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Showing papers on "Single-machine scheduling published in 2011"


Journal ArticleDOI
TL;DR: In this article, the authors consider a two-agent scheduling problem in which the actual processing time of a job in a schedule is a function of the sum-of-processing-times-based learning and a control parameter of the learning function.

103 citations


Book
08 Sep 2011
TL;DR: An efficient branch-bound algorithm is presented for solving the n-job, sequence-independent, single machine scheduling problem where the goal is to minimize the total penalty costs resulting from tardiness of jobs.
Abstract: An efficient branch-bound algorithm is presented for solving the n-job, sequence-independent, single machine scheduling problem where the goal is to minimize the total penalty costs resulting from tardiness of jobs. The algorithm and computational results are given for the case of linear penalty functions. The modifications needed to handle the case of nonlinear penalty functions are also presented.

78 citations


Journal ArticleDOI
TL;DR: A single machine scheduling problem, where two agents compete on the use of a single processor, and an efficient solution algorithm is introduced, where n is the total number of jobs.

71 citations


Journal ArticleDOI
TL;DR: A new learning effect model is proposed in which the actual job processing time is a general function of the normal processing time of jobs already processed and its scheduled position.
Abstract: In this paper, we propose a new learning effect model in which the actual job processing time is a general function of the normal processing time of jobs already processed and its scheduled position. This model has the advantage that different learning curves can be constructed easily, such as the plateau function. It is found that most of the models in the literature are special cases of our proposed model. The optimal sequences for some single-machine problems are then provided.

65 citations


Journal ArticleDOI
TL;DR: In this paper, an increasing linear deterioration model is introduced into the two-agent single-machine scheduling, where the goal is to minimize the objective function of the first agent with the restriction that the objective functions of the second agent cannot exceed a given upper bound.

63 citations


Book
24 Aug 2011
TL;DR: This paper examines how setups, due dates, and the mix of standardized and customized products affect the scheduling of a single machine operating in a dynamic and stochastic environment and conjecture that an averaging principle holds for this queueing system in the heavy traffic limit.
Abstract: This paper examines how setups, due dates, and the mix of standardized and customized products affect the scheduling of a single machine operating in a dynamic and stochastic environment. We restrict ourselves to the class of dynamic cyclic policies, where the machine busy/idle policy and lot-sizing decisions are controlled in a dynamic fashion, but different products must be produced in a fixed sequence. As in earlier work, we conjecture that an averaging principle holds for this queueing system in the heavy traffic limit, and optimize over the class of dynamic cyclic policies. The results allow for a detailed discussion of the interactions between the due-date, setup, and product mix facets of the problem.

52 citations


Journal ArticleDOI
TL;DR: A dynamic programming algorithm and a branch-and-bound algorithm are proposed to solve a single machine problem in which job processing and machine maintenance have to be scheduled simultaneously to minimize total completion time of jobs for both resumable and nonresumable cases.

52 citations


Journal ArticleDOI
TL;DR: Under the proposed learning model, it is shown that some single-machine scheduling problems can be solved in polynomial time and the worst-case error bounds for the problems to minimize the maximum lateness and total weighted completion time are provided.

51 citations


Journal ArticleDOI
TL;DR: This paper shows that the single-machine scheduling problems to minimize the makespan, sum of the kth power of completion times, total lateness and sum of earliness penalties (with a common due date) are polynomially solvable under the proposed model.
Abstract: Learning and job deterioration co-exist in many realistic scheduling situations. This paper introduces a general scheduling model with the effects of learning and deterioration simultaneously which is a significant generalization of some existing models in the literature. By the effects of learning and deterioration, we mean that job processing times are defined by functions of their start times and positions in the sequence. This paper shows that the single-machine scheduling problems to minimize the makespan, sum of the kth power of completion times, total lateness and sum of earliness penalties (with a common due date) are polynomially solvable under the proposed model. It further shows that the problems to minimize the total weighted completion time, discounted total weighted completion time, maximum lateness, maximum tardiness, total tardiness and total weighted earliness penalties (with a common due date) are polynomially solvable under certain conditions.

48 citations


Journal ArticleDOI
TL;DR: Heuristic algorithms are presented by using the optimal permutations for the corresponding single machine scheduling problems with a general position-dependent learning effects to minimize one of the five regular performance criteria.
Abstract: A real industrial production phenomenon, referred to as learning effects, has drawn increasing attention. However, most research on this issue considers only single machine problems. Motivated by this limitation, this paper considers flow shop scheduling problems with a general position-dependent learning effects. By the general position-dependent learning effects, we mean that the actual processing time of a job is defined by a general non-increasing function of its scheduled position. The objective is to minimize one of the five regular performance criteria, namely, the total completion time, the makespan, the total weighted completion time, the total weighted discounted completion time, and the sum of the quadratic job completion times. We present heuristic algorithms by using the optimal permutations for the corresponding single machine scheduling problems. We also analyze the worst-case bound of our heuristic algorithms.

47 citations


Journal ArticleDOI
TL;DR: Three multi-objective algorithms based on Variable Neighborhood Search (VNS) heuristic are compared to solve the single machine scheduling problem with sequence dependent setup times and distinct due windows and the proposed algorithms outperform the original MOVNS algorithm in terms of solution quality.

Journal ArticleDOI
TL;DR: A branch-and-bound algorithm is developed for the optimal solution of a single-machine problem with the sum of processing times based learning effect and release times, and a simulated-annealing heuristic algorithm is proposed for a near-optimal solution.

Journal ArticleDOI
TL;DR: It is proved that the weighted sum of squared completion times minimization problem with strong chains and weak chains can be solved in polynomial time, respectively.
Abstract: In this paper we consider a single machine scheduling problem with deteriorating jobs. By deteriorating jobs, we mean that the processing time of a job is a simple linear function of its execution starting time. For the jobs with chain precedence constraints, we prove that the weighted sum of squared completion times minimization problem with strong chains and weak chains can be solved in polynomial time, respectively.

Journal ArticleDOI
TL;DR: In this article, the authors considered scheduling with deteriorating jobs in which the actual processing time of a job is a function of the logarithm of the total processing times of the jobs processed before it.

Journal ArticleDOI
TL;DR: A branch-and-bound algorithm and an evolutionary algorithm to find a schedule that minimizes the total tardiness of the first agent, provided that no tardy job is allowed for the second agent are proposed.
Abstract: We consider a problem of scheduling a set of independent jobs by two agents on a single machine. Every agent has its own subset of jobs to be scheduled and uses its own optimality criterion. The processing time of each job proportionally deteriorates with respect to the starting time of the job. The problem is to find a schedule that minimizes the total tardiness of the first agent, provided that no tardy job is allowed for the second agent. We prove basic properties of the problem and give a lower bound on the optimal value of the total tardiness criterion. On the basis of these results, we propose a branch-and-bound algorithm and an evolutionary algorithm for the problem. Computational experiments show that the exact algorithm solves instances up to 50 jobs in a reasonably short time and that solutions obtained by the metaheuristic are close to optimal ones.

Journal ArticleDOI
TL;DR: This work considers single machine scheduling problems with a non-renewable resource and presents some properties of feasible schedules for several problems of these types with standard objective functions, including the minimization of makespan and total tardiness.

Journal ArticleDOI
TL;DR: The goal is to determine an optimal combination of theDue date assignment strategy and job schedule so as to minimize an objective function that includes earliness, tardiness, due date assignment and flow time costs.

Journal ArticleDOI
TL;DR: In this paper, a mixed-integer programming model was proposed to solve the problem of single machine scheduling with availability constraints and sequence-dependent setup costs, with the aim of minimizing the makespan.

Journal ArticleDOI
TL;DR: A branch-and-bound algorithm incorporating with several dominance properties and lower bounds is developed to derive the optimal solution of a single-machine problem with the unequal release times under learning effect and deteriorating jobs when the objective is minimizing the makespan.

Journal ArticleDOI
TL;DR: This paper shows that the vertex cover graph associated with the scheduling problem is exactly the graph of incomparable pairs defined in the dimension theory of partial orders, and presents a framework for obtaining (2-2/f)-approximation algorithms, provided that the set of precedence constraints has fractional dimension of at most f.
Abstract: We consider the single-machine scheduling problem to minimize the weighted sum of completion times under precedence constraints. In a series of recent papers, it was established that this scheduling problem is a special case of minimum weighted vertex cover. In this paper, we show that the vertex cover graph associated with the scheduling problem is exactly the graph of incomparable pairs defined in the dimension theory of partial orders. Exploiting this relationship allows us to present a framework for obtaining (2-2/f)-approximation algorithms, provided that the set of precedence constraints has fractional dimension of at most f. Our approach yields the best-known approximation ratios for all previously considered special classes of precedence constraints, and it provides the first results for bounded degree and orders of interval dimension 2. On the negative side, we show that the addressed problem remains NP-hard even when restricted to the special case of interval orders. Furthermore, we prove that the general problem, if a fixed cost present in all feasible schedules is ignored, becomes as hard to approximate as vertex cover. We conclude by giving the first inapproximability result for this problem, showing under a widely believed assumption that it does not admit a polynomial-time approximation scheme.

Journal ArticleDOI
TL;DR: This paper considers a single-machine scheduling problem with deteriorating jobs and setup times to minimize the maximum tardiness, and provides a branch-and-bound algorithm to solve this problem.

Journal ArticleDOI
TL;DR: The contribution of this paper is to design and implement a solution approach based on metaheuristic procedures for sequencing jobs in a machine with programmed preventive maintenance and sequence-dependent setup times.
Abstract: In this paper we study a problem of sequencing jobs in a machine with programmed preventive maintenance and sequence-dependent setup times. To the authors' knowledge, this problem has not been treated as such in the operations research literature. Computational experiments show that it is very hard to solve the problem by exact methods. Therefore, the contribution of this paper is to design and implement a solution approach based on metaheuristic procedures. The proposed method finds high quality solutions in very short computational times.

Book ChapterDOI
17 Aug 2011
TL;DR: In this article, a primal-dual pseudo-polynomial-time (2 + e)-approximation algorithm was proposed for the problem. But this algorithm requires the machine's speed to vary over time arbitrarily.
Abstract: We consider the following single-machine scheduling problem, which is often denoted 1||Σfj: we are given n jobs to be scheduled on a single machine, where each job j has an integral processing time pj, and there is a nondecreasing, nonnegative cost function fj (Cj) that specifies the cost of finishing j at time Cj; the objective is to minimize n Σj=1n fj (Cj). Bansal & Pruhs recently gave the first constant approximation algorithm and we improve on their 16-approximation algorithm, by giving a primal-dual pseudo-polynomial-time algorithm that finds a solution of cost at most twice the optimal cost, and then show how this can be extended to yield, for any e > 0, a (2 + e)-approximation algorithm for this problem. Furthermore, we generalize this result to allow the machine's speed to vary over time arbitrarily, for which no previous constant-factor approximation algorithm was known.

Journal ArticleDOI
TL;DR: This paper considers single-machine scheduling problem with controllable processing times and learning effect, and focuses on minimizing a cost function containing makespan, total completion time, total absolute differences in completion times, and total compression cost.
Abstract: In this paper, we consider single-machine scheduling problem with controllable processing times and learning effect, ie, 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

Journal ArticleDOI
TL;DR: This paper shows that the main results in a recent paper by Zhang and Yan are incorrect as an important reason is missing, that is, the processing time of a job is variable according to a general learning effect, and gives a revised model with a generallearning effect.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a new model, with non-linear terms and integer variables which cannot be solved efficiently for large size problems due to its NP-hardness.
Abstract: This paper concerns with the concept of preemption in just-in-time single machine scheduling problem, with allowable machine idle time. We proposed a new model, with non-linear terms and integer variables which cannot be solved efficiently for large size problems due to its NP-hardness. To solve the model for real size applications, genetic algorithm is applied. These genetic procedures are also quite close to the optimum and provided an optimal solution for most of the test problems. Numerical examples show that the proposed algorithm is efficient and effective.

01 Jan 2011
TL;DR: A new model, with non-linear terms and integer variables which cannot be solved efficiently for large size problems due to its NP-hardness is proposed, and genetic algorithm is applied to solve the model for real size applications.
Abstract: This paper concerns with the concept of preemption in just-in-time single machine scheduling problem, with allowable machine idle time. We proposed a new model, with non-linear terms and integer variables which cannot be solved efficiently for large size problems due to its NP-hardness. To solve the model for real size applications, genetic algorithm is applied. These genetic procedures are also quite close to the optimum and provided an optimal solution for most of the test problems. Numerical examples show that the proposed algorithm is efficient and effective.

Journal ArticleDOI
TL;DR: It is shown that the single-machine scheduling problems under the proposed model can be solved in polynomial time if the objective is to minimize the total lateness or minimize the sum of earliness penalties.

Patent
11 Mar 2011
TL;DR: In this paper, a main multi-machine scheduling problem is defined as a plurality of single machine scheduling problems, and the problem is solved by solving the plurality of scheduling problems independently.
Abstract: Computerized scheduling methods and computerized scheduling systems according to exemplary embodiments A computerized scheduling method may be stored in a memory and executed on one or more processors The method may include defining a main multi-machine scheduling problem as a plurality of single machine scheduling problems; independently solving the plurality of single machine scheduling problems thereby calculating a plurality of near optimal single machine scheduling problem solutions; integrating the plurality of near optimal single machine scheduling problem solutions into a main multi-machine scheduling problem solution; and outputting the main multi-machine scheduling problem solution

Journal ArticleDOI
TL;DR: This study considers the problem of scheduling a set of jobs on a single CNC machine to minimize the sum of total weighted tardiness, tooling and machining costs, and formulated the joint problem, which is NP-hard, as a nonlinear mixed integer program.