Showing papers on "Single-machine scheduling published in 2013"
TL;DR: Numerical experiments show that significant energy savings can be obtained by applying effective machine operations schedule, and tradeoff between productivity and energy-efficiency in production systems is discussed and the energy-efficient production problem is formulated as a constrained optimization problem.
Abstract: Control of production operations is considered as one of the most economical methods to improve energy efficiency in manufacturing systems. This paper investigates energy consumption reduction in production systems through effective scheduling of machine startup and shutdown. Specifically, we consider serial production lines with finite buffers and machines having Bernoulli reliability model. This machine reliability model is applicable in production situations, where the downtime is relatively short and comparable to machine cycle time (e.g., automotive paint shops and general assembly). In this paper, using transient analysis of the systems at hand, an analytical performance evaluation technique is developed for Bernoulli serial lines with time-dependent machine efficiencies. In addition, tradeoff between productivity and energy-efficiency in production systems is discussed and the energy-efficient production problem is formulated as a constrained optimization problem. The effects and practical implications of operations schedule are demonstrated using a numerical study on automotive paint shop operations. Note to Practitioners - This paper develops an effective analytical tool to evaluate the performance of production systems with time-varying parameters of machine reliability. Using this tool, production engineers and managers can predict the performance of the production systems in real-time with high accuracy. In addition, based on this tool, production operators can determine the machine startup and shutdown schedule based on the current status of the line and production requirement. Numerical experiments show that significant energy savings can be obtained by applying effective machine operations schedule.
132 citations
TL;DR: This paper focuses 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 shows that the problems remain polynomially solvable under the proposed model.
55 citations
30 Dec 2013
TL;DR: This work proposes a new approach for solving sequencing problems based on multivalued decision diagrams (MDDs), which are compact graphical representations of Boolean functions, originally introduced for applications in circuit design by Lee and widely studied and applied in computer science.
Abstract: Sequencing problems are among the most widely studied problems in operations research. Specific variations of sequencing problems include single machine scheduling, the traveling salesman problem with time windows, and precedence-constrained machine scheduling. In this work we propose a new approach for solving sequencing problems based on multivalued decision diagrams (MDDs). Decision diagrams are compact graphical representations of Boolean functions, originally introduced for applications in circuit design by Lee [7], and widely studied and applied in computer science. They have been recently used to represent the feasible set of discrete optimization problems, as demonstrated in [2] and [3, 4]. This is done by perceiving the constraints of a problem as a Boolean function f(x) representing whether a solution x is feasible. Nonetheless, such MDDs can grow exponentially large, which makes any practical computation prohibitive in general.
52 citations
TL;DR: This paper assesses works done to minimize the weighted number of tardy jobs by providing an extensive review of authors, methods and techniques used.
Abstract: This paper presents a review of single machine scheduling to minimize the weighted number of tardy jobs. The problem involves processing n jobs on a single machine, each having processing time $p_j$ and due date $d_j$. The aim is to schedule the jobs to meet their due date. A job is tardy if the completion time of job $j$ is $C_j>d_j$ and on-time otherwise. This paper assesses works done to minimize the weighted number of tardy jobs by providing an extensive review of authors, methods and techniques used. Finally, the possible direction for future research is presented.
46 citations
TL;DR: Inspired by the importance of ready times, the single-machine two-agent scheduling problem with releases times and deadlines is studied to minimise the number of tardy jobs of one agent under the restriction that the maximum lateness of the jobs of the other agent cannot exceed a given value Q.
Abstract: Multiple-agent scheduling has attracted considerable research attention in recent years. However, studies of multiple-agent scheduling with release times and deadlines are few. In the presence of ready times, sometimes it is beneficial to wait for future job arrivals in constructing a schedule. Inspired by the importance of ready times, we study the single-machine two-agent scheduling problem with releases times and deadlines to minimise the number of tardy jobs of one agent under the restriction that the maximum lateness of the jobs of the other agent cannot exceed a given value Q. Having established that the problem is strongly NP-hard, we provide a branch-and-bound and a simulated annealing algorithm to search for the optimal and approximate solutions, respectively. The results of computational experiments reveal that the SA algorithm can generate near-optimal solutions quickly.
45 citations
TL;DR: In this study, the objective is determining a set of compression/expansion of processing times in addition to a sequence of jobs simultaneously, so that total tardiness and earliness are minimized.
42 citations
TL;DR: A novel hybrid metaheuristic, named as PHVNS, is developed for this NP-hard problem of earliness/tardiness scheduling and shows high competitiveness.
42 citations
TL;DR: A deterministic approximation algorithm with performance ratio of O(lnK) for the min-max version of the problem is proposed and it is shown that both min- Max and min- max regret problems are not approximable within any constant factor unless P=NP, which strengthens the results known up to date.
39 citations
TL;DR: This paper develops properties of optimal solutions and design a branch and bound algorithm and a dynamic programming algorithm with two extensions and empirically derive parameter settings leading to instances which are hard to solve on a single machine.
Abstract: This paper focuses on single machine scheduling subject to inventory constraints. Jobs add or remove items to or from the inventory, respectively. Jobs that remove items cannot be processed if the required number of items is not available. We consider scheduling problems on a single machine where the objective is to minimize the total weighted completion time. We develop properties of optimal solutions and design a branch and bound algorithm and a dynamic programming algorithm with two extensions. We compare the approaches in our computational study and empirically derive parameter settings leading to instances which are hard to solve.
37 citations
TL;DR: It is shown in this paper that the classic single-machine scheduling to minimize the total earliness and tardiness is strongly NP-hard.
36 citations
TL;DR: A heuristic is proposed to implement the reactive scheduling of the jobs in the dynamic production environment and it is proposed that priority scheduling is applied, which determines the next state of the system based on priority values of certain system elements.
TL;DR: The structural properties of the optimal schedules are derived and it is shown that the variants TETDC, TEWNTDC and TEW NTDS are all polynomially solvable and the complexity status of the variant WNTDD is still open, but it is also shown that two special cases of it are polynomegal solvable.
TL;DR: It is shown that several single machine problems remain polynomially solvable even with the introduction of the proposed model to job processing times, and the worst-case bound of the heuristic algorithms is analysed.
Abstract: In this paper we consider the single machine scheduling problem with truncated exponential learning functions. By the truncated exponential learning functions, we mean that the actual job processing time is a function which depends not only on the total normal 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. We show that even with the introduction of the proposed model to job processing times, several single machine problems remain polynomially solvable. For the following three objective functions, the total weighted completion time, the discounted total weighted completion time, the maximum lateness, we present heuristic algorithms according to the corresponding problems without truncated exponential learning functions. We also analyse the worst-case bound of our heuristic algorithms.
TL;DR: The goal of this paper is to minimize the total weighted number of tardy jobs of the first agent subject to the condition that the maximum lateness of the second agent is allowed to have an upper bound.
TL;DR: In this article, a single machine scheduling problem with deteriorating processing time of jobs and multiple preventive maintenances which reset deteriorated processing time to the original processing time was studied. And the authors proposed a number of heuristics and design genetic algorithms for the problems.
Abstract: In this paper, we study a single machine scheduling problem with deteriorating processing time of jobs and multiple preventive maintenances which reset deteriorated processing time to the original processing time. In this situation, we consider three kinds of problems whose performance measures are makespan, total completion time, and total weighted completion time. First, we formulate integer programming formulations, and using the formulations, one can find optimal solutions for small problems. Since these problems are known to be NP-hard and the size of real problem is very large, we propose a number of heuristics and design genetic algorithms for the problems. Finally, we conduct some computational experiments to evaluate the performance of the proposed algorithms.
TL;DR: A branch-and-bound algorithm and four heuristic algorithms to search for the optimal and near-optimal solutions to a single-machine problem with learning effects, where the objective is to minimize the total weighted completion time of jobs from the first agent.
TL;DR: This paper considers a variation of the classical single machine scheduling problem with tool changes and proposes three sets of algorithms based on the studies of a new bin packing problem and six algorithms that can solve instances with up to 5000 jobs in about 0.5s.
Abstract: This paper considers a variation of the classical single machine scheduling problem with tool changes. In the variation, two sets of jobs, namely special jobs and normal jobs, are considered. By special jobs, we mean that each special job must be processed within the first prefixed time units of a tool life. To solve the scheduling problem with small size and moderate size, we propose two mathematical programming models. To solve the scheduling problem with large size, we propose three sets of algorithms and focus on the performance of six algorithms based on the studies of a new bin packing problem. Worst-case analysis is conducted. Numerical experiment shows that each of the six algorithms can solve instances with up to 5000 jobs in about 0.5 s with an average relative error less than 4%.
TL;DR: It is shown that even with the introduction of a general learning effect to job processing times, some single machine scheduling problems are still polynomially solvable under the proposed model and some special cases of the flow shop scheduling problems can be solved in polynomial time.
TL;DR: Some heuristic algorithms by using the optimal permutations for the corresponding single machine scheduling problems are presented, and the worst-case bound of these heuristics are also analyzed.
Abstract: This article considers flow shop scheduling problems with a learning effect. By the learning effect, we mean that the processing time of a job is defined by a function of its position in a processing permutation. The objective is to minimize the total weighted completion time. Some heuristic algorithms by using the optimal permutations for the corresponding single machine scheduling problems are presented, and the worst-case bound of these heuristics are also analyzed.
TL;DR: The single machine scheduling problem with time-dependent deterioration and multiple RMAs is considered and a mathematical model for an optimal solution to minimize the makespan is derived and genetic algorithms are proposed.
Abstract: In this paper, the integration of two emerging classes of scheduling problems, the class of scheduling problems with time-dependent deterioration and the class of scheduling problems with rate-modifying activities, are addressed. The scheduling problems have been studied independently. However, the integration of these classes is motivated by human operators of tasks who have fatigue while carrying out the operation of a series of tasks. This situation is also applicable to machines that experience performance degradation over time due to mal-position or mal-alignment of jobs, abrasion of tools, and scraps of operations, etc. It requires maintenance in order to sustain acceptable production rates. We consider the single machine scheduling problem with time-dependent deterioration and multiple RMAs. A mathematical model for an optimal solution to minimize the makespan is derived and genetic algorithms are proposed. The performance of the genetic algorithms is evaluated using randomly generated examples.
TL;DR: This research investigated two scheduling problems in a stochastic setting in the class of non-preemptive static list policies with minimizing the number of tardy jobs using efficient algorithms, which have been developed for the deterministic version of the problems.
TL;DR: This work presents a polynomial-time algorithm based on dynamic programming for the case when the number of scenarios and the values of the instance are bounded by some constant, and proves that the unweighted version is NP-hard to approximate within a factor less than 6/5.
20 Jun 2013
TL;DR: New GP frameworks to evolve high-performance scheduling rules/heuristics for OAS are developed based on separating acceptance and sequencing decisions, and enhancing the quality of scheduling rules by embedding heuristic search mechanisms.
Abstract: This paper focuses on order acceptance and scheduling (OAS) problem, where both acceptance and sequencing decisions have to be handled simultaneously. Because of its complexity, designing effective heuristics or meta-heuristics for OAS is challenging. This paper will investigate how genetic programming (GP) can be used to deal with OAS. The goal of this paper is to develop new GP frameworks to evolve high-performance scheduling rules/heuristics for OAS. The new frameworks are developed based on two key aspects: (1) separating acceptance and sequencing decisions, and (2) enhancing the quality of scheduling rules by embedding heuristic search mechanisms. The experimental results show that separating decisions is not trivial and can easily lead to overfitting issues. Meanwhile, embedding heuristic ideas into the scheduling rules can help search for better solutions for OAS.
TL;DR: This paper presents heuristic algorithms by using the optimal permutations for the special cases of the corresponding single machine scheduling problems by exploiting the time-dependent learning effect of jobs scheduled in front of the job on the machine.
TL;DR: A heuristic method is proposed for solving the problem of sequencing jobs in a machine with programmed preventive maintenance and sequence-dependent set-up times, which hybridizes multi-start strategies with Tabu Search.
Abstract: In this paper we study a problem of sequencing jobs in a machine with programmed preventive maintenance and sequence-dependent set-up times. The problem combines two NP-hard problems, so we propose a heuristic method for solving it, which hybridizes multi-start strategies with Tabu Search. We compare our method with the only published metaheuristic algorithm for this problem on a set of 420 instances. The comparison favors the method developed in this work, showing that is able to find high quality solutions in very short computational times.
TL;DR: This study introduces an actual time-dependent and job-dependent learning effect into single-machine scheduling problems and shows that the complexity results of the makespan minimization problem and the sum of weighted completion time minimization problems are all NP-hard.
TL;DR: A single-machine scheduling with deteriorating jobs and aging effects under an optional maintenance activity is studied and a fully polynomial-time approximation scheme (FPTAS) for the proposed problem is presented to minimize the makespan.
Abstract: This article studies a single-machine scheduling with deteriorating jobs and aging effects under an optional maintenance activity. We assume that after maintenance activity, the machine will revert to its initial condition and the aging effects will start anew. Moreover, due to the restriction of budget of maintenance, the limitation of the maintenance frequency on the machine is assumed to be known in advance. The optional maintenance activity of this study means that the starting time of the maintenance activity is unknown in advance. It can be scheduled immediately after the processing of any job that has been completed. Therefore, the planner must to make decision on whether or when to schedule the maintenance activity during the scheduling horizon to optimal the performance measures. The objective is to minimize the makespan. We first show that the addressed problem is NP-hard in the strong sense. Then a fully polynomial-time approximation scheme (FPTAS) for the proposed problem is presented.
TL;DR: To solve permutation flow shop scheduling problems, approximation algorithms based on the optimal permutations for the corresponding single machine scheduling problems are presented and their worst-case error bound is analyzed.
Abstract: Machine learning exists in many realistic scheduling situations. This study focuses on permutation flow shop scheduling problems, where the actual processing time of a job is defined by a general non-increasing function of its scheduled position, i.e., general position-dependent learning effects. The objective functions are to minimize the total completion time, the makespan, the total weighted completion time, and the total weighted discounted completion time, respectively. To solve these problems, we present approximation algorithms based on the optimal permutations for the corresponding single machine scheduling problems and analyze their worst-case error bound.
TL;DR: This paper addresses some single-machine scheduling problems with past-sequence-dependent (p-s-d) delivery times and a linear deterioration, and shows that some special cases of the problems are polynomially solvable.
Abstract: 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 job
processing 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 to
minimize 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.
TL;DR: In this article, a novel evolutionary-based approach is utilized for efficiently solving the NP-hard problem of scheduling numerous common-due-date jobs on a single machine, where minimizing the sum of earliness and tardiness penalties for all jobs is considered as the target function.
Abstract: In this paper a novel evolutionary-based approach is utilised for efficiently solving the NP-hard problem of scheduling numerous common-due-date jobs on a single machine. Minimising the sum of earliness and tardiness penalties for all jobs is considered as the target function. The performance of the proposed approach is examined through a computational comparative study with 280 benchmark problems with up to 1000 jobs where the numerical results indicate that it can produce ‘better’ solutions in less computational time when compared to benchmark results and the methods available in the literature, namely genetic algorithm (GA), Tabu search (TS) and differential evolution (DE).