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Single Machine Scheduling With a Non-Renewable Financial Resource
Otto-von-Guericke Universitaet
,
2010.
№ 7.
Gafarov E., Lazarev A. A., Werner F.
In this paper, we consider single machine scheduling problems with a non-renewable resource. This type of problems has not been intensively investigated in the literature so far. For several problems of this type with standard objective functions (namely the minimization of makespan, total tardiness, number of tardy jobs, total completion time and maximum lateness), wepresent some complexity results. Particular attention is given to the problem of minimizing total tardiness. In addition, for the so-called budget scheduling problem with minimizing the makespan, we present some properties of feasible schedules.
Lazarev A. A., Werner F., Mathematical and Computer Modelling 2009 Vol. 49 No. 9-10 P. 2061-2072
The scheduling problem of minimizing total tardiness on a single machine is known to be NP-hard in the ordinary sense. In this paper, we consider the special case of the problem when the processing times p_j and the due dates d_j of the jobs are oppositely ordered: p_1 >= p_2>=...>=p_n and d_1. ...
Added: November 24, 2012
A Graphical Realization of the Dynamic Programming Method for Solving NP-Hard Combinatorial Problems
Lazarev A. A., Werner F., Computers & Mathematics with Applications 2009 No. 58 P. 619-631
In this paper we consider a graphical realization of dynamic programming. The concept is discussed on the partition and knapsack problems. In contrast to dynamic programming, the new algorithm can also treat problems with non-integer data without necessary transformations of the corresponding problem. We compare the proposed method with existing algorithms for these problems on ...
Added: November 24, 2012
Gafarov E., Lazarev A. A., Werner F., Автоматика и телемеханика 2010 № 10 С. 63-79
In this paper, we consider two scheduling problems on a single machine, where a specific objective function has to be maximized in contrast to usual minimization problems. We propose exact algorithms for the single machine problem of maximizing total tardiness 1‖max-ΣT j and for the problem of maximizing the number of tardy jobs ...
Added: November 24, 2012
Lazarev A. A., Musatova E. G., Kvaratskhelia A. et al., М. : Физический факультет МГУ, 2012
Данное учебное пособие посвящено задачам теории расписаний, возникающим на транспорте. Представлены основы теории расписаний, а также способы построения моделей и методы решения задач управления транспортными системами. Изложенный материал предназначен для студентов и преподавателей вузов математических специальностей, специалистов в области управления и практиков, занимающихся решением задач планирования грузовых перевозок. ...
Added: December 10, 2012
Gafarov E., Lazarev A. A., Werner F., / Otto-von-Guericke Universitaet. 2010. No. 8.
Problem RCPSP may be formulated as follows. Given a set $N=\{1,\dots,n\}$ of jobs. A constant amount (quantity) of $Q_k>0$ units of resource $k, k=1,\dots,K,$ is available at any time. Job $j\in N$has to be processed for $p_j\geq 0$ time units without preemption. During this period, a constant amount (quantity) of $q_{jk} \geq 0$ units of ...
Added: March 4, 2013
Gafarov E., Lazarev A. A., Werner F., / Otto-von-Guericke Universitaet. 2010. No. 11.
In this paper, we consider some scheduling problems on a single machine, where a specific objective function has to be maximized in contrast to usual minimization problems. These problems are theoretically important and have also practical interpretations. We present some complexity results for such maximization problems with classical objective functions (e.g. total tardiness, number of ...
Added: March 4, 2013
Werner F., Lazarev A. A., Automation and Remote Control 2010 Vol. 71 No. 10 P. 2019-2020
Foreword to the thematical issue devoted to the seventieth anniversary of Academician V.S. Tanaev ...
Added: November 23, 2012
Lazarev A. A., Werner F., / Otto-von-Guericke Universitaet. 2008. No. 15.
In this paper we consider a graphical realization of dynamic programming. The concept is discussed on the partition and knapsack problems. In contrast to dynamic programming, the new algorithm can also treat problems with non-integer data without necessary transformations of the corresponding problem. We compare the proposed method with existing algorithms for these problems on ...
Added: March 4, 2013
Lazarev A. A., Kvaratskhelia A., Автоматика и телемеханика 2010 № 10 С. 80-89
In this paper, we consider the minimizing total weighted completion time in preemptive equal-length job with release dates scheduling problem on a single machine. This problem is known to be open. Here, we give some properties of optimal schedules for the problem and its special cases. ...
Added: November 24, 2012
Lazarev A. A., Werner F., / Otto-von-Guericke Universitaet. 2008. No. 12.
The scheduling problem of minimizing total tardiness on a single machine is knownto be NP-hard in the ordinary sense. In this paper, we consider the special case of the problem when the processing times $p_j$ and the due dates $d_j$ of the jobs $j, \, j \in N = \{ 1, 2, \ldots, n \}$, ...
Added: March 4, 2013
Gafarov E., Lazarev A. A., Werner F., / Otto-von-Guericke Universitaet. 2009. No. 38.
We consider single machine problems with opposite criteria, namely we consider the maximization of total tardiness, the maximization of the number of tardy jobs and the maximization of total completion time (in contrast to usual minimization problems)and a minimization version of the Knapsack problem. ...
Added: March 4, 2013
Lazarev A. A., Автоматика и телемеханика 2007 № 4 С. 13-23
Consideration was given to a graphic realization of the method of dynamic programming. Its concept was demonstrated by the examples of the partition and knapsack problems. The proposed method was compared with the existing algorithms to solve these problems. ...
Added: November 23, 2012
Lazarev A. A., Kvaratskhelia A., Gafarov E., Доклады Академии наук 2007 Т. 412 № 6 С. 739-742
27.47.19 Исследование операций
28.15.19 Нелинейные детерминированные системы
28.19.15 Оптимальные системы
28.29.15 Методы исследования операций ...
Added: November 23, 2012
Lazarev A. A., Садыков Р. Р., Севастьянов С., Дискретный анализ и исследование операций 2006 Т. 13 № 1 С. 57-76
Рассматривается NP-трудная в сильном смысле задача теории расписаний о минимизации максимального временного смещения на одном приборе при неодновременном поступлении работ. Представлена схема приближенного решения, основанная на отыскании по заданному примеру другого (наиболее близкого в некоторой метрике) примера, принадлежащего к известному полиномиально разрешимому классу примеров. Для нескольких конкретных вариантов схемы (с использованием различных полиномиально разрешимых классов ...
Added: November 23, 2012
Gafarov E., Lazarev A. A., Information Processing Letters 2012 Т. 112 № 3 С. 72-76
In this note, we consider a single machine scheduling problem with generalized total tardiness objective function.
A pseudo-polynomial time solution algorithm is proposed for a special case of this problem. Moreover, we present a new
graphical algorithm for another special case, which corresponds to the classical problem of minimizing the weighted number
of tardy jobs on a single ...
Added: November 24, 2012
Gafarov E., Lazarev A. A., Werner F., Mathematical Social Sciences 2011 No. 62 P. 7-13
We consider single machine scheduling problems with a non-renewable resource. These types of problems have not been intensively investigated in the literature so far. For several problems of these types with standard objective functions (namely the minimization of makespan, total tardiness, number of tardy jobs, total completion time and maximum lateness), we present some complexity ...
Added: November 24, 2012
Lazarev A. A., Журнал вычислительной математики и математической физики 2007 Т. 47 № 6 С. 1087-1099
The classical NP-hard (in the ordinary sense) problem of scheduling jobs in order to minimize the total tardiness for a single machine 1‖ΣT j is considered. An NP-hard instance of the problem is completely analyzed. A procedure for partitioning the initial set of jobs into subsets is proposed. Algorithms are constructed for finding ...
Added: November 23, 2012
Gafarov E., Lazarev A. A., Werner F., Annals of Operations Research 2012 Vol. 196 No. 1 P. 247-261
We consider the problem of maximizing total tardiness on a single machine, where the first job starts at time zero and idle times between the processing of jobs are not allowed.We present a modification of an exact pseudo-polynomial algorithm based on a graphical approach, which has a polynomial running time. This result settles the complexity ...
Added: November 24, 2012
Lazarev A. A., Gafarov E., Доклады Академии наук 2008 Т. 424 № 1 С. 7-9
27.47.19 Исследование операций
28.15.19 Нелинейные детерминированные системы
28.19.15 Оптимальные системы
28.29.15 Методы исследования операций ...
Added: November 23, 2012
Gafarov E., Lazarev A. A., Werner F., / Otto-von-Guericke Universitaet. 2010. No. 10.
In this note, we consider a single machine scheduling problem with generalized total tardiness objective function. An NP-hardness proof and a pseudo-polynomial time solution algorithm are proposed for a special case of this problem. Moreover, we present a new graphical algorithm for another special case, which corresponds to the classical problem of minimizing the weighted ...
Added: March 4, 2013
Gafarov E., Lazarev A. A., Werner F., / Otto-von-Guericke Universitaet. 2010. No. 12.
In this paper, we consider the problem of maximizing total tardiness on a single machine, where the first job starts at time zero and idle times between the processing of jobs are not allowed. We present a modification of an exact pseudo-polynomial algorithm based on a graphical approach, which has a polynomial running time. ...
Added: March 4, 2013
Lazarev A. A., Gafarov E., Автоматика и телемеханика 2008 № 12 С. 86-104
Consideration was given to the resource-constrained project scheduling problem and its special cases. The existing lower estimates of the objective function—minimization of the project time—were compared. It was hypothesized that the optimal value of the objective function of the nonpreemptive resource-constrained project scheduling problem is at most twice as great as that of the objective ...
Added: November 23, 2012
Lazarev A. A., Kvaratskhelia A., Доклады Академии наук 2010 Т. 432 № 6 С. 746-749
Одним из актуальных вопросов разработки математической теории расписаний является построение метрик, которые можно использовать при разработке точных и приближенных алгоритмов решения задач. Введение метрических пространств для $NP$-трудных задач теории расписаний позволяет применять общие математические подходы к нахождению приближенного решения с гарантированной абсолютной погрешностью. Ранее для $NP$-трудных задач с критерием минимизации максимального временн\'ого смещения $\{P,R,Q\}|prec,r_j|\{L_{\max},C_{\max}\}$ была ...
Added: November 23, 2012
Cheng T., Lazarev A. A., Gafarov E., Computers & Operations Research 2012 Vol. 36 No. 2 P. 308-315
We propose a hybrid algorithm based on the Ant Colony Optimization (ACO) meta-heuristic, in conjunction with four well-known elimination rules, to tackle the NP-hard single-machine scheduling problem to minimize the total job tardiness. The hybrid algorithm has the same running time as that of ACO. We conducted extensive computational experiments to test the performance of ...
Added: November 23, 2012