Showing papers on "Single-machine scheduling published in 2007"
TL;DR: This paper proves that the WSPT rule and the EDD rule can construct the optimal sequence under some special cases, respectively for the following objective functions: the weighted sum of completion times and the maximum lateness.
Abstract: In this paper, we consider the single-machine scheduling problems with the effects of learning and deterioration. By the effects of learning and deterioration, we mean that job processing times are defined by functions of their starting times and positions in the sequence. It is shown that even with the introduction of learning effect and deteriorating jobs to job processing times, single-machine makespan and sum of completion times (square) minimization problems remain polynomially solvable, respectively. But for the following objective functions: the weighted sum of completion times and the maximum lateness, this paper proves that the WSPT rule and the EDD rule can construct the optimal sequence under some special cases, respectively.
171 citations
TL;DR: It is proved that the worst-case ratio of the classical LPT algorithm is 2 and there is no polynomial time approximation algorithm with a worst- case ratio less than 2 unless P = NP, which implies that the L PT algorithm is the best possible.
159 citations
TL;DR: The scheduling problems arising when several agents, each owning a set of nonpreemptive jobs, compete to perform their respective jobs on one shared processing resource are considered.
Abstract: We consider the scheduling problems arising when several agents, each owning a set of nonpreemptive jobs, compete to perform their respective jobs on one shared processing resource. Each agent wants to minimize a certain cost function, which depends on the completion times of its jobs only. The cost functions we consider in this paper are maximum of regular functions (associated with each job), number of late jobs and total weighted completion time. The different combinations of the cost functions of each agent lead to various problems, whose computational complexity is analysed in this paper. In particular, we investigate the problem of finding schedules whose cost for each agent does not exceed a given bound for each agent.
158 citations
TL;DR: It is shown that the schedule produced by the largest growth rate rule is unbounded for the model, although it is an optimal solution for the scheduling problem with deteriorating jobs and no learning.
105 citations
TL;DR: The problem of minimizing total tardiness is examined in a learning effect situation and the solutions of the large size problems with up to 1000 jobs are found by these methods.
89 citations
TL;DR: Polynomial time algorithms are proposed to optimally solve the single machine scheduling problem with setup times and learning considerations and the following objectives are considered: the makespan, the total completion time, the TOTAL differences in completion times and the sum of earliness, tardiness and common due-date penalty.
79 citations
TL;DR: The genetic lot scheduling (GLS) procedure is developed, combining an extended solution structure with a new item scheduling approach, allowing a greater number of potential schedules to be considered while being the first to explicitly state the assignment of products to periods as part of the solution structure.
74 citations
TL;DR: This work reports extensive computational results demonstrating the speed and effectiveness of the solution approach based on a time-indexed preemptive relaxation of the single machine earliness/tardiness scheduling problem with general weights, ready times and due dates.
Abstract: We consider a single machine earliness/tardiness scheduling problem with general weights, ready times and due dates. Our solution approach is based on a time-indexed preemptive relaxation of the problem. For the objective function of this relaxation, we characterize cost coefficients that are the best among those with a piecewise linear structure with two segments. From the solution to the relaxation with these best objective function coefficients, we generate feasible solutions for the original non-preemptive problem. We report extensive computational results demonstrating the speed and effectiveness of this approach.
69 citations
TL;DR: In this paper, a tabu search (TS) approach to the single machine total weighted tardiness problem (SMTWT) is presented, which consists of a set of independent jobs with distinct processing times, weights and due dates to be scheduled on a single machine.
62 citations
01 Jan 2007
TL;DR: This paper presents a totally deterministic TS algorithm with a hybrid neighborhood and dynamic tenure structure, and investigates the strength of several candidate list strategies based on problem specific characteristics in increasing the efficiency of the search.
Abstract: In this study, a tabu search (TS) approach to the single machine total weighted tardiness problem (SMTWT) is presented. The problem consists of a set of independent jobs with distinct processing times, weights and due dates to be scheduled on a single machine to minimize total weighted tardiness. The theoretical foundation of single machine scheduling with due date related objectives reveal that the problem is NP-hard, rendering it a challenging area for meta-heuristic approaches. This paper presents a totally deterministic TS algorithm with a hybrid neighborhood and dynamic tenure structure, and investigates the strength of several candidate list strategies based on problem specific characteristics in increasing the efficiency of the search. The proposed TS approach yields very high quality results for a set of benchmark problems obtained from the literature. � 2005 Elsevier B.V. All rights reserved.
61 citations
TL;DR: A static stochastic single machine scheduling problem in which jobs have random processing times with arbitrary distributions, due dates are known with certainty, and fixed individual penalties are imposed on both early and tardy jobs is studied.
TL;DR: A polynomial-time algorithm is provided to find the optimal job sequence, due date values, and resource allocations that minimize an integrated objective function, which includes the weighted number of tardy jobs, and due date assignment, makespan, and total resource consumption costs.
Abstract: With the increased emphasis on the effective management of operational issues in supply chains, the timely delivery of products has become even more important. Companies have to quote attainable delivery dates and then meet these, or face large tardiness penalties. We study systems that can be modeled by single-machine scheduling problems with due date assignment and controllable job-processing times, which are either linear or convex functions of the amount of a continuously divisible and nonrenewable resource that is allocated to the task. The due date assignment methods studied include the common due date, the slack due date, which reflects equal waiting time allowance for the jobs, and the most general method of unrestricted due dates, when each job may be assigned a different due date. For each combination of due date assignment method and processing-time function, we provide a polynomial-time algorithm to find the optimal job sequence, due date values, and resource allocations that minimize an integrated objective function, which includes the weighted number of tardy jobs, and due date assignment, makespan, and total resource consumption costs.
TL;DR: A dynamic programming algorithm that runs in pseudo-polynomial time for any constant U ⩾ 2 and optimal algorithms are provided for two special cases: (i) jobs have a linear precedence constraint, and (ii) jobs satisfy the agreeable ratio assumption.
TL;DR: The first mixed integer linear programming formulation for the resulting optimization problem is proposed and it is explained how some known preprocessing rules can be translated into valid inequalities for this formulation.
Abstract: We consider a version of the total flow time single machine scheduling problem where uncertainty about processing times is taken into account. Namely an interval of equally possible processing times is considered for each job, and optimization is carried out according to a robustness criterion. We propose the first mixed integer linear programming formulation for the resulting optimization problem and we explain how some known preprocessing rules can be translated into valid inequalities for this formulation. Computational results are finally presented.
01 Jul 2007
TL;DR: A new hierarchical method is proposed for the flexible job-shop scheduling problem (FJSP) with high flexibility and is based on the decomposition of the problem in an assignment subproblem and a sequencing subproblem.
Abstract: In this paper, we propose a new hierarchical method for the flexible job-shop scheduling problem (FJSP). This approach is mainly adapted to a job-shop problem (JSP) with high flexibility and is based on the decomposition of the problem in an assignment subproblem and a sequencing subproblem. For the first subproblem, we propose two methods: the first one is based successively on a heuristic approach and a local search; the second one, however, is based on a branch-and-bound algorithm. The quality of the assignment is evaluated by a lower bound. For the second subproblem we apply a hybrid genetic algorithm to deal with the sequencing problem. Computational tests are finally presented.
TL;DR: A sequential exchange approach utilizing a job exchange procedure and three previously established properties in common due date scheduling was developed and tested with a set of benchmark problems, generating results better than those of the existing dedicated heuristics but also in many cases those of meta-heuristic approaches.
TL;DR: A parametric O(nlog n)-algorithm H is presented with which better worst-case error bounds can be obtained and it turns out that randomly generated instances with up to 1000 jobs can be solved.
TL;DR: It is found that the strongest bound of those provided by transportation problem relaxations can be computed by solving a linear program and the equivalence of this strongest bound and the bound provided by the LP relaxation of the time-indexed integer programming formulation is shown.
Abstract: New observations are made about two lower bound schemes for single-machine min-sum scheduling problems. We find that the strongest bound of those provided by transportation problem relaxations can be computed by solving a linear program. We show the equivalence of this strongest bound and the bound provided by the LP relaxation of the time-indexed integer programming formulation. These observations lead to a new lower bound scheme that yields fast approximation of the time-indexed bound. Several techniques are developed to facilitate the effective use of the new lower bound in branch-and-bound. Numerical experiments are conducted on 375 benchmark problems of the total weighted tardiness problem from OR-Library. Results obtained with our new method are spectacular; we are able to solve all 125 open problems to optimality.
TL;DR: This paper addresses scheduling a set of jobs on a single machine for delivery in batches to customers or to other machines for further processing by considering the possibility of delivering jobs in batches and introducing batch delivery costs.
TL;DR: Complex results for a single-machine scheduling problem of minimizing the number of late jobs are presented and it is shown that the studied problem remains 𝒩𝒫-hard even if there are only two different due-date values.
Abstract: This note presents complexity results for a single-machine scheduling problem of minimizing the number of late jobs. In the studied problem, the processing times of the jobs are defined by positional learning effects. A recent paper proposed a polynomial time algorithm for the case with a common due date and conjectured the general problem to be 𝒩𝒫-hard. We confirm that the general problem is strongly 𝒩𝒫-hard and show that the studied problem remains 𝒩𝒫-hard even if there are only two different due-date values.
TL;DR: This paper considers the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time, and several dispatching heuristics are proposed, and their performance is analysed on a wide range of instances.
Abstract: This paper considers the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. Several dispatching heuristics are proposed, and their performance is analysed on a wide range of instances. The heuristics include simple scheduling rules, as well as a procedure that takes advantage of the strengths of these rules. Linear early/quadratic tardy dispatching rules are also considered, as well as a greedy-type procedure. Extensive experiments are performed to determine appropriate values for the parameters required by some of the heuristics. The computational tests show that the best results are given by the linear early/quadratic tardy dispatching rule. This procedure is also quite efficient, and can quickly solve even very large instances. [Received 15 December 2006; Revised 20 July 2007; Accepted 24 July 2007]
TL;DR: In this article, single machine scheduling problems with group technology (GT) and deteriorating jobs are considered, where a sequence independent setup is required to process a job from a different group and jobs in each group are processed together.
Abstract: This paper considers single machine scheduling problems with group technology (GT) and deteriorating jobs. A sequence independent setup is required to process a job from a different group and jobs in each group are processed together. We consider the case of jobs whose processing times are a decreasing function of their starting time. The objectives of scheduling problems are to minimize the makespan and the total completion time, respectively. We also provide polynomial time algorithms to solve these problems.
TL;DR: An integrated optimization model of production planning and scheduling for a three-stage manufacturing system composed of a forward chain of three kinds of workshops: a job shop, a parallel flow shop consisting of parallel production lines, and a single machine shop is presented.
Abstract: This paper presents an integrated optimization model of production planning and scheduling for a three-stage manufacturing system, which is composed of a forward chain of three kinds of workshops: a job shop, a parallel flow shop consisting of parallel production lines, and a single machine shop. As the products at the second stage are assembled from the parts produced in its upstream workshop, a complicated production process is involved. On the basis of the analysis of the batch production, a dynamic batch splitting and amalgamating algorithm is proposed. Then, a heuristic algorithm based on a genetic algorithm (known as the integrated optimization algorithm) is proposed for solving the problem. Note to Practitioners-This paper presents a method for integrated production planning and scheduling in a three-stage manufacturing system consisting of a forward chain of three kinds of workshops, which is common in such enterprises as producers of automobiles and household electric appliances, as in the case of an autobody plant usually with the stamping workshop, the welding and assembling workshop, and the painting workshop. Herein, the production planning and scheduling problems are simultaneously addressed in the way that a feasible production plan can be obtained and the inventory reduced. A batch splitting and amalgamating algorithm is proposed for balancing the production time of the production lines. And a case study of the integrated planning and scheduling problem in a real autobody plant verifies the effectiveness of our method
TL;DR: In this article, a branch-and-bound algorithm for solving an approximate formulation of the model is proposed, and the algorithm is exact when exactly one job is disrupted during schedule execution.
Abstract: Robust scheduling aims at the construction of a schedule that is protected against uncertain events. A stable schedule is a robust schedule that changes only little when variations in the input parameters arise. This paper presents a model for single-machine scheduling with stability objective and a common deadline. We propose a branch-and-bound algorithm for solving an approximate formulation of the model. The algorithm is exact when exactly one job is disrupted during schedule execution.
TL;DR: A mathematical programming model is developed for the bicriteria scheduling problem, and optimal solutions are only obtained up to 25 jobs, and heuristic methods based on tabu search and random search are proposed to solve large size problems.
Abstract: This paper considers a bicriteria scheduling problem with a learning effect on a single machine to minimize a weighted sum of total completion time and total tardiness. A mathematical programming model is developed for the problem, and optimal solutions are only obtained up to 25 jobs. Since the problem is NP‐hard, heuristic methods based on tabu search and random search are proposed to solve large size problems, and their effectiveness is comparatively investigated considering 3600 problems.
TL;DR: A genetic algorithm is developed by exploiting its general structure and utilizing a heuristic algorithm on the initial population to minimize the number of tardy jobs and maximum earliness for single machine, in which the idle time is not allowed.
TL;DR: In this paper, the authors provide optimal algorithms to solve a new scheduling problem in which there is a possibility that a disruption will happen at a particular time and last for a period of time with a certain probability.
TL;DR: This paper presents polynomial time algorithms to find the job sequence, the partition of theJob sequence into batches and the resource allocation, which minimize the total completion time or the total production cost (inventory plus resource costs).
Abstract: In this paper we study the single-machine batch scheduling problem under batch availability, where both setup and job processing times are controllable by allocating a continuously divisible nonrenewable resource. Under batch availability a set of jobs is processed contiguously and completed together, when the processing of the last job in the batch is finished. We present polynomial time algorithms to find the job sequence, the partition of the job sequence into batches and the resource allocation, which minimize the total completion time or the total production cost (inventory plus resource costs).
TL;DR: This study introduces an actual time-dependent learning effect into single-machine scheduling problems and shows that it remains polynomially solvable for three objectives, that is, minimizing the makespan, the total completion time and the sum of the kth power of completion times.
Abstract: In this study, we introduce an actual time-dependent learning effect into single-machine scheduling problems. The actual time-dependent learning effect of a job is assumed to be a function of the total actual processing time of jobs scheduled in front of it. We introduce it into single-machine scheduling problems and we show that it remains polynomially solvable for three objectives, that is, minimizing the makespan, the total completion time and the sum of the kth power of completion times. We also provide a polynomial time solution to minimize the sum of the weighted completion times if jobs have agreeable weights.
TL;DR: A polynomial time algorithm is presented that constructs an efficient trade-off curve between maximal lateness and total resource consumption using a bicriteria approach assuming a specified general type of convex decreasing resource consumption function.
Abstract: We extend the classical single-machine maximal lateness scheduling problem to the case where the job processing times are controllable by allocating a continuous and nonrenewable resource to the processing operations. Our aim is to construct an efficient trade-off curve between maximal lateness and total resource consumption using a bicriteria approach. We present a polynomial time algorithm that constructs this trade-off curve assuming a specified general type of convex decreasing resource consumption function. We illustrate the algorithm with a numerical example.