Showing papers on "Single-machine scheduling published in 1999"
TL;DR: It is shown in this paper that even with the introduction of learning to job processing times two important types of single-machine problems remain polynomially solvable.
678 citations
TL;DR: This paper reviews the rapidly growing literature on single machine scheduling models with time dependent processing times and attention is focused on linear, piecewise linear and non-linear processing time functions for jobs.
Abstract: In classical scheduling theory job processing times are constant However, there are many situations where processing time of a job depends on the starting time of the job in the queue This paper reviews the rapidly growing literature on single machine scheduling models with time dependent processing times Attention is focused on linear, piecewise linear and non-linear processing time functions for jobs We survey known results and introduce new solvable cases Finally, we identify the areas and give directions where further research is needed
471 citations
TL;DR: Three heuristic algorithms and a branch and bound algorithm are proposed to minimise total completion time of jobs and the problem is proved to be NP-hard in the strong sense.
Abstract: This paper considers a single machine scheduling problem with preventive maintenance. In many cases, a machine must be maintained after it continuously works for a period of time. But most papers in the literature ignore non-availability of the machine. For this reason, this paper studies the problem of scheduling processing of jobs and maintenance of machine simultaneously. The objective is to minimise total completion time of jobs. The problem is proved to be NP-hard in the strong sense. Three heuristic algorithms and a branch and bound algorithm are proposed. Computational experiments are done to evaluate the effectiveness of the algorithms.
216 citations
TL;DR: This paper presents pseudopolynomial time dynamic programming algorithms for both objective functions and shows that the problem of minimizing the total weighted completion times in this scenario is NP-complete, while the shortest processing time (SPT) rule and the earliest due date (EDD) rule are optimal for the total completion time problem and the maximum lateness problem respectively.
Abstract: The majority of scheduling literature assumes that the machines are available at all times. In this paper, we study single machine scheduling problems where the machine maintenance must be performed within certain intervals and hence the machine is not available during the maintenance periods. We also assume that if a job is not processed to completion before the machine is stopped for maintenance, an additional setup is necessary when the processing is resumed. Our purpose is to schedule the maintenance and jobs to minimize some performance measures. The objective functions that we consider are minimizing the total weighted job completion times and minimizing the maximum lateness. In both cases, maintenance must be performed within a fixed period T, and the time for the maintenance is a decision variable. In this paper, we study two scenarios concerning the planning horizon. First, we show that, when the planning horizon is long in relation to T, the problem with either objective function is NP-complete, and we present pseudopolynomial time dynamic programming algorithms for both objective functions. In the second scenario, the planning horizon is short in relation to T. However, part of the period T may have elapsed before we schedule any jobs in this planning horizon, and the remaining time before the maintenance is shorter than the current planning horizon. Hence we must schedule one maintenance in this planning horizon. We show that the problem of minimizing the total weighted completion times in this scenario is NP-complete, while the shortest processing time (SPT) rule and the earliest due date (EDD) rule are optimal for the total completion time problem and the maximum lateness problem respectively. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 845–863, 1999
167 citations
10 May 1999
TL;DR: A new genetic algorithm to solve the flexible job-shop scheduling problem with makespan criterion and it is shown that this algorithm can find out high-quality schedules.
Abstract: Genetic algorithms have been applied to the scheduling of job shops-a class of very complicated combinatorial optimization problems. Among these algorithms for job shops, a common assumption is that the routes that jobs visit machines are fixed, this is not true for flexible job shops such as flexible manufacturing systems, where jobs have machine route flexibility. The paper presents a new genetic algorithm to solve the flexible job-shop scheduling problem with makespan criterion. The representation of solutions for the problem by chromosomes consists of two parts. The first part defines the routing policy and the second part the sequence of the operations on each machine. Genetic operators are introduced and used in the reproduction process of the algorithm. Numerical experiments show that our algorithm can find out high-quality schedules.
165 citations
TL;DR: This paper shows that the problem of minimizing the weighted number of late jobs to be scheduled on a single machine when processing times are equal, as well as its preemptive variant, are strongly polynomial.
Abstract: We study the problem of minimizing the weighted number of late jobs to be scheduled on a single machine when processing times are equal In this paper, we show that this problem, as well as its preemptive variant, are strongly polynomial When preemption is not allowed (1∣pj=p, rj∣ΣwjUj), the problem can be solved in O(n7) In the preemptive case, (1∣pj=p, pmtn, rj ∣ΣwjUj), the problem can be solved in O(n10) Both algorithms are based upon dynamic programming Copyright © 1999 John Wiley & Sons, Ltd
113 citations
TL;DR: This problem of scheduling jobs with release dates and sequence‐dependent processing times on a single machine is considered to minimize the total completion time and a dynamic programming formulation from which lower bounds are derived is given.
Abstract: We consider the problem of scheduling jobs with release dates and sequence‐dependentprocessing times on a single machine to minimize the total completion time. We show thatthis problem is equivalent to the Cumulative Traveling Salesman Problem with additionaltime constraints. For this latter problem, we give a dynamic programming formulation fromwhich lower bounds are derived. Two heuristic algorithms are proposed. Performanceanalysis of both lower bounds and heuristics on randomly generated test problems are carriedout. Moreover, the application of the model and algorithms to the real problem of sequencinglanding aircraft in the terminal area of a congested airport is analyzed. Computational resultson realistic data sets show that heuristic solutions can be effective in practical contexts.
83 citations
TL;DR: This work studies the problem of minimizing, in the preemptive case, the number of late jobs on a single machine (1|pmtn,r"j|@?U"j) and proposes a new dynamic programming algorithm whose complexities are respectively O(n^4) and O( n^2).
71 citations
TL;DR: In this article, a Lagrangian relaxation based approach is developed for single-machine scheduling with sequence dependent setup times that is based on a list scheduling concept in conjunction with Lagrangians.
Abstract: This paper addresses the NP-hard problem of scheduling N independent jobs on a single machine with release dates, due dates, sequence dependent setup times, and no preemption where the objective is to minimize the weighted sum of squared tardiness. A Lagrangian relaxation based approach is developed for single-machine scheduling with sequence dependent setup times that is based on a list scheduling concept in conjunction with Lagrangian relaxation. Sequence dependent setup times are formulated as capacity constraints, and then are relaxed using Lagrangian multipliers. The primal problem is decomposed into job-level subproblems which are solved optimally and an approximate dual problem is then solved using a sub-gradient technique. The result of the relaxation is a list of jobs sequenced by beginning times that is then improved via a three-way swap. Experimental results are compared with EDD (Earliest Due Date) and ATCS (Apparent Tardiness Cost with Setups) dispatching rules, a four-way swap local search, tabu search, and simulated annealing. The adopted approach results in superior solution quality with respect to EED, ATCS, four-way swap, and tabu search results. It has comparable solution quality to the simulated annealing results, but is substantially more computationally efficient. Overall, the approach is capable of dealing with realistically sized single machine scheduling problems with release dates, due dates, and sequence dependent setup times.
71 citations
TL;DR: This work gives complete characterizations of all facet inducing inequalities with integral coefficients and right-hand side 1 or 2 for the convex hull of the set of feasible partial schedules, i.e., schedules in which all jobs have to be started.
Abstract: We report new results for a time-indexed formulation of nonpreemptive single-machine scheduling problems. We give complete characterizations of all facet inducing inequalities with integral coefficients and right-hand side 1 or 2 for the convex hull of the set of feasible partial schedules, i.e., schedules in which not all jobs have to be started. Furthermore, we identify conditions under which these facet inducing inequalities are also facet inducing for the original polytope, which is the convex hull of the set of feasible complete schedules, i.e., schedules in which all jobs have to be started. To obtain insight in the effectiveness of these classes of facet-inducing inequalities, we develop a branch-and-cut algorithm based on them. We evaluate its performance on the strongly NP-hard single machine scheduling problem of minimizing the weighted sum of the job completion times subject to release dates.
67 citations
TL;DR: Several properties that justify the modified due date version of the algorithm and produce an easy-to-implement new lower bound are established and an explanation why using the increased due dates may improve the efficiency of certain algorithms is provided.
Abstract: The paper deals with the solution of the single machine total tardiness model. It improves and generalizes an important rule to decompose the model into two subproblems. It also provides a O(n2) procedure to implement this rule and its generalization. Those two rules, along with some known results, are incorporated in a branch and bound algorithm that efficiently handles instances with up to 300 jobs and uses the original and maximally increased due dates to solve the original problem. Several properties that justify the modified due date version of our algorithm and produce an easy-to-implement new lower bound are established. The paper also provides an explanation why using the increased due dates may improve the efficiency of certain algorithms. Copyright © 1999 John Wiley & Sons, Ltd.
TL;DR: It is shown that complex scheduling problems like general shop problems, problems with multi-processor tasks, problemsWith multi-purpose machines, and problems with changeover times can be reduced to single-machine problems with positive and negative time-lags between jobs.
TL;DR: A hybrid genetic algorithm (HGA) is proposed for the single machine, single stage, scheduling problem in a sequence dependent setup time environment within a fixed planning horizon (SSSDP), which incorporates the elitist ranking method, genetic operators, and a hill-climbing technique in each searching area.
Abstract: A hybrid genetic algorithm (HGA) is proposed for the single machine, single stage, scheduling problem in a sequence dependent setup time environment within a fixed planning horizon (SSSDP). It incorporates the elitist ranking method, genetic operators, and a hill-climbing technique in each searching area. To improve the performance and efficiency, hill climbing is performed by uniting the Wagner-Whitin Algorithm with the problem-specific knowledge. The objective of the HGA is to minimize the sum of setup cost, inventory cost, and backlog cost. The HGA is able to obtain a superior solution, if it is not optimal, in a reasonable time. The computational results of this algorithm on real life SSSDP problems are promising. In our test cases, the HGA performed up to 50% better than the Just-In-Time heuristics and 30% better than the complete batching heuristics.
01 Oct 1999
TL;DR: A modified genetic algorithm is proposed for the single machine scheduling problem with ready times by introducing two new steps: a filtering step to filter out the worst solutions in each generation and fill in their positions with the best solutions of previous generations.
Abstract: In this paper we propose a modified genetic algorithm for the single machine scheduling problem with ready times. This algorithm improves the simple genetic algorithm by introducing two new steps: (1) a filtering step to filter out the worst solutions in each generation and fill in their positions with the best solutions of previous generations; and (2) a selective cultivation step to cultivate the most promising individual when no improvement is made for certain generations. Improvement is also made on the crossover operation for the problem. Computational experiments are carried out, comparing the performance of the proposed algorithm, the simple genetic algorithm and special purpose heuristics. The contribution of each modification measure to the performance improvement is also analyzed.
TL;DR: The objective is to find an optimal permutation of the jobs, an optimal due date and the optimal processing times which jointly minimize a cost function consisting of the earliness, tardiness, completion time and compressing costs.
Abstract: The paper considers the problem of scheduling nindependent and simultaneously available jobs on a single machine, where the job processing times are compressible as a linear cost function. The objective is to find an optimal permutation of the jobs, an optimal due date and the optimal processing times which jointly minimize a cost function consisting of the earliness, tardiness, completion time and compressing costs. It shows that the problem can be solved as an assignment problem.
01 Aug 1999
TL;DR: This work applies the Hopfield neural network and the normalized mean field annealing technique, respectively, to resolve a multiprocessor problem with no process migration, constrained times and limited resources.
Abstract: The Hopfield neural network is extensively applied to obtaining an optimal/feasible solution in many different applications such as the traveling salesman problem (TSP), a typical discrete combinatorial problem. Although providing rapid convergence to the solution, TSP frequently converges to a local minimum. Stochastic simulated annealing is a highly effective means of obtaining an optimal solution capable of preventing the local minimum. This important feature is embedded into a Hopfield neural network to derive a new technique, i.e., mean field annealing. This work applies the Hopfield neural network and the normalized mean field annealing technique, respectively, to resolve a multiprocessor problem (known to be a NP-hard problem) with no process migration, constrained times (execution time and deadline) and limited resources. Simulation results demonstrate that the derived energy function works effectively for this class of problems.
TL;DR: This paper presents a bounding scheme for the calculation of different lower bounds based on the overlap elimination procedure on a Just-In-Time schedule and some extensions of the approach are discussed.
Abstract: An n job, single machine scheduling problem in which each job has a distinct due date, d i , is studied in this paper. The objective is to determine an optimal schedule π 0 s for a set of jobs, S , such that the total absolute deviation of the schedule is minimized. This objective function is based on the due date value and on the earliness or tardiness of each job in the selected sequence. This paper presents a bounding scheme for the calculation of different lower bounds based on the overlap elimination procedure on a Just-In-Time schedule. Properties and theorems of the overlap elimination procedure are also provided. Finally, a numerical example is illustrated and some extensions of the approach are also discussed.
TL;DR: Borders on the position of the smallest job in an optimal sequence are developed and a new heuristic method to solve the problem of scheduling jobs on a single machine is developed.
TL;DR: In this article, a single machine scheduling problem with ready and due times constraints on jobs, shutdown constraints on the machine and sequence dependent set-up times among jobs is considered, and an optimization algorithm based on the branch-and-bound method is developed to minimize the maximum tardiness for solving the problem.
Abstract: This paper considers a single machine scheduling problem with ready and due times constraints on jobs, shutdown constraints on the machine and sequence dependent set-up times among jobs. The shutdown is a disruptive event such as holiday, breaks or machine maintenance, and has a prespecified period when the machine will be interrupted. If no pre-emption is allowed for jobs, shutdown constraints divide the planning horizon into disconnected time windows. An optimization algorithm based on the branch-and-bound method is developed to minimize the maximum tardiness for solving the problem. This paper further develops the post-processing algorithm that manipulates the starting time of the shutdown period so as to reduce the obtained maximum tardiness. The post-processing algorithm can determine plural schedules to reduce the maximum tardiness, and the production manager will select the objective schedule among them for the interest of overall efficiency. Computational results for the proposed algorithms will i...
06 Jul 1999
TL;DR: A genetic algorithm approach is proposed in which the sequence of jobs on each machine as well as the assignment of jobs to machines are determined directly by referring to a string and the start time of each job is fixed by solving the linear programming problem and a feasible schedule is obtained.
Abstract: This paper deals with identical parallel machine scheduling problems with two kinds of objective functions, i.e., both regular and non-regular objective functions, and proposes a genetic algorithm approach in which (a) the sequence of jobs on each machine as well as the assignment of jobs to machines are determined directly by referring to a string (genotype), and (b) the start time of each job is fixed by solving the linear programming problem and a feasible schedule (phenotype) is obtained. As for (b), we newly introduce a method of representing the problem to determine the start time of each job as a linear programming problem whose objective function is formed as a weighted sum of the original multiple objective functions. This method enables us to obtain a lot of potential schedules. Moreover, through computational experiments by using our genetic algorithm approach, the effectiveness for generating a variety of Pareto-optimal schedules is investigated.
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TL;DR: In this article, the authors considered the problem of minimizing the average weighted completion time of n jobs with release dates on a single machine and proved that a O(n log n) greedy algorithm leads to optimal solutions to both relaxations.
Abstract: We consider the scheduling problem of minimizing the average weighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on a time-indexed formulation, the other on a completion-time formulation. We show their equivalence by proving that a O(n log n) greedy algorithm leads to optimal solutions to both relaxations. The proof relies on the notion of mean busy times of jobs, a concept which enhances our understanding of these LP relaxations. Based on the greedy solution, we describe two simple randomized approximation algorithms, which are guaranteed to deliver feasible schedules with expected objective value within factors of 1.7451 and 1.6853, respectively, of the optimum. They are based on the concept of common and independent alpha-points, respectively. The analysis implies in particular that the worst-case relative error of the LP relaxations is at most 1.6853, and we provide instances showing that it is at least e/(e-1) = 1.5819. Both algorithms may be derandomized, their deterministic versions running in O(n2) time. The randomized algorithms also apply to the on-line setting, in which jobs arrive dynamically over time and one must decide which job to process without knowledge of jobs that will be released afterwards
21 Jul 1999
TL;DR: In this paper, the traditional idea of exchanging the position of two jobs is replaced by the idea of "exchanging jobs not apart more than a given number of positions (considered as a parameter of the algorithm).
Abstract: Some general features of single-machine scheduling problems are described, and some of their structural properties are used to design local search procedures based on alternative definitions of neighbourhoods. In particular, the traditional idea of "exchanging the position of two jobs" is replaced by the idea of "exchanging jobs not apart more than a given number of positions (considered as a parameter of the algorithm)". For generating initial solutions, some traditional priority rules were tested with some degree of randomisation, introducing in general, a positive effect in the performance of the algorithms. Through a set of computational tests, the importance of the different parameters was evaluated, and their values for different meta-heuristic procedures (tabu search, and randomised local search) were tuned. Though these tests have been exhaustive only for a given problem (weighted tardiness), the results already available show these approaches are robust and flexible, and that, in general, satisfactory solutions can be obtained in an efficient way.
TL;DR: Five lemmas and a polynomial-time algorithm are presented to determine the optimal common due date and the optimal sequence to minimize an objective function of the sum of the Earliness/Tardiness penalties and the additional penalties (including two dimensions, namely due date penalties and completion times penalties).
Abstract: This paper is concerned with the optimal due dates and the optimal sequence to a set of jobs on a single-machine. The common due date assignment method is used, in which all jobs are assigned a common flow allowance. The objective is to find the optimal common due date and the optimal sequence to minimize an objective function of the sum of the Earliness/Tardiness (E/T) penalties and the additional penalties (including two dimensions, namely due date penalties and completion times penalties). It is assumed that E/T penalties will not occur if a job is completed within the due window. However, E/T penalties will occur if a job is completed outside the due window. Five lemmas and a polynomial-time algorithm are presented to determine the optimal common due date and the optimal sequence, a numerical example is provided to illustrate our algorithm.
TL;DR: Two generalizations of the relocation problem in the context of single machine scheduling with due date constraints are studied and it is proved that the first problem is NP-hard even when all the jobs have the same tardy weight and the same resource requirement.
TL;DR: A heuristic algorithm is proposed which manipulates the starting and completion times of the shutdown period so as to minimize approximately the sum of the holding cost and the reduction cost in shutdown times.
TL;DR: A branch and bound algorithm for solving the single‐machine scheduling problem with the objective of minimizing the maximum tardiness of any job, subject to the constraint that the total number of tardy jobs is minimum.
Abstract: This paper develops a branch and bound algorithm for solving the single‐machine schedulingproblem with the objective of minimizing the maximum tardiness of any job, subjectto the constraint that the total number of tardy jobs is minimum. The algorithm uses a newlower bounding scheme, which is based on due date relaxation. Various dominance rules areused in the algorithm to limit the size of the search tree. Results of extensive computationaltests show that the proposed branch and bound algorithm is effective in solving problemswith up to 1000 jobs.
22 Jun 1999
TL;DR: In this paper, a hybrid GA with crossover and mutation operators was proposed to adjust the job sequencing to minimize the sum of earliness and tardiness with different release times and due dates.
Abstract: The article addresses the n-job, non-preemptive and single machine scheduling problem of minimizing the sum of earliness and tardiness with different release times and due dates. To solve the problem, it proposes a hybrid genetic algorithm with a new crossover and mutation operators to adjust the job sequencing. To investigate the suitability of the parameters set and the quality of the solution, the article evaluates the number of corresponding solutions and the speed of converging to an optimal solution which is solved by an enumeration method for small size problems. To demonstrate the performance of the proposed GA, it is empirically evaluated by solving a large number of problems and compared with solutions obtained by genetic algorithms using the existing operators.
TL;DR: The results indicate that local search with combined insert and swap neighborhood structure under randomly generated initial solution also generates better results which is comparable to the three benchmark heuristics in opiimaiity performance.
TL;DR: In this paper, a single machine scheduling problem is considered, where the jobs processing times are controllable (i.e., they may take any value within a certain range) and non-precisely defined.