Absolute Differences In Completion Times Research Articles

Two-stage no-wait proportionate flow shop scheduling with minimal service time variation and optional job rejection

We consider two-stage no-wait proportionate flow shops with the objective of minimizing service time variation measured by defining the mid-processing point of a job and minimizing the Total Absolute Deviation of mid-processing Points (TADZ). We show that the two-stage no-wait proportionate flow shop with the TADZ objective is solvable in O(nlogn) time. Our findings provide an affirmative answer to an open research question posed by Kovalev et al. (2019) regarding existence of a solvable variant of the two-stage no-wait proportionate flow shop problem with the Total Absolute Deviation of Completion Times (TADC) objective. Moreover, we show when a generic two-stage no-wait proportionate flow shop scheduling problem is solvable in O(nlogn) time. We present practical applications where TADZ is more suitable than TADC as a scheduling objective. We also introduce a new metric defined as the sum of all partial schedule lengths SPSL and show that the two-stage no-wait proportionate flow shop with the SPSL objective is solvable in O(nlogn) time; thus, an additional solvable variant of the two-stage no-wait proportionate flow shop with the SPSL objective is identified and solved. Finally, we consider the option of rejecting a job from the schedule by paying a job-specific penalty for each rejected job and solve the resulting problem with the TADZ objective and the rejection option in O(n3) time by dynamic programming.

Some Scheduling Problems With Job Rejection And A Learning Effect

AbstractIn this paper, we examined single and parallel machine scheduling problems with a learning effect and job rejection simultaneously. In real life, job processing times decrease when there is a learning effect. In some cases, producers cannot process all the jobs and pay the penalty cost for these jobs that they do not process. In our study, learning effect and job rejection are considered at the same time. We examined four different objective functions. Our objectives for single-machine scheduling problems are makespan and rejection cost minimization, total completion time and rejection cost minimization and total absolute deviation of completion times (TADC) and rejection cost minimization. Our objective for parallel machines is makespan and rejection cost minimization. The problems are solved by mathematical models, and four different algorithms are proposed for the problems. From these algorithms, the same results are obtained with single-machine makespan and rejection cost minimization, parallel machine makespan and rejection cost minimization and total completion time and rejection cost minimization. The accuracy for these models is obtained as 100%. The proposed algorithm for TADC and rejection cost minimization yielded close-to-optimal results. Mathematical model and algorithm results for 10 jobs, 20 jobs and 30 jobs are compared and the results are presented. The obtained solutions are obtained in polynomial time.

총 준비시간과 처리시간에 따른 학습효과를 고려한 단일설비 일정계획

This paper considers the single machine scheduling problems with learning effect on either the setup or processing times, where the setup or processing times decrease according to increasing both the total amount of setups and processing already. Our objective is to find the optimal schedules which minimize makespan, mean flow time, or total absolute differences in completion times (TADC) of the jobs. We characterize the optimal schedules for each scheduling measure and show the optimal scheduling rules to solve the problems with 0(n log n) time. Furthermore, we show that the problems for minimization a weighted sum of makespan and mean flow time are also solved in polynomial-time complexity. The optimal schedules for the bi-criteria are useful for the various environments by fitting the weight of each criterion, makespan and mean flow time, on the aim of the scheduling in the environments.

Scheduling controllable processing time jobs in seru production system with resource allocation

In this article, four scheduling problems with controllable processing times and resource allocation in seru production system (SPS) are first studied. The objective is to minimize the total processing cost plus scheduling measures, which are the total waiting time, the total absolute differences in completion times, the total absolute differences in waiting times and the total earliness and tardiness, respectively. A general exact solution method is proposed to show that these four problems can be transformed into assignment problems and solved in polynomial time if the number of serus and processing times are given in advance. Computational experiments are made finally, and results indicate that the exact solution method is effective to return optimal schedules for four seru scheduling problems. Further, the schedule flexibility of SPS can be enhanced by considering controllable processing times, and workload balance is also need to be concern in seru production practice.

Single-machine slack due-window assignment scheduling with multiple maintenance activities and position-and-resource-dependent processing times

This paper studies the slack due-window assignment method for single-machine scheduling problems with position-and resource-dependent processing times, for which the actual processing time is a continuous bivariate non-increasing convex function involving position and resource allocation. Only the slack due-window assignment method will be used. Two linear combination problems concerning position-dependent effects and resource allocation will be studied, in which the machine requires multiple maintenance activities. We present the optimal properties or design optimal algorithms to minimise the combination of the makespan, the total completion time and the total absolute deviation of completion time and to minimise the combination of the total costs of tardiness, the slack due date, the earliness cost, and the resource amount. Finally, we also consider the bi-criteria scheduling problem with nonmaintenance activities to minimise the combination of the total resource allocation cost, the weighted number of tardy jobs, and slack due-window assignment costs. A pseudo-polynomial time algorithm is designed to solve the bi-criteria scheduling problem.

Single-Machine Scheduling Problems with Variable Processing Times and Past-Sequence-Dependent Delivery Times

Scheduling problems with variable processing times and past-sequence-dependent delivery times are considered on a single-machine. The delivery times of jobs depend on their waiting times of processing. A job’s actual processing time depends on its position in a sequence, its starting time and its allocation of non-renewable resources. Under the linear resource consumption function, the goal (version) is to determine the optimal sequence and optimal resource allocation such that the sum of scheduling cost and total resource consumption cost is minimized. Under the convex resource consumption function, three versions of the scheduling cost and total resource consumption cost are discussed. We prove that these four versions can be solved in polynomial time, respectively. Some applications are also given by using the scheduling cost, which involve the makespan, total completion time, total absolute differences in completion times (TADC), and total absolute differences in waiting times (TADW).

Single-machine scheduling problems with job rejection, deterioration effects and past-sequence-dependent setup times

ABSTRACT This article considers single-machine problems in which the actual processing time of a job is a function of its position in a sequence (i.e. position-dependent deterioration effects). In this model, a job is either accepted or rejected. If the job is accepted, it is processed on a single machine, but if the job is rejected, a penalty (cost) is imposed. The goal is to minimize the sum of the given scheduling objectives, including the makespan, the total completion time, the total absolute differences in completion times and the total absolute differences in waiting times of the accepted jobs and total rejection penalty of the rejected jobs. It is illustrated that these problems remain polynomially solvable under the proposed models. Finally, computational results demonstrate that the proposed algorithms can solve instances of various size problems in attractive times. An extension to the problems is offered by assuming time-dependent deterioration effects.

A note: minimizing total absolute deviation of job completion times on unrelated machines with general position-dependent processing times and job-rejection

We study a scheduling problem with the objective of minimizing total absolute deviation of completion times (TADC). TADC is considered here in the most general form studied so far: the machine setting is that of parallel unrelated, job processing time are assumed to be position-dependent with no restrictions on the functional form, and the option of processing only a subset of the jobs (i.e., job-rejection) is allowed. We show that minimizing TADC in this very general form remains polynomially solvable in the number of jobs.

A note on resource allocation scheduling with position-dependent workloads

ABSTRACTIn this note, single machine scheduling with concurrent resource allocation and position-dependent workloads is studied. The aim is to find jointly the optimal sequence and the optimal resource allocation. A bicriteria analysis of the problem is provided where the first criterion is to minimize the scheduling cost (i.e. makespan, total completion time, total absolute differences in completion times, total absolute differences in waiting times) and the second criterion is to minimize the total resource consumption cost. It is proved that four bicriteria problems can be solved efficiently.

A Bicriteria Approach for Single Machine Scheduling with Resource Allocation, Learning Effect and a Deteriorating Maintenance Activity

This paper considers the single machine scheduling with learning effect, resource allocation and deteriorating maintenance activity simultaneously. For the convex resource allocation consumption function, we provide a bicriteria analysis where the first (schedule) criterion is to minimize the total weighted sum of makespan, total completion time and total absolute differences in completion times, and the second (resource) criterion is to minimize the total weighted resource consumption. Our aim is to find the optimal resource allocations and job sequence that minimize the three different models of considering the two criterion. We show that these three models are polynomially solvable respectively.

Multitasking scheduling with multiple rate‐modifying activities

AbstractThis paper considers scheduling problems with human operators having the option to perform multiple rate‐modifying activities (MRMAs) while they are carrying out multitasking. Thus, the processing of a selected task suffers jointly from interruptions by other available but unfinished tasks and MRMAs. Two types of objective functions are studied: single‐criterion minimizing the total completion time, and multicriteria minimizing a weighted combination of the total completion time, the total absolute differences in completion times, and a weighted combination of the total waiting time and the total absolute differences in waiting times. We propose optimal solution algorithms for all the studied problems and also analyze some special cases of them.

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.

Scheduling jobs with controllable processing time, truncated job-dependent learning and deterioration effects

In this paper, we consider single machine scheduling problems with controllable processing time (resource allocation), truncated job-dependent learning and deterioration effects. The goal is to find the optimal sequence of jobs and the optimal resource allocation separately for minimizing a cost function containing makespan (total completion time, total absolute differences in completion times) and/or total resource cost. For two different processing time functions, i.e., a linear and a convex function of the amount of a common continuously divisible resource allocated to the job, we solve them in polynomial time respectively.

Resource-dependent scheduling with deteriorating jobs and learning effects on unrelated parallel machine

The focus of this paper is to analyze unrelated parallel-machine resource allocation scheduling problem with learning effect and deteriorating jobs. The goal is to find the optimal sequence of jobs and the optimal resource allocation separately for minimizing the cost function including the total load, the total completion time, the total absolute deviation of completion time and the total resource cost. We show that the problem is polynomial time solvable if the number of machines is a given constant.

Two-machine no-wait flowshop scheduling with learning effect and convex resource-dependent processing times

Two-machine no-wait flowshop scheduling problems in which the processing time of a job is a function of its position in the sequence and its resource allocation are considered in the study. The primary objective is to find the optimal sequence of jobs and the optimal resource allocation separately. Here we propose two separate models: minimizing a cost function of makespan, total completion time, total absolute differences in completion times and total resource cost; minimizing a cost function of makespan, total waiting time, total absolute differences in waiting times and total resource cost. Since each model is strongly NP-hard, we solve both models by breaking them down to two sub-problems, the optimal resource allocation problem for any job sequence and the optimal sequence problem with its optimal resource allocation. Specially, we transform the second sub-problem into the minimum of the bipartite graph optimal matching problem (NP-hard), and solve it by using the classic KM (Kuhn–Munkres) algorithm. The solutions of the two sub-problems demonstrate that the target problems remain polynomial solvable under the proposed model.

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.

Scheduling problems with effects of deterioration and truncated job-dependent learning

We study the scheduling problems with effects of deterioration and truncated job-dependent learning effect on a single machine, where the actual processing time of a job is a function of the job-dependent learning effect, its starting time, and a control parameter. The objective functions are to minimize the makespan, the total completion time, the total waiting time, the total absolute deviation of completion time, the total absolute deviation of waiting time, the earliness, tardiness and common (CON) (slack (SLK), unrestricted (DIF)) due date penalty, respectively. For the general case, by reducing them to a linear assignment problem, we solve them in polynomial time \(O(n^3)\). For the special case where all the jobs have a common learning rate, we present an \(O(n \log n)\) algorithm to obtain the optimal solution.

Unrelated parallel machines scheduling with deteriorating jobs and resource dependent processing times

We consider unrelated parallel machines scheduling problems involving resource dependent (controllable) processing times and deteriorating jobs simultaneously, i.e., the actual processing time of a job is a function of its starting time and its resource allocation. Two generally resource consumption functions, the linear and convex resource, were investigated. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. This paper focus on the objectives of minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost, and a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. If the number of unrelated parallel machines is a given constant, we show that the problems remain polynomially solvable under the proposed model.

Scheduling Problems with Human and Machine Effects

We discuss single machine scheduling problems with learning effects of setup and removal times and deterioration effects of processing time, i.e., the processing (setup or removal) time of a job is a function of its position . The objective functions are finding the optimal sequence of jobs to minimize a cost function containing makespan, total completion time and total absolute differences in completion times and to minimize a cost function containing makespan, total waiting time and total absolute differences in waiting times. The problems are modeled as an assignment problem respectively, and thus can be solved in polynomial time.

Unrelated Parallel-Machine Scheduling with Controllable Processing Time

This paper explores an unrelated parallel-machine resource allocation scheduling problem with controllable processing time. The objective is to minimize the cost function containing the weighted of total load, total completion time, total absolute deviation of completion time, and total compression cost. We show that the proposed problem is polynomial time solvable. We also discuss a special case of the problem and show that it can be optimally solved by lower order algorithm.