Showing papers on "Single-machine scheduling published in 2009"
TL;DR: This paper develops a general model with learning effects where the actual processing time of a job is not only a function of the total normal processing times of the jobs already processed, but also afunction of the job's scheduled position.
179 citations
TL;DR: Based on the computational results, which MIP formulation might work best for various single machine scheduling problems is studied and two sets of inequalities that can be used to improve the formulation with assignment and positional date variables are presented.
122 citations
TL;DR: This paper considers the single machine scheduling problem with release dates and rejection, shows that the problem is NP-hard in the ordinary sense, and provides two pseudo-polynomial-time algorithms that can be solved in polynomial-time.
107 citations
TL;DR: This work presents polynomial-time dynamic programming algorithms in the case of two popular due date assignment methods: CON and SLK.
93 citations
TL;DR: Numerical experiments show that the proposed algorithm can optimally solve 300 jobs instances of the total weighted tardiness problem and thetotal weighted earliness-tardness problem, and that it outperforms the previous algorithms specialized for these problems.
Abstract: This study proposes an exact algorithm for the general single-machine scheduling problem without machine idle time to minimize the total job completion cost. Our algorithm is based on the Successive Sublimation Dynamic Programming (SSDP) method. Its major drawback is heavy memory usage to store dynamic programming states, although unnecessary states are eliminated in the course of the algorithm. To reduce both memory usage and computational efforts, several improvements to the previous algorithm based on the SSDP method are proposed. Numerical experiments show that our algorithm can optimally solve 300 jobs instances of the total weighted tardiness problem and the total weighted earliness-tardiness problem, and that it outperforms the previous algorithms specialized for these problems.
88 citations
TL;DR: This work considers several single machine scheduling problems in which the processing time of a job is a linear function of its starting time and jobs can be rejected by paying penalties, and shows that these problems are NP-hard.
86 citations
TL;DR: In this article, a branch-and-bound algorithm for hard two-agent scheduling problems is proposed, where each agent has an objective function which depends on the completion times of its jobs only.
Abstract: In this paper, we develop branch-and-bound algorithms for several hard, two-agent scheduling problems, i.e., problems in which each agent has an objective function which depends on the completion times of its jobs only. Our bounding approach is based on the fact that, for all problems considered, the Lagrangian dual gives a good bound and can be solved exactly in strongly polynomial time. The problems addressed here consist in minimizing the total weighted completion time of the jobs of agent A, subject to a bound on the cost function of agent B, which may be: (i) total weighted completion time, (ii) maximum lateness, (iii) maximum completion time. An extensive computational experience shows the effectiveness of the approach.
84 citations
17 Nov 2009
TL;DR: A hybrid algorithm is presented that combines the EM methodology and genetic operators to obtain the best/optimal schedule for this single machine scheduling problem, which attempts to achieve convergence and diversity effect when they iteratively solve the problem.
Abstract: Electromagnetism-like algorithm (EM) is a population-based meta-heuristic which has been proposed to solve continuous problems effectively. In this paper, we present a new meta-heuristic that uses the EM methodology to solve the single machine scheduling problem. Single machine scheduling is a combinatorial optimization problem. Schedule representation for our problem is based on random keys. Because there is little research in solving the combinatorial optimization problem (COP) by EM, the paper attempts to employ the random-key concept enabling EM to solve COP in single machine scheduling problem. We present a hybrid algorithm that combines the EM methodology and genetic operators to obtain the best/optimal schedule for this single machine scheduling problem, which attempts to achieve convergence and diversity effect when they iteratively solve the problem. The objective in our problem is minimization of the sum of earliness and tardiness. This hybrid algorithm was tested on a set of standard test problems available in the literature. The computational results show that this hybrid algorithm performs better than the standard genetic algorithm.
82 citations
TL;DR: This work proposes a new learning model where the actual job processing time is a function of the sum of the logarithm of the processing times of the jobs already processed, and shows that the scheduling problems to minimize the makespan and total completion time can be solved in polynomial time.
80 citations
TL;DR: An efficient (polynomial time) solution for a single machine scheduling and due-window assignment problem to minimize the total cost consisting of earliness, tardiness, andDue-window starting time and size is introduced.
74 citations
TL;DR: It is shown that even with the introduction of a time-dependent learning effect and deteriorating jobs to job processing times, the single machine makes the total completion time minimization problem remain polynomially solvable.
Abstract: The paper deals with the single machine scheduling problems with a time-dependent learning effect and deteriorating jobs. By the effects of time-dependent learning and deterioration, we mean that the processing time of a job is defined by function of its starting time and total normal processing time of jobs in front of it in the sequence. It is shown that even with the introduction of a time-dependent learning effect and deteriorating jobs to job processing times, the single machine makespan minimization problem remain polynomially solvable. But for the total completion time minimization problem, the classical shortest processing time first rule or largest processing time first rule cannot give an optimal solution.
TL;DR: The single machine scheduling problem with exponential time-dependent learning effect and past-sequence-dependent (p-s-d) setup times is considered and it is shown that the total weighted completion time minimization problem and the maximum lateness minimization problems can be solved in polynomial time under certain conditions.
Abstract: In this paper we consider the single machine scheduling problem with exponential time-dependent learning effect and past-sequence-dependent (p-s-d) setup times. By the exponential time-dependent learning effect, we mean that the processing time of a job is defined by an exponent function of the total normal processing time of the already processed jobs. The setup times are proportional to the length of the already processed jobs. We consider the following objective functions: the makespan, the total completion time, the sum of the quadratic job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the quadratic job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.
TL;DR: In this article, the authors studied the single machine scheduling problem with learning effect and deteriorating jobs simultaneously and proved that the problem is polynomially solvable for the makespan, the total completion time and the sum of the k th power of completion times minimization problems.
TL;DR: In this paper, the setup times of a job are proportional to the length of the already processed jobs, i.e., the job completion times are past-sequence-dependent (p-s-d).
Abstract: The paper deals with some single-machine scheduling problems with setup time considerations where the processing time of a job is given as a function of its starting times and position in a sequence. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We consider the following objective functions: the makespan, the total completion time, the sum of the δth (\( \delta \geqslant 0 \)) power of job completion times, the total weighted completion time, the maximum lateness and the number of tardy jobs. We show that the makespan minimization problem, the total completion time minimization problem, and the sum of the δth power of job completion times minimization problem can be solved in polynomial time, respectively. We also show that the total weighted completion time minimization problem, the maximum lateness minimization problem and the number of tardy jobs minimization problem can be solved in polynomial time under certain conditions.
TL;DR: This paper considers a single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time, and proposes a genetic approach based on a random key alphabet that clearly outperform the existing heuristics, and are quite close to the optimum solutions.
TL;DR: A new scheduling model in which deteriorating jobs and learning effect are both considered simultaneously is introduced, and it is shown that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain conditions.
TL;DR: A dynamic programming algorithm and it is shown that the single machine scheduling problem with a fixed non-availability interval has an FPTAS (Fully Polynomial Time Approximation Algorithm) by exploiting the well-known approach of Ibarra and Kim.
Abstract: In this article, we consider the non-resumable case of the single machine scheduling problem with a fixed non-availability interval. We aim to minimize the makespan when every job has a positive tail. We propose a polynomial approximation algorithm with a worst-case performance ratio of 3/2 for this problem. We show that this bound is tight. We present a dynamic programming algorithm and we show that the problem has an FPTAS (Fully Polynomial Time Approximation Algorithm) by exploiting the well-known approach of Ibarra and Kim (J. ACM 22:463–468, 1975). Such an FPTAS is strongly polynomial. The obtained results outperform the previous polynomial approximation algorithms for this problem.
TL;DR: This paper considers a single-machine scheduling problem with both deterioration and learning effects and several polynomial time algorithms are proposed to optimally solve the problem with the above objectives.
Abstract: This paper considers a single-machine scheduling problem with both deterioration and learning effects. The objectives are to respectively minimize the makespan, the total completion times, the sum of weighted completion times, the sum of the kth power of the job completion times, the maximum lateness, the total absolute differences in completion times and the sum of earliness, tardiness and common due-date penalties. Several polynomial time algorithms are proposed to optimally solve the problem with the above objectives.
TL;DR: The problem is proved to be NP- hard, and an introduction of a pseudo-polynomial dynamic programming algorithm indicates that it is NP-hard in the ordinary sense.
Abstract: We study a single machine scheduling problem. The processor needs to go through a maintenance activity, which has to be completed prior to a given deadline. The objective function is minimum total weighted completion time. The problem is proved to be NP-hard, and an introduction of a pseudo-polynomial dynamic programming algorithm indicates that it is NP-hard in the ordinary sense. We also present an efficient heuristic, which is shown numerically to perform well.
TL;DR: In this article, a branch-and-bound algorithm was proposed to solve the problem of single machine total flow time problem with non-resumable jobs and preventive maintenance activities of known starting times and durations.
Abstract: We consider the single machine total flow time problem in which the jobs are non-resumable and the machine is subject to preventive maintenance activities of known starting times and durations. We propose a branch-and-bound algorithm that employs powerful optimality properties and bounding procedures. Our extensive computational studies show that our algorithm can solve large-sized problem instances with up to 80 jobs in reasonable times. We also study a two-alternative maintenance planning problem with minor and major maintenances. We give a polynomial-time algorithm to find the optimal maintenance times when the job sequence is fixed.
TL;DR: In this paper, the authors considered a single-machine scheduling problem with each job having an uncertain processing time which can take any real value within each corresponding closed interval before completing the job, and established necessary and sufficient conditions for the existence of a job permutation which remains optimal for any possible realizations of these n uncertain processing times.
TL;DR: A simulated annealing algorithm with the new neighborhood of the problem of minimizing the maximum lateness on a single machine with family setups can obtain better near optimal solutions than the existing algorithm.
TL;DR: Results indicated that the computational effort required to reach optimality rose with the number of jobs to be scheduled and with decreased variance in due dates, but the model remained viable for optimizing research scale problems.
Abstract: A simple mixed integer programming model for the N job/single machine scheduling problem with possibly sequence-dependent setup times, differing earliness/tardiness cost penalties, and variable due dates is proposed and evaluated for computational efficiency. Results indicated that the computational effort required to reach optimality rose with the number of jobs to be scheduled and with decreased variance in due dates. Though computational effort was significant for the largest problems solved, the model remained viable for optimizing research scale problems.
TL;DR: It is shown that the problem of single machine scheduling problem with deteriorating jobs and group technology remains solvable in polynomial time when general linear deterioration and grouptechnology are considered simultaneously.
Abstract: In this paper, we consider a single machine scheduling problem with deteriorating jobs and group technology assumption. By deteriorating jobs and group technology assumption, we mean that the group setup times and job processing times are both increasing functions of their starting times, i.e., group setup times and job processing times are both described by function, which is a general linear function of time. The objective of the scheduling problem is to minimize the makespan. We show that the problem remains solvable in polynomial time when general linear deterioration and group technology are considered simultaneously.
TL;DR: In this article, the single machine makespan minimization problem with time-dependent deterioration was studied and it was shown that the problem is polynomially solvable with respect to normal job processing times.
Abstract: The paper deals with the single-machine scheduling problems with a time-dependent deterioration By 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 We show that, even with the introduction of time-dependent deterioration to job processing times, the single-machine makespan minimization problem remains polynomially solvable We also show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to normal job processing times
TL;DR: This paper studies the single machine common due date assignment and scheduling problem with the possibility to perform a rate-modifying activity (RMA) for changing the processing times of the jobs following this activity.
TL;DR: A non-linear mathematical programming model is developed for the single machine scheduling problem with unequal release dates and a learning effect which belongs to NP-hard class and is effective in solving problems with up to 30 jobs.
TL;DR: In this article, the authors investigated a single machine scheduling problem with deteriorating jobs, where the job deterioration is described by a function which is proportional to a linear function of time, and the objective is to find a schedule that minimizes total absolute differences in completion times.
TL;DR: The learning/aging effect in an n job single machine scheduling problem with common due date is considered and two bounds B[alpha] and for the learning index [alpha] are derived.
TL;DR: A heuristic algorithm with time complexity O( n 3 ) and a branch and bound algorithm to solve a single machine scheduling problem with dual criteria, i.e., the minimization of the total weighted earliness subject to minimum number of tardy jobs is developed.