Showing papers on "Single-machine scheduling published in 2018"
TL;DR: The mathematical model of the low-carbon flexible job shop scheduling problem is established with the objective of minimizing the sum of the energy consumption cost and the earliness/tardiness cost.
Abstract: Flexible job shop scheduling problem (FJSP) is a typical discrete combinatorial optimization problem, which can be viewed as an extended version of the classical job shop scheduling problem. In previous researches, the scheduling problem has historically emphasized the production efficiency. Recently, scheduling problems with green criterion have been paid great attention by researchers. In this paper, the mathematical model of the low-carbon flexible job shop scheduling problem is established with the objective of minimizing the sum of the energy consumption cost and the earliness/tardiness cost. For solving the model, a kind of bi-population based discrete cat swarm optimization algorithm (BDCSO) is presented to obtain the optimal scheduling scheme in the workshop. In the framework of the BDCSO, two sub-populations are used to adjust the machine assignment and operation sequence respectively. At the initialization stage, a two-component discrete encoding mechanism is first employed to represent each individual, and then a heuristic method is adopted to generate the initial solutions with good quality and diversity. By considering the discrete characteristics of the scheduling problem, the modified updating methods are developed for the seeking and tracing modes to ensure the algorithm work directly in a discrete domain. To coordinate the global and local search in each sub-population, six adjustment curves are used to change the number of cats in the seeking and tracing modes, based on which six algorithms are developed, i.e., LBDCSO, SinBDCSO, CosBDCSO, TanBDCSO, LnBDCSO, and SquareBDCSO. In addition, the information exchanging strategy is introduced to implement the cooperation of the two sub-populations. Finally, extensive simulation based on random instances and benchmark instances is carried out. The comparisons results demonstrate the effectiveness of the proposed algorithms in solving the FJSP under study.
48 citations
TL;DR: A single machine scheduling problem where deteriorating jobs and flexible periodic maintenance are considered is studied, using a set-partitioning model and a branch-and-price algorithm to solve the pricing problem in column generation.
41 citations
38 citations
TL;DR: Computation experiments indicate that GA-TVNS performs the best among all the compared scheduling algorithms, and two new learning-based neighborhood structures are designed based on the classical school learning process of teaching–learning-based optimization.
Abstract: Rapid changes in production environments have motivated researchers and industrial manufacturers to coordinate the production and distribution in supply chain management. This paper aims to address the permutation flow shop scheduling problem with batch delivery to multiple customers. In this problem, products are first manufactured in a permutation flow shop, and subsequently delivered to multiple customers in batches. To optimize the tradeoff between customer service and distribution cost, the objective of this paper is to minimize the total cost of tardiness and batch delivery. To deal with such optimization problem, two simple heuristics and a novel meta-heuristic (GA-TVNS) are developed to determine integrated production and distribution schedules. GA-TVNS hybridizes genetic algorithm and variable neighborhood search (VNS) to provide better exploration and exploitation in the search space. Moreover, to improve the local search of VNS, two new learning-based neighborhood structures are designed based on the classical school learning process of teaching–learning-based optimization. Computation experiments on both small-sized and large-sized test problems indicate that GA-TVNS performs the best among all the compared scheduling algorithms.
35 citations
TL;DR: Using a improved formulation of the problem of sequencing jobs in a single machine with programmed preventive maintenance and sequence-dependent set-up times, a heuristic method based on the Variable Neighborhood Search (VNS) is proposed, which obtains very close-to-optimal solutions.
Abstract: In this paper we study the problem of sequencing jobs in a single machine with programmed preventive maintenance and sequence-dependent set-up times. This is an NP-hard problem that has practical relevance because of its industrial applications (textile industry, chemical industry, manufacturing of printed circuit boards, etc.), in which machines need periodic preventive maintenance. An improved formulation of this problem is proposed. Using this new formulation computational experiments show that commercial software can solve exactly not only small-sized instances but also almost all medium-sized instances as well. For solving large-sized instances a heuristic method based on the Variable Neighborhood Search (VNS) is proposed. Specifically, a Skewed VNS with memory, that is, it allows, under certain conditions, the current solution to move to a worse solution and for the incorporation of memory in the search process. Computational experiments show the good performance of our proposed VNS-based method. For small- and medium-sized instances specifically, this method obtains very close-to-optimal solutions, finding the optimal solution in the almost every case. In larger instances our method performs better than previously published algorithms. Several statistical tests support these conclusions. All instances used in computational experiments have been taken from the literature.
30 citations
TL;DR: The computational results on 320 benchmark instances show that the proposed DQGA is comparable to the state-of-the-art methods in the literature and outperforms the existing methods for some instances, as could improve the reported “best-known solutions” in notably less time.
30 citations
TL;DR: This paper addresses the problem of scheduling jobs on a single machine with cyclical machine availability periods, and proposes new approximate solution procedures for the problem, similar to the classical bin packing problem.
29 citations
TL;DR: It is proved that the problem is NP-hard and both a constant factor approximation algorithm and a fully polynomial time approximation scheme (FPTAS) are developed for solving it.
29 citations
TL;DR: The goal is to determine jointly the optimal job sequence and the common due date so as to minimise the expected value of an integrated cost function that includes the earliness, tardiness and due date assignment costs.
Abstract: This paper studies a single-machine due date assignment and scheduling problem in a disruptive environment, where a machine disruption may occur at a particular time that will last for a period of time with a certain probability, and the job due dates are determined by the decision-maker using the popular common due date assignment method. The goal is to determine jointly the optimal job sequence and the common due date so as to minimise the expected value of an integrated cost function that includes the earliness, tardiness and due date assignment costs. We analyse the computational complexity status of various cases of the problem, and develop pseudo-polynomial-time solution algorithms, randomised adaptive search algorithms, and fully polynomial-time approximation schemes for them, if viable. Finally, we conduct extensive numerical testing to assess the performance of the proposed algorithms.
27 citations
TL;DR: This study addresses an NP-Hard problem of minimizing the total tardiness on a single machine with sequence-dependent setup times and a position-based learning effect on processing times and develops a branch and bound algorithm for solving the problem.
24 citations
TL;DR: This work proposes an exact algorithm based on the iterative solution of three alternative arc-time-indexed models for single-machine scheduling problem with periodic maintenances and sequence-dependent setup times, and compares the results found by all formulations with those obtained by the best available mathematical formulation.
TL;DR: This research focuses on the problem of scheduling jobs that come from two agents on a single machine under periodic maintenance constraint with the objective of minimising the total completion time of the jobs of the first agent while keeping the maximum tardiness of other agent below or at a fixed level UB.
Abstract: Scheduling with periodic maintenance has been widely studied. However, multi-agent scheduling with simultaneous considerations of periodic maintenance has hardly been considered until now. In view of this, this research focuses on the problem of scheduling jobs that come from two agents on a single machine under periodic maintenance constraint with the objective of minimising the total completion time of the jobs of the first agent while keeping the maximum tardiness of other agent below or at a fixed level UB. We present some new dominance properties for this strongly NP-hard problem. And next, using these properties, we develop a novel imperialist competitive algorithm for the problem. Various parameters of the proposed algorithm are reviewed by means of Taguchi experimental design. For the evaluation of the proposed ICA, problem data was generated to compare it against a genetic algorithm. The results of computational experiments show the good performance of the proposed algorithm.
TL;DR: In this paper, the authors considered the class of single machine scheduling problems with the objective to minimize the weighted number of late jobs, under the assumption that completion due-dates are not known precisely at the time when decision-maker must provide a schedule.
TL;DR: One of these algorithms allows us to compute a lower bound for the NP-hard problem NSP–NSD, which is used in a branch-and-bound (B&B) algorithm to solve problem N SP-NSD.
Abstract: In this paper, we study an integrated production and outbound distribution scheduling model with one manufacturer and one customer. The manufacturer has to process a set of jobs on a single machine and deliver them in batches to the customer. Each job has a release date and a delivery deadline. The objective of the problem is to issue a feasible integrated production and distribution schedule minimizing the transportation cost subject to the delivery deadline constraints. We consider three problems with different ways how a job can be produced and delivered: non-splittable production and delivery (NSP-NSD) problem, splittable production and non-splittable delivery (SP-NSD) problem and splittable production and delivery (SP-SD) problem. We provide a polynomial-time algorithm that solves two special cases of SP-NSD and SP-SD problems. Solving these problems allows us to compute a lower bound for the NP-hard problem NSP-NSD, which we use in a branch and bound (B&B) algorithm to solve problem NSP-NSD. The computational results show that the B&B algorithm outperforms a MILP formulation of the problem implemented on a commercial solver. keywords: single machine scheduling production and delivery release dates deadlines transportation costs branch and bound.
TL;DR: A more general learning model is introduced for scheduling problems that generalizes existing ones and brings the consideration of learning and forgetting effects closer to reality, and it is demonstrated that some single machine scheduling problems are polynomially solvable under this general model.
Abstract: Workers with different levels of experience and knowledge have different effects on job processing times. By taking into account 1) the sum-of-processing-time; 2) the job-position; and 3) the experience of workers, a more general learning model is introduced for scheduling problems. We show that this model generalizes existing ones and brings the consideration of learning and forgetting effects closer to reality. We demonstrate that some single machine scheduling problems are polynomially solvable under this general model. Considering the forgetting effect caused by the idle time on the second machine, we construct a learning-forgetting model for the two-machine permutation flow shop scheduling problem with makespan minimization. A branch-and-bound method and four heuristics are presented to find optimal and approximate solutions, respectively. The proposed heuristics are evaluated over a large number of randomly generated instances. Experimental results show that the proposed heuristics are effective and efficient.
TL;DR: Experimental results confirm the robustness of schedules produced and advantages of the proposed TSH over other algorithms in terms of solution quality and run time, and develop a method to calculate the lower bound of the suggested model.
Abstract: We study a single machine scheduling problem (SMSP) with uncertain job release times (JRTs) under the maximum waiting time (MWT) criterion. To deal with the uncertainty, a robust model is establish...
TL;DR: The computational analysis indicates that the proposed heuristic algorithms are more efficient for the smaller ageing factor, whereas the Modified Shortest Processing Time algorithm is more efficient than the proposedHeuristic algorithms for the larger ageing factor.
Abstract: We consider single-machine scheduling problems with a batch-dependent ageing effect and variable maintenance activities between batches. The machine can process several jobs as a batch. It requires...
TL;DR: This article considered the single machine scheduling with controllable processing time (resource allocation) and deterioration effect concurrently and proved that these problems can be solved in polynomial time.
Abstract: This article considered the single machine scheduling with controllable processing time (resource allocation) and deterioration effect concurrently. It discussed the minimization of three objectives, which involve the weighted sum of the makespan and the total resource consumption cost, the total resource consumption cost under the condition that the makespan (total flow time) is restricted to a fixed constant and the optimal resource allocation and the optimal job sequence is what we need to make decision. Considering the makespan constraint, it proved that these problems can be solved in polynomial time. A special case of the last problem can be solved in polynomial time with respect to the total flow time constraint.
TL;DR: This work considers the approach to minimizing the number of late jobs on a single machine as a combination of two-stage stochastic programming and recoverable robustness, and presents some sufficient conditions that allow it to find a part of the optimal solution in polynomial time.
Abstract: Minimizing the number of late jobs on a single machine is a classic scheduling problem, which can be used to model the situation that from a set of potential customers, we have to select as many as possible whom we want to serve, while selling no to the other ones. This problem can be solved by Moore–Hodgson’s algorithm, provided that all data are deterministic. We consider a stochastic variant of this problem, where we assume that there is a small probability that the processing times differ from their standard values as a result of some kind of disturbance. When such a disturbance occurs, then we must apply some recovery action to make the solution feasible again. This leads us to the area of recoverable robustness, which handles this uncertainty by modeling each possible disturbance as a scenario; in each scenario, the initial solution must then be made feasible by applying a given, simple recovery algorithm to it. Since we cannot accept previously rejected customers, our only option is to reject customers that would have been served in the undisturbed case. Our problem therefore becomes to find a solution for the undisturbed case together with a feasible recovery to every possible disturbance. Our goal hereby is to maximize the expected number of served customers; we assume here that we know the probability that a given scenario occurs. In this respect, our problem falls outside the area of the ‘standard’ recoverable robustness, which contains the worst-case recovery cost as a component of the objective. Therefore, we consider our approach as a combination of two-stage stochastic programming and recoverable robustness. We show that this problem is $$\mathcal{NP}$$
-hard in the ordinary sense even if there is only one scenario, and we present some sufficient conditions that allow us to find a part of the optimal solution in polynomial time. We further evaluate several solution methods to find an optimal solution, among which are dynamic programming, branch-and-bound, and branch-and-price.
TL;DR: This work studies a single-machine scheduling problem in a flexible framework, where both job processing times and due dates are decision variables to be determined by the scheduler, and designs approximation algorithms for minimising the total resource consumption cost.
Abstract: We study a single-machine scheduling problem in a flexible framework, where both job processing times and due dates are decision variables to be determined by the scheduler. We consider the case wh...
TL;DR: The stability approach is applied to the considered uncertain scheduling problem using a relative perimeter of the optimality box as a stability measure of the optimal job permutation.
Abstract: We consider a single machine scheduling problem with uncertain durations of the given jobs. The objective function is minimizing the sum of the job completion times. We apply the stability approach to the considered uncertain scheduling problem using a relative perimeter of the optimality box as a stability measure of the optimal job permutation. We investigated properties of the optimality box and developed algorithms for constructing job permutations that have the largest relative perimeters of the optimality box. Computational results for constructing such permutations showed that they provided the average error less than 0 . 74 % for the solved uncertain problems.
TL;DR: In this paper, a comprehensive mathematical model with adjustable processing time is established, and a hybrid multi-objective evolutionary algorithm based on decomposition and particle swarm optimization is adopted for solving FJISP.
Abstract: In reality, uncertainties may still encounter after a scheduling scheme is generated. These may make the original schedule non-optimal or even impossible. Traditional scheduling methods are not effective in dealing with these situations. In response to this phenomenon, by introducing the idea of inverse optimization into the scheduling field, a new scheduling strategy called “inverse scheduling” has been proposed. To the best of our knowledge, this is the first study to be conducted on flexible job shop inverse scheduling problem (FJISP). In this paper, first, a comprehensive mathematical model with adjustable processing time is established. Then, a hybrid multi-objective evolutionary algorithm based on decomposition and particle swarm optimization is adopted for solving FJISP. To make the proposed algorithm solving FJISP more efficiently, some new strategies are used. A 3-D coding scheme is employed to represent the particles, multiple strategies are designed for generating a high-quality initial population, and effective discrete crossover and mutation operators are specially designed according to the FJISP’s characteristics. Finally, computational experiments are carried out using extended benchmarks, and the results demonstrate the effectiveness of the proposed algorithm for solving the FJISP.
TL;DR: A new scheduling model with a learning effect matrix is proposed and it is shown that the makespan and the total completion time problems can be optimally solved in polynomial time.
Abstract: Scheduling problems with learning effects have been widely studied in numerous publication. However, the learning effect might accelerate, especially in the steel plates and the human interaction systems. In this paper, we propose a new scheduling model with a learning effect matrix. We show that the makespan and the total completion time problems can be optimally solved in polynomial time. We present heuristic sequencing rules and analyze the worst-case bounds for performance ratios to minimize the total weighted completion time, the maximum lateness, and the total tardiness. We also show that these heuristic rules can be optimal under some agreeable conditions between the normal processing times and job due dates or weights.
TL;DR: A pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme are presented for the single-machine scheduling with an operator non-availability period to minimize total weighted completion time.
TL;DR: A new greedy insertion heuristic algorithm with a multi-stage filtering mechanism including coarse granularity and fine granularity filtering is developed in this paper, which can quickly filter out many impossible positions in the coarse granular filtering stage, and then, each job can find its optimal position in a relatively large space in the finegranularity filtering stage.
Abstract: To improve energy efficiency and maintain the stability of the power grid, time-of-use (TOU) electricity tariffs have been widely used around the world, which bring both opportunities and challenges to the energy-efficient scheduling problems. Single machine scheduling problems under TOU electricity tariffs are of great significance both in theory and practice. Although methods based on discrete-time or continuous-time models have been put forward for addressing this problem, they are deficient in solution quality or time complexity, especially when dealing with large-size instances. To address large-scale problems more efficiently, a new greedy insertion heuristic algorithm with a multi-stage filtering mechanism including coarse granularity and fine granularity filtering is developed in this paper. Based on the concentration and diffusion strategy, the algorithm can quickly filter out many impossible positions in the coarse granularity filtering stage, and then, each job can find its optimal position in a relatively large space in the fine granularity filtering stage. To show the effectiveness and computational process of the proposed algorithm, a real case study is provided. Furthermore, two sets of contrast experiments are conducted, aiming to demonstrate the good application of the algorithm. The experiments indicate that the small-size instances can be solved within 0.02 s using our algorithm, and the accuracy is further improved. For the large-size instances, the computation speed of our algorithm is improved greatly compared with the classic greedy insertion heuristic algorithm.
TL;DR: A preprocessing rule is devised to identify jobs that cannot belong to any optimal schedule, and the resulting reduced problem is solved to optimality by a branch-and-bound algorithm and two integer linear programming formulations.
Abstract: We study a prize-collecting single-machine scheduling problem with hard deadlines, where the objective is to minimize the difference between the total tardiness and the total prize of the selected jobs. This problem is motivated by industrial applications, both as a stand-alone model and as a pricing subproblem in column-generation algorithms for parallel machine scheduling problems. A preprocessing rule is devised to identify jobs that cannot belong to any optimal schedule. The resulting reduced problem is solved to optimality by a branch-and-bound algorithm and two integer linear programming formulations. The algorithm and the formulations are experimentally compared on randomly generated benchmark instances.
TL;DR: This paper aims to provide a history of the field and some of the techniques used to develop and evaluate these techniques, as well as some examples of how they are being used in practice and in the literature.
Abstract: Article history: Received July 18 2017 Received in Revised Format July 29 2017 Accepted August 19 2017 Available online August 2
06 Jul 2018
TL;DR: A bi-objective mixed integer linear programming model is developed employing this speed scaling scheme and the augmented ε-constraint method with a time limit to obtain a set of non-dominated solutions for each instance of the problem.
Abstract: This study considers single machine scheduling with the machine operating at varying speed levels for different jobs with release dates and sequence-dependent setup times, in order to examine the trade-off between makespan and total energy consumption. A bi-objective mixed integer linear programming model is developed employing this speed scaling scheme. The augmented e-constraint method with a time limit is used to obtain a set of non-dominated solutions for each instance of the problem. An energy-efficient multi-objective variable block insertion heuristic is also proposed. The computational results on a benchmark suite consisting of 260 instances with 25 jobs from the literature reveal that the proposed algorithm is very competitive in terms of providing tight Pareto front approximations for the problem.
TL;DR: A mathematical formulation of the studied problem that is expressed in the constraint programming (CP) paradigm as a set of linear constraints is proposed and a heuristic algorithm is provided to deal with lager instances of the problem.
TL;DR: One heuristic and an Ant Colony Optimization algorithm are proposed to solve two-agent scheduling problem with a single machine which is responsible for processing jobs from two agents.