Міністерство освіти і науки України Сумський державний університет 40007, м.Суми, вул.Римського-К... more Міністерство освіти і науки України Сумський державний університет 40007, м.Суми, вул.Римського-Корсакова, 2; тел. (0542) 33 53 83; факс 33 40 58 ЗАТВЕРДЖУЮ Проректор з наукової роботи д-р. фіз.-мат. наук, проф. __________________А.М.Чорноус ЗВIТ ПРО НАУКОВО-ДОСЛIДНУ РОБОТУ Економетричне моделювання механізму запобігання тіньовим схемам виведення капіталу через податкові та інвестиційні канали в Україні ДОСЛІДЖЕННЯ ТЕОРЕТИЧНИХ ОСНОВ ТІНЬОВОГО ВИВЕДЕННЯ КАПІТАЛУ ЗА КОРДОН В УМОВАХ ЄВРОІНТЕГРАЦІЙНИХ ПРОЦЕСІВ (проміжний) Начальник НДЧ канд.фіз.-мат. наук, доцент Д. І. Курбатов Керівник НДР д-р. екон. наук, професор.
This paper deals with a variation of the single machine earliness/tardiness scheduling problem: p... more This paper deals with a variation of the single machine earliness/tardiness scheduling problem: preemption is allowed and, in order to penalize job interruptions, earliness costs depend on the starting time of the job while tardiness costs depend on the end times as in the usual models. We propose dominance properties and a polynomial time algorithm is given to solve the particular case where the sequence of the start and completion of the jobs is fixed.
We use the Akers-Friedman geometric approach to solve the two jobs job-shop problem when there is... more We use the Akers-Friedman geometric approach to solve the two jobs job-shop problem when there is an earliness cost on the first operation and a tardiness cost on the last operation of each job. We then generalize the problem by imposing earliness and tardiness costs on each operation and finally, we solve it using a dynamic programming algorithm.
ABSTRACT This paper deals with the problem of scheduling $n_\mathrm{A}$ n A malleable and $n_\mat... more ABSTRACT This paper deals with the problem of scheduling $n_\mathrm{A}$ n A malleable and $n_\mathrm{B}$ n B non-malleable jobs to be executed together on two parallel identical machines to minimize mean flow time. We propose a set of dominant schedules for this problem, and a dynamic programming algorithm that finds an optimal schedule in this dominant set in time $O(n_\mathrm{A}^2n_\mathrm{B})$ O ( n A 2 n B ) .
This paper addresses the one-machine scheduling problem where the objective is to minimize a sum ... more This paper addresses the one-machine scheduling problem where the objective is to minimize a sum of costs such as earliness–tardiness costs. Since the sequencing problem is NP-hard, local search is very useful for finding good solutions. Unlike scheduling problems with regular cost functions, the scheduling (or timing) problem is not trivial when the sequence is fixed. Therefore, the local search
Earliness–tardiness criteria with distinct due dates usually induce NP-complete problems. Researc... more Earliness–tardiness criteria with distinct due dates usually induce NP-complete problems. Researchers have focused on particular cases like the timing problem, which is to look for the optimal schedule when the jobs sequence is already known. These timing algorithms are very useful since they can be used in more complex procedures. In the first part of this paper we provide the most efficient and fairly general algorithm to solve the one-machine timing problem. It is then adapted to a permutation flow shop problem.
This paper investigates the notion of preemption in scheduling, with earliness and tardiness pena... more This paper investigates the notion of preemption in scheduling, with earliness and tardiness penalties. Starting from the observation that the classical cost model where penalties only depend on completion times does not capture the just-in-time philosophy, we introduce a new model where the earliness costs depend on the start times of the jobs. To solve this problem, we propose an efficient representation of dominant schedules, and a polynomial algorithm to compute the best schedule for a given representation. Both a local search algorithm and a branch-and-bound procedure are then derived. Experiments finally show that the gap between our upper bound and the optimum is very small.
Міністерство освіти і науки України Сумський державний університет 40007, м.Суми, вул.Римського-К... more Міністерство освіти і науки України Сумський державний університет 40007, м.Суми, вул.Римського-Корсакова, 2; тел. (0542) 33 53 83; факс 33 40 58 ЗАТВЕРДЖУЮ Проректор з наукової роботи д-р. фіз.-мат. наук, проф. __________________А.М.Чорноус ЗВIТ ПРО НАУКОВО-ДОСЛIДНУ РОБОТУ Економетричне моделювання механізму запобігання тіньовим схемам виведення капіталу через податкові та інвестиційні канали в Україні ДОСЛІДЖЕННЯ ТЕОРЕТИЧНИХ ОСНОВ ТІНЬОВОГО ВИВЕДЕННЯ КАПІТАЛУ ЗА КОРДОН В УМОВАХ ЄВРОІНТЕГРАЦІЙНИХ ПРОЦЕСІВ (проміжний) Начальник НДЧ канд.фіз.-мат. наук, доцент Д. І. Курбатов Керівник НДР д-р. екон. наук, професор.
This paper deals with a variation of the single machine earliness/tardiness scheduling problem: p... more This paper deals with a variation of the single machine earliness/tardiness scheduling problem: preemption is allowed and, in order to penalize job interruptions, earliness costs depend on the starting time of the job while tardiness costs depend on the end times as in the usual models. We propose dominance properties and a polynomial time algorithm is given to solve the particular case where the sequence of the start and completion of the jobs is fixed.
We use the Akers-Friedman geometric approach to solve the two jobs job-shop problem when there is... more We use the Akers-Friedman geometric approach to solve the two jobs job-shop problem when there is an earliness cost on the first operation and a tardiness cost on the last operation of each job. We then generalize the problem by imposing earliness and tardiness costs on each operation and finally, we solve it using a dynamic programming algorithm.
ABSTRACT This paper deals with the problem of scheduling $n_\mathrm{A}$ n A malleable and $n_\mat... more ABSTRACT This paper deals with the problem of scheduling $n_\mathrm{A}$ n A malleable and $n_\mathrm{B}$ n B non-malleable jobs to be executed together on two parallel identical machines to minimize mean flow time. We propose a set of dominant schedules for this problem, and a dynamic programming algorithm that finds an optimal schedule in this dominant set in time $O(n_\mathrm{A}^2n_\mathrm{B})$ O ( n A 2 n B ) .
This paper addresses the one-machine scheduling problem where the objective is to minimize a sum ... more This paper addresses the one-machine scheduling problem where the objective is to minimize a sum of costs such as earliness–tardiness costs. Since the sequencing problem is NP-hard, local search is very useful for finding good solutions. Unlike scheduling problems with regular cost functions, the scheduling (or timing) problem is not trivial when the sequence is fixed. Therefore, the local search
Earliness–tardiness criteria with distinct due dates usually induce NP-complete problems. Researc... more Earliness–tardiness criteria with distinct due dates usually induce NP-complete problems. Researchers have focused on particular cases like the timing problem, which is to look for the optimal schedule when the jobs sequence is already known. These timing algorithms are very useful since they can be used in more complex procedures. In the first part of this paper we provide the most efficient and fairly general algorithm to solve the one-machine timing problem. It is then adapted to a permutation flow shop problem.
This paper investigates the notion of preemption in scheduling, with earliness and tardiness pena... more This paper investigates the notion of preemption in scheduling, with earliness and tardiness penalties. Starting from the observation that the classical cost model where penalties only depend on completion times does not capture the just-in-time philosophy, we introduce a new model where the earliness costs depend on the start times of the jobs. To solve this problem, we propose an efficient representation of dominant schedules, and a polynomial algorithm to compute the best schedule for a given representation. Both a local search algorithm and a branch-and-bound procedure are then derived. Experiments finally show that the gap between our upper bound and the optimum is very small.
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