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1

Minimizing Tardiness in a Scheduling Environment with Jobs' Hierarchy

Sinai Michal, Tamir Tami

Annals of Computer Science and Information Systems

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2021

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Vol. 25

201--209

EN

In many scheduling environments, some jobs have higher priority than others. We consider a new model, motivated by real-life behavior, in which the priority among jobs is defined by a dominance hierarchy. Specifically, the jobs are arranged in hierarchy levels, and high ranking jobs are ready to accept only outcomes in which the service they receive is better than the service of subordinate jobs. We define the model and the set of feasible schedules formally, and provide algorithms and hardness proofs for two classical problems: minimizing the maximal tardiness and minimizing the number of tardy jobs. We provide optimal algorithms or hardness proofs for these problems, distinguishing between a global objective function and a multi-criteria objective.

2

Bisimulation Minimisation of Weighted Automata on Unranked Trees

Högberg J., Maletti A.

Fundamenta Informaticae

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2009

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Vol. 92, nr 1-2

103-130

EN

Several models of automata are available that operate unranked trees. Two well-known examples are the stepwise unranked tree automaton (suta) and the parallel unranked tree automaton (puta). By adding a weight, taken from some semiring, to every transition we generalise these two qualitative automata models to quantitative models, thereby obtaining weighted stepwise unranked tree automata (wsuta) and weighted parallel unranked tree automata (wputa); the qualitative automata models are reobtained by choosing the BOOLEAN semiring. The weighted versions have applications in natural language processing, XML-based data management and quantitative information retrieval. We address the minimisation problem of wsuta and wputa by using (forward and backward) bisimulations and we prove the following results: (1) for every wsuta an equivalent forward (resp. backward) bisimulation minimal wsuta can be computed in time O(mn) where n is the number of states and m is the number of transitions of the given wsuta; (2) the same result is proved for wputa instead of wsuta; (3) if the semiring is additive cancellative or the BOOLEAN semiring, then the bound can be improved to O(mlog n) for both wsuta and wputa; (4) for every deterministic puta we can compute a minimal equivalent deterministic puta in time O(mlog n); (5) the automata models wsuta, wputa, and weighted unranked tree automaton have the same computational power.

3

Techniczne i technologiczne parametry produkcji rzepaku ozimego

Šařec O., Šařec P., Dobek T.

Inżynieria Rolnicza

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2005

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R. 9, nr 4

227--234

PL

Celem badań było określenie, które ze stosowanych technologii, z uwzględnieniem regionu produkcji, są technicznie i ekonomicznie najbardziej przydatne. Badania prowadzone były w latach 2001 – 2003. Obejmowały one liczbę roślin które przezimowały, uzyskane plony, zużycie paliwa, nakłady pracy, koszty produkcji (materiałów, surowców i eksploatacji maszyn). Do oceny technologii przyjęto dwie grupy z podziałem na podgrupy. Pierwsza grupa to technologie tradycyjne z tradycyjnym przygotowaniem roli oraz z nawożeniem obornikiem i bez nawożenia obornikiem, druga grupa to technologie z płytkim przygotowaniem roli do siewu czyli technologia uproszczona i uproszczona z nawożeniem pod redlicę wykonanym przy siewie. Z przeprowadzonych badań wynika, że różnice w kosztach, nakładach pracy i plonowaniu przy produkcji rzepaku ozimego w badanych technologiach tradycyjnych i uproszczonych nie były istotne.

EN

In 2001 - 2003, field experiments focused on various technologies of soil cultivation and drilling of oilseed rape have been carried out all. Over the Czech Republic. The technologies in question were divided according to intensity or depth of soil cultivation, manure application and production regions. The first year results have shown slightly higher seed yield as compared with traditional technologies from plots with reduced soil treatment technologies. On the other hand, fuel consumption and labour requirement of oilseed rape growing using traditional technologies were higher. Production unit costs of technologies did not differ.

4

Sliding mode control of the third order system with state constraints

Bartoszewicz A., Nowacka A.

Systems Science

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2004

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Vol. 30, no 2

35-44

EN

In this paper, a new sliding mode control algorithm for the third order, nonlinear system subject to velocity and acceleration constraints is considered. The algorithm guarantees fast transient behaviour, zero steady state error and insensitivity of the system with respect to matched model uncertainty and external disturbance from the very beginning of the control process. For that purpose, the algorithm employs a time varying switching plane selected in such a way that at the initial time the representative point of the system belongs to the plane. Afterwards, the plane moves in a finite time towards the origin of the coordinate frame and then remains fixed. A proper choice of the plane parameters ensures non-oscillatory system response and the minimisation of the integral of the absolute value of the system position error.

5

Property of symmetry for some single processor scheduling problems with due interval assignment

Janiak A., Marek M.

Systems Science

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2004

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Vol. 30, no 2

97-107

EN

In this paper, we consider two single processor scheduling problems, in which a due interval should be assigned to each job. The due interval is a generalization of a due date and describes a time interval in which a job should be finished. Both problems considered have different mathematical models of the due intervals and the same criterion in which we minimize the weighted sum of the total earliness, the total tardiness and me due interval size. At first, we prove some properties of the optimal solution and we construct an optimal algorithm to solve the first problem. Next, we establish a property of symmetry, which helps us to solve the second problem based on the solution of the first one.

6

Zastosowanie koncepcji pinczu wody do obliczania optymalnego odzysku ciepła

Jeżowski J., Jeżowska A.

Inżynieria i Aparatura Chemiczna

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2004

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Nr 3s

70-71

EN

A simple graphical method was developed for calculating optimal usage of heating and cooling utilities in heat integration. The approach is based on analogy to water pinch concept.

7

Parametric minimization of influence of stochastic didtribution in linear systems

Banek T.

Archives of Control Sciences

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1998

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Vol. 7, no. 1/2

99-104

EN

A structure optimization problem in linear systems is considered. It is shown that parametric minimization (in the mean square sense) of influence of stochastic disturbation can be reduced to some nonlinear programming problem. Sufficient condition for equivalence of these problems and existence of their solutions are given. It is also shown how to apply the results to controlled systems.