single-machine scheduling problems with past-sequence-dependent (p-s-d) delivery times and a linear deterioration. The p-s-d delivery time of a job is proportional to the job's waiting time. It is assumed that the deterioration process is reflected in the jobprocessing times being an increasing function of their starting times. We consider the following objectives: the makespan, total completion time, total weighted completion time, maximum lateness, and total absolute differences in completion times. We seek the optimal schedules for the problems to minimize the makespan and total completion time.Despite that the computational complexities of the problems tominimize the total weighted completion time and maximum lateness remain open, we present heuristics and analyze their worst-case performance ratios, and show that some special cases of the problems are polynomially solvable. We also show that the optimal schedule for the problem to minimize the total absolute differences in completion times is $V$-shaped with respect to the normal job processing times.

Single machine total completion time minimization scheduling with a time-dependent learning effect and deteriorating jobs

In this article, we consider a single machine scheduling problem with a time-dependent learning effect and deteriorating jobs. By the effects of time-dependent learning and deterioration, we mean that the job processing time is defined by a function of its starting time and total normal processing time of jobs in front of it in the sequence. The objective is to determine an optimal schedule so as to minimize the total completion time. This problem remains open for the case of −1 < a < 0, where a denotes the learning index; we show that an optimal schedule of the problem is V-shaped with respect to job normal processing times. Three heuristic algorithms utilising the V-shaped property are proposed, and computational experiments show that the last heuristic algorithm performs effectively and efficiently in obtaining near-optimal solutions.

The single processor total weighted completion time scheduling problem with the sum-of-processing-time based learning model

In this paper, we analyse the single processor total weighted completion time scheduling problem with the learning effect, where the processing time of each job is a non-increasing function dependent on the sum of the normal processing times of preceding jobs. We prove that the considered problem is at least NP-hard. Moreover, a pseudopolynomial time dynamic programming algorithm that optimally solves the problem with a step learning function (curve) is constructed. Furthermore, fast approximation algorithms for the general version of the problem, where job processing times are described by arbitrary functions dependent on the sum of the normal job processing times, are provided. Their efficiency is verified numerically and for Weighted Shortest Processing Times algorithm a worst case analysis is also performed.

Some polynomial solvable single-machine scheduling problems with a truncation sum-of-processing-times-based learning effect

Recently, scheduling with learning effects has received growing attention. A well-known learning model is called ‘sum-of processing-times-based learning’ where the actual processing time of a job is a non-increasing function of the jobs already processed. However, the actual processing time of a given job drops to zero precipitously when the normal job processing times are large. Motivated by this observation, this paper develops a truncated learning model in which the actual job processing time not only depends on the processing times of the jobs already processed but also depends on a control parameter. The use of the truncated function is to model the phenomenon that the learning of a human activity is limited. In this paper, some single-machine scheduling problems can be solved in polynomial time. Besides, the error bounds are also provided for the problems to minimise the maximum lateness and the total weighted completion time.

A Truncated Sum of Processing‐Times–Based Learning Model for a Two‐Machine Flowshop Scheduling Problem

AbstractScheduling with learning effects has gained increasing attention in recent years. A well‐known learning model is called “sum‐of‐processing‐times‐based learning” in which the actual processing time of a job is a nonincreasing function of the jobs already processed. However, the actual processing time of a given job drops to zero precipitously when the normal job processing times are large. Moreover, the concept of learning process is relatively unexplored in a flowshop environment. Motivated by these observations, this article addresses a two‐machine flowshop problem with a truncated learning effect. The objective is to find an optimal schedule to minimize the total completion time. First, a branch‐and‐bound algorithm incorporating with a dominance property and four lower bounds is developed to derive the optimal solution. Then three simulated annealing algorithms are also proposed for near‐optimal solution. The experimental results indicated that the branch‐and‐bound algorithm can solve instances up to 18 jobs, and the proposed simulated annealing algorithm performs well in item of CPU time and error percentage. © 2011 Wiley Periodicals, Inc.

Some single-machine scheduling problems with a truncation learning effect

Scheduling with learning effects has received growing attention nowadays. A well-known learning model is called “sum-of processing-times-based learning” in which the actual processing time of a job is a non-increasing function of the jobs already processed. However, the actual processing time of a given job drops to zero precipitously when the normal job processing times are large. Motivated by this observation, we propose a truncation learning model where the actual job processing time is a function which depends not only on the processing times of the jobs already processed but also on a control parameter. The use of the truncated function is to model the phenomenon that the learning of a human activity is limited. Under the proposed learning model, we show that some single-machine scheduling problems can be solved in polynomial time. In addition, we further provide the worst-case error bounds for the problems to minimize the maximum lateness and total weighted completion time.

Scheduling jobs with general learning functions

This paper deals with single-machine scheduling problems with a more general learning effect based on sum-of-processing-time. In this study, sum-of-processing-time-based learning effect means that the processing time of a job is defined by a decreasing function of the total normal processing time of jobs that come before it in the sequence. Results show that even with the introduction of the sum-of-processing-time-based learning effect to job processing times, single-machine makespan minimization problems remain polynomially solvable. The curves of the optimal schedule of a total completion time minimization problem are V-shaped with respect to job normal processing times.

Single-machine scheduling simultaneous with position-based and sum-of-processing-times-based learning considerations under group technology assumption

This paper considers the problems of scheduling with the effect of learning on a single-machine under group technology assumption. We propose a new learning model where the job actual processing time is linear combinations of the scheduled position of the job and the sum of the normal processing time of jobs already processed. We show that the makespan minimization problem is polynomially solvable. We also prove that the total completion time minimization problem with the group availability assumption remains polynomially solvable under agreeable conditions.

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.

Single-machine total completion time scheduling with a time-dependent deterioration

In this paper, we consider the single-machine scheduling problems with a time-dependent deterioration. By the time-dependent deterioration, we mean that the processing time of a job is defined by an increasing function of total normal processing time of jobs in front of it in the sequence. The objective is to minimize the total completion time. We develop a mixed integer programming formulation for the problem. The complexity status of this problem remains open. Hence, we use the smallest normal processing time (SPT) first rule as a heuristic algorithm for the general cases and analyze its worst-case error bound. Two heuristic algorithms utilize the V-shaped property are also proposed to solve the problem. Computational results are presented to evaluate the performance of the proposed algorithms.

Minimizing total completion time on a batching machine with job processing time compatibilities

Abstract The problem of scheduling n jobs on an unbounded batching machine to minimize the total completion time is studied. The machine can process any number of jobs simultaneously in a batch, subject to an additional constraint that, in the same batch, the job processing times are compatible. There are given normal job processing times. An actual job processing time can exceed its normal value up to a certain percent. This percent is the same for all jobs. Thus, there are processing time intervals for the jobs. The job processing times are compatible if the corresponding processing time intervals intersect. The processing time of a batch is given by the longest processing time of the tasks in the batch and it correspnds to the left endpoint of the intersection of the job processing time intervals in this batch. For the total completion time a dynamic programming algorithm is provided.

Single-machine scheduling with a nonlinear deterioration function

In deteriorating job scheduling problems, most of the researchers assume that the actual job processing time is a function of its starting time. In this paper, we propose a new deterioration 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 at the same time. We show that some single-machine scheduling problems remain polynomially solvable.