Absolute Differences In Completion Times Research Articles

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.

Parallel machines scheduling with deterioration effects and resource allocations

This article studies multi-objective scheduling problems involving deterioration effects and resource allocations simultaneously on an unrelated parallel-machine setting. The linear and convex resource consumption models are examined, respectively. We aim to find the optimal resource allocation and the optimal job sequence to minimize the cost function including the total completion time, the total machine load, the total absolute differences in completion times and the resource allocation and the cost function including the total waiting time, the total absolute differences in waiting times, and the resource allocation, respectively. We develop polynomial time algorithms for all the problems studied.

Unrelated Parallel-Machine Scheduling with Deteriorating Jobs and Rejection

This paper aimed to investigate the unrelated parallel-machine scheduling with deteriorating jobs and rejection. The objective is to find the rejected jobs, the non-rejected jobs, and the optimal non-rejected job sequence so that the cost function that includes the weighted of total load, total completion time, and total absolute deviation of completion time plus the total penalty of the rejected jobs would be minimized. Results showed that the problem is polynomial time solvable when the number of machine is fixed.

Unrelated parallel-machine scheduling with position-dependent deteriorating jobs and resource-dependent processing time

This paper is to analyze unrelated parallel-machine scheduling resource allocation problems with position-dependent deteriorating jobs. Two general resource consumption functions, the linear and convex resource, are investigated. The objectives are to minimize the cost function that includes the weights of total load, total completion time, total absolute deviation of completion time, and total resource cost. Moreover, we try to minimize the cost function that includes the weights of total load, total waiting time, total absolute deviation of waiting time, and total resource cost. Although each job processing time can be compressed through incurring an additional cost, we show that the problems are polynomial time solvable when the number of machines is fixed.

Single-machine scheduling problems with past-sequence-dependent delivery times and position-dependent processing times

This paper considers single-machine scheduling problems with job delivery times where the actual job processing time of a job is defined by a function dependent on its position in a schedule. We assume that the job delivery time is proportional to the job waiting time. We investigate the minimization problems of the sum of earliness, tardiness, and due-window-related cost, the total absolute differences in completion times, and the total absolute differences in waiting times on a single-machine setting. The polynomial time algorithms are proposed to optimally solve the above objective functions. We also investigate some special cases of the problem under study and show that they can be optimally solved by lower order algorithms.

Single machine scheduling with truncated job-dependent learning effect

In this paper we consider the single machine scheduling problem with truncated job-dependent learning effect. By the truncated job-dependent learning effect, we mean that the actual job processing time is a function which depends not only on the job-dependent learning effect (i.e., the learning in the production process of some jobs to be faster than that of others) but also on a control parameter. The objectives are to minimize the makespan, the total completion time, the total absolute deviation of completion time, the earliness, tardiness and common (slack) due-date penalty, respectively. Several polynomial time algorithms are proposed to optimally solve the problems with the above objective functions.

Parallel-machine scheduling with non-simultaneous machine available time

We consider a problem of scheduling n independent jobs on m parallel identical machines. The jobs are available at time zero, but the machines may not be available simultaneously at time zero. We concentrate on two goals separately, namely, minimizing a cost function containing total completion time and total absolute differences in completion times; minimizing a cost function containing total waiting time and total absolute differences in waiting times. In this paper, we present polynomial time algorithm to solve this problem.

Minimizing makespan subject to minimum total absolute deviation of completion time on identical parallel machines

This study addresses the identical parallel machine scheduling problem with the objective of minimizing makespan subject to minimum total absolute deviation of job completion time (TADC). An optimization algorithm is first proposed to solve TADC on an identical parallel machine and an iterative procedure based on a polynomial binary integer programming model is then proposed to minimize makespan. Computational experiments show that the proposed algorithm is efficient. The worst case performance, which refers to the largest average execution for each scenario of the experiments, is 229.10 seconds for the problem with n=200, m=30 and p j from a uniform [1, 100].

SCHEDULING JOBS WITH PROCESSING TIMES DEPENDENT ON POSITION, STARTING TIME, AND ALLOTTED RESOURCE

We consider single-machine scheduling problem in which the processing time of a job is a function of its position in a sequence, its starting time, and its resource allocation. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. We concentrate on two goals separately, namely, minimizing a cost function containing makespan, total completion time, total absolute differences in completion times, and total resource cost; minimizing a cost function containing makespan, total waiting time, total absolute differences in waiting times, and total resource cost. The problem is modeled as an assignment problem, and thus can be solved in polynomial time. Some extensions of the problem are also shown.

Single-machine scheduling with convex resource dependent processing times and deteriorating jobs

In this study, we consider scheduling problems with convex resource dependent processing times and deteriorating jobs, in which the processing time of a job is a function of its starting time and its convex resource allocation. The objective is to find the optimal sequence of jobs and the optimal convex resource allocation separately. This paper focus on the single-machine problems with 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. It shows that the problems remain polynomially solvable under the proposed model.

Parallel machines scheduling with deteriorating and learning effects

In this paper parallel identical machines scheduling problems with deteriorating jobs and learning effects are considered. In this model, job processing times are defined by functions of their starting times and positions in the sequence. We concentrate on two goals separately, namely, minimizing a cost function containing total completion time and total absolute differences in completion times; minimizing a cost function containing total waiting time and total absolute differences in waiting times. We show that the problems remain polynomially solvable under the proposed model.

New results on single-machine scheduling with past-sequence-dependent delivery times

Scheduling with past-sequence-dependent (psd) delivery times is motivated by questions that arise in the electronic manufacturing industry: an electronic component may be exposed to certain a electromagnetic field while waiting for processing and is required to neutralize the effect of electromagnetism. The time spent on the neutralization process has been modeled as psd delivery time in the literature. In this paper, we consider single-machine scheduling problems with psd delivery times. We respectively derive polynomial algorithms for the following objective functions: the minimization of the total weighted completion time, the total weighted discounted completion time, the total absolute differences in completion times and the sum of earliness, tardiness and common due date penalty. At last, for the criteria of minimization the total weighted tardiness, we propose a polynomial algorithm to optimally solve the problem under a certain condition.

Solving the single machine scheduling problem with general job-dependent past-sequence-dependent setup times and learning effects

This paper deals with a single machine scheduling problem with general past-sequence-dependent (psd) setup time and log-linear learning in which the setup times and learning effects are job-dependent. The setup times are unique functions of the length of already processed jobs, and the learning effects show that processing times are unique decreasing functions of job positions. The goal is to find the optimal sequences that minimise objective functions such as the makespan, total completion time, total lateness, total waiting cost, total waiting time, total absolute differences in completion times, and the sum of earliness, tardiness and common due date penalty. Special cases of the resulting problems are solvable in polynomial time; however, the general problems are difficult to solve. We propose branch-and-bound (B&B) methods to derive the optimal sequences for such problems. Computational results show that the proposed methods can solve relatively large problem instances in reasonable amounts of time.

Single-machine scheduling with time-and-resource-dependent processing times

We consider single-machine scheduling problems in which the processing time of a job is a function of its starting time and its resource allocation. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. We concentrate on two goals separately, namely, minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost; minimizing a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. We show that the problems remain polynomially solvable under the proposed model.

Minimizing mean absolute deviation of completion time about a common due window subject to maximum tardiness for a single machine

Abstract This study deals with the problem of scheduling jobs on a single machine to minimize the mean absolute deviation of the job completion time about a large common due window subject to the maximum tardiness constraint. Using the well-known three-field notation, the problem is identified as MAD/large DueWindow/Tmax. The common due window is set to be large enough to allow idle time prior to the beginning of a schedule to investigate the effect of the Tmax constraint. Penalties arise if a job is completed outside the due window. A branch and bound algorithm and a heuristic are proposed. Many properties of the solutions and precedence relationships are identified. Our computational results reveal that the branch and bound algorithm is capable of solving problems of up to 50 jobs and the heuristic algorithm yields approximate solutions that are very close to the exact solution.

An efficient local search scheme for minimizing mean absolute deviation of completion times

We present a two phase local search scheme for finding a sequence of n jobs to be performed on a single machine such that mean absolute deviation of completion times from the mean completion time (MADMC) is minimum. By exploiting the structure of the MADMC function, we show that partial dominance exists among the n! feasible sequences. With the help of these dominance relations we are able to show that the complexity of our local search algorithm is a polynomial in the number of jobs. The asymptotic optimality result of Mosheiov apply to our heuristic also since we begin our search from Mosheiov’s heuristic solution, the alternating sequence, and hence improve upon it.

Considerations of single-machine scheduling with deteriorating jobs

This paper considers some scheduling problems with deteriorating jobs. The objectives are to minimize the makespan, the total completion time, the total absolute deviation of completion time, the earliness, tardiness, and due date penalty, the sum of earliness penalties subject to no tardy jobs, respectively. We also explore two resource constrained scheduling problems: how to minimize the resource consumption with makespan constraints and how to minimize the makespan with the total resource consumption constraints. Several polynomial time algorithms are proposed to optimally solve the problems with the above objective functions.

Parallel machine scheduling with a deteriorating maintenance activity and total absolute differences penalties

In this paper we consider identical parallel machines scheduling problems with a deteriorating maintenance activity. In this model, each machine has a deteriorating maintenance activity, that is, delaying the maintenance increases the time required to perform it. We need to make a decision on when to schedule the rate-modifying activities and the sequence of jobs to minimize some objective function. We concentrate on two goals separately, namely, minimizing the total absolute differences in completion times (TADC) and the total absolute differences in waiting times (TADW). We show that the problems remain polynomially solvable under the proposed model.

Single-machine scheduling with controllable processing times and learning effect

In this paper, we consider single-machine scheduling problem with controllable processing times and learning effect, i.e., processing times of jobs are controllable variables with linear costs and also are defined as functions of positions in a schedule. We concentrate on two goals separately, namely minimizing a cost function containing makespan, total completion time, total absolute differences in completion times, and total compression cost and minimizing a cost function containing makespan, total waiting time, total absolute differences in waiting times, and total compression cost. The problem is modeled as an assignment problem and thus can be solved with the well-known algorithms.

Parallel identical machines scheduling with deteriorating jobs and total absolute differences penalties

In this paper we consider parallel identical machines scheduling problems with deteriorating jobs. In this model, job processing times are defined by functions of their starting times. We concentrate on two goals separately, namely, minimizing the total absolute differences in completion times (TADC) and the total absolute differences in waiting times (TADW). We show that the problems remains polynomially solvable under the proposed model.