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EN
The constrained regulation problem (CRP) for fractional-order nonlinear continuous-time systems is investigated. New existence conditions of a linear feedback control law for a class of fractional-order nonlinear continuous-time systems under constraints are proposed. A computation method for solving the CRP for fractional-order nonlinear systems is also presented. Using the comparison principle and positively invariant set theory, conditions guaranteeing positive invariance of a polyhedron for fractional-order nonlinear systems are established. A linear feedback controller model and the corresponding algorithm of the CRP for fractional nonlinear systems are also proposed by using the obtained conditions. The presented model of the CRP is formulated as a linear programming problem, which can be easily implemented from a computational point of view. Numerical examples illustrate the proposed method.
EN
The strategy should be designed in such a way as the risk management can operate not only as a system for avoiding losses, but also risk management should allow recognizing and making use of occasions and create new opportunities for the organization. Risk management includes both an evaluation (analytical and evaluation) undertaking as well as planning and control activities aimed at minimizing (reducing) risk or maintaining it at an acceptable level. Security management can in particular be reduced to the issue of risk management, because risk is a quantitative expression of the functioning of systems in an environment where there are active sources of threats to system security. The article presents the problem of personnel allocation in hazardous conditions, emphasizing the possibilities of undertaking optimization actions in the safety management process. A mathematical model was formulated for this issue. An algorithm solving the problem of personnel allocation is presented. The proposed analysis is the starting point for determining the risk when using multi-station work.
EN
The allocation of production tasks to specific production resources is an important part of preparing the manufacturing process. The amount of profit and costs incurred depends on this division. The efficiency of production resources depends not only on the technologies used, but also on the tasks that will be carried out on them. Therefore, the management of machine efficiency includes both an evaluation (analytical and assessment undertaking, e.g. OEE) and planning activities aimed at maximizing the efficiency of machines by appropriately assigning production tasks to them. The article presents the problem of the allocation of production of various products to various production resources, including the efficiency of the use of machines and devices, emphasizing the possibilities of undertaking optimization actions in the cost management process. A mathematical model was formulated for this issue. An algorithm solving the problem of allocation of production tasks is presented. The solution was obtained using the Octave computing environment.
EN
This paper is centred on a binary classification problem in which it is desired to assign a new object with multivariate features to one of two distinct populations as based on historical sets of samples from two populations. A linear discriminant analysis framework has been proposed, called the minimised sum of deviations by proportion (MSDP) to model the binary classification problem. In the MSDP formulation, the sum of the proportion of exterior deviations is minimised subject to the group separation constraints, the normalisation constraint, the upper bound constraints on proportions of exterior deviations and the sign unrestriction vis-à-vis the non-negativity constraints. The two-phase method in linear programming is adopted as a solution technique to generate the discriminant function. The decision rule on group-membership prediction is constructed using the apparent error rate. The performance of the MSDP has been compared with some existing linear discriminant models using a previously published dataset on road casualties. The MSDP model was more promising and well suited for the imbalanced dataset on road casualties.
EN
The presented method is constructed for optimum scheduling in production lines with parallel machines and without intermediate buffers. The production system simultaneously performs operations on various types of products. Multi-option products were taken into account – products of a given type may differ in terms of details. This allows providing for individual requirements of the customers. The one-level approach to scheduling for multioption products is presented. The integer programming is used in the method – optimum solutions are determined: the shortest schedules for multi-option products. Due to the lack of the intermediate buffers, two possibilities are taken into account: no-wait scheduling, possibility of the machines being blocked by products awaiting further operations. These two types of organizing the flow through the production line were compared using computational experiments, the results of which are presented in the paper.
EN
The linear programming (LP) approach to solve the Bellman equation in dynamic programming is a well-known option for finite state and input spaces to obtain an exact solution. However, with function approximation or continuous state spaces, refinements are necessary. This paper presents a methodology to make approximate dynamic programming via LP work in practical control applications with continuous state and input spaces. There are some guidelines on data and regressor choices needed to obtain meaningful and well-conditioned value function estimates. The work discusses the introduction of terminal ingredients and computation of lower and upper bounds of the value function. An experimental inverted-pendulum application will be used to illustrate the proposal and carry out a suitable comparative analysis with alternative options in the literature.
EN
Positively invariant sets play an important role in the theory and applications of dynamical systems. The stability in Lyapunov sense of equilibrium x = 0 is equivalent to the existence of the ellipsoidal positively invariant sets. The constraints on the state and control vectors of dynamical systems can be formulated as polyhedral positively invariant sets in practical engineering problems. Numerical checking method of positive invariance of polyhedral sets is addressed in this paper. The validation of the positively invariant sets can be done by solving LPs which can be easily implemented numerically. The effectiveness of the proposed checking method is illustrated by examples. Compared with the now existing algebraic methods, numerical checking method is attractive and, importantly, easy to be implemented.
EN
In this paper,we consider an infinite dimensional linear systems. It is assumed that the initial state of system is not known throughout all the domain Ω C Rn, the initial state x0 ϵ L2(Ω) is supposed known on one part of the domain Ω and uncertain on the rest. That means Ω = ω1 U ω2 U... U ωt with ωi ∩ ωj = ∅, ∀i ≠ j ϵ {1,...,t}, i ≠ j where ωi ≠ ∅ and x0(θ) = αi for θ ϵ ωi, ∀i, i.e., x0(θ) = [wzór] (θ) where the values α1,...,αr are supposed known and αr+1,...,αt unknown and 1ωi is the indicator function. The uncertain part (α1,...,(α)rof the initial state x0 is said to be (ɛ1,...,ɛr )-admissible if the sensitivity of corresponding output signal (yi)i≥0 relatively to uncertainties (αk)1≤k≤r is less to the treshold ɛk, i.e., ∥∂yi)/(∂αk∥ ≤ ɛk, ∀i≥ 0, ∀k ϵ {1,...,r]. The main goal of this paper is to determine the set of all possible gain operators that makes the system insensitive to all uncertainties. The characterization of this set is investigated and an algorithmic determination of each gain operators is presented. Some examples are given.
9
Content available Optimization of ship’s crew change schedule
EN
Seaborne shipping must often cope with issues related to planning, ship scheduling, and arranging crews and optimal shipping routes between ports. Human resources departments typically plan ship crew shifts with regards to the seafarers’ right to vacation days. It is difficult to harmonize all the requirements and to satisfy both the seafarers and the company. Ideally, arrangements are made for the crewmember to sign off upon completion of a contract, with the vessel being at a port convenient to change the crew at a minimum cost. The latter may vary greatly, depending on the size of the crew to be replaced, the distance of the port from the crew destination, and the available taking-over crew at a specific place and time, etc. In these situations, linear programming (LP) is frequently used as a mathematical method to determine the optimal results. This study suggests the use of a linear-binary programming model in LINGO software to arrange the ship’s crew change schedule.
EN
The method intended to build the possibly shortest assembly schedules is presented in the paper. The method is constructed for assembly lines without parallel machines. The intermediate buffers are located between the assembly machines. A flow of products of different types is unidirectional in the assembly line. The proposed method is a heuristic because the fixed tasks are characterized by a large size and considerable computational complexity. It is a relaxation heuristic. The linear mathematical model is used in the mentioned heuristic method. The method is constructed for assembly scheduling for multioption products. Assembly of various types of products in different variants is the reply to the contemporary challenges faced by the manufacturers, who try to satisfy the demands of individual customers. The planned downtimes of machines are regarded in the method, for example downtime of machines connected with maintenance. The results of computational experiments with proposed heuristic method are presented. The described heuristic method is compared with optimal method based on the integer programming. The fixed makespans and computational fixed times using heuristic method and optimal method are compared.
PL
Przedstawiono metodę przeznaczoną do budowy najkrótszych harmonogramów montażu produktów w liniach montażowych bez maszyn równoległych. Konfiguracja linii montażowej uwzględnia obecność buforów międzyoperacyjnych pomiędzy maszynami. Przepływ równocześnie montowanych produktów różnych typów jest jednokierunkowy. Ze względu na rozmiary rozwiązywanych problemów i związaną z tym złożoność obliczeniową metoda jest heurystyką. Jest to heurystyka relaksacyjna, w której wykorzystano model zadania programowania liniowego. Metoda dotyczy produktów wielowariantowych. Produkty danego typu mogą różnić się wariantami wykonania - specyficznymi cechami, uwzględniającymi wymagania odbiorców. Metodę wyróżnia także uwzględnienie planowanych przestojów maszyn, np. przeznaczonych na konserwację. Zaprezentowano wyniki eksperymentów obliczeniowych, za pomocą których oceniono jakość opracowanej metody. Długości harmonogramów wyznaczanych za pomocą przedstawionej metody porównano z długościami harmonogramów optymalnych, znanymi dzięki zastosowaniu modelu zadania programowania całkowitoliczbowego. Porównano także czasochłonność obliczeń.
EN
The proper organization of work is to set the workflow to the slightest effort of man and machine operation to obtain maximum results. The article presents the problem of the allocation of personnel that occurs in a real company. The mathematical model for this issue was formulated. An algorithm solving the problem of personnel allocation is presented. The proposed analysis is a starting point for determining the production capacity and load of each workstation, which is particularly important when using multi-station work and balancing the production line.
PL
W artykule rozpatrujemy problem maksymalizacji przepustowości ruchowej kratowych sieci radiowych z pakietowym ruchem multicastowym obsługiwanym w trybie wielodostępu czasowego TDMA. W tego typu sieciach pakiety kierowane są od źródeł do ujść po drogach określonych za pomocą drzewa routingowego. W przedstawionych rozważaniach, zilustrowanych obliczeniowo, badamy, jak rożne sposoby doboru drzew routingowych wpływają na przepustowość ruchową sieci. Badania takie mogą być pomocne przy konfigurowaniu sieci sensorowych.
EN
In this paper we consider an optimization problem of maximizing traffic throughput in wireless mesh networks with multicast packet traffic. In such networks the way packets are transmitted from sources to destinations is controlled by means of routing trees. In the presented numerical study we examine impact of different routing trees selection methods on network’s traffic throughput efficiency. The considerations can be helpful in wireless sensor networks operation.
EN
This research paper is about the renewal, improvement and development of railroad transportation industry and planning for its contribution to the national and regional economic development. A theoretical exploration provided a guide for the necessary assessments. A research method based on the case study of almost all elements of the Iran railroad transportation system has been performed. The implementation of the observation by means of some indicators proves that hinders shall be removed to achieve maximum profit of the rail transport industry. Strengths, weaknesses, opportunities and threats (SWOT) analysis aided to evaluate the features of the industry. The analysis revealed that the present system of the railroad transportation is unable to assist the national macro economy. The failure corresponds to scarcely investing, funding, managing, infrastructure, operating conditions, and international/regional trade limitations. However, with the help of the improvement plans the prospects for the rail transport development will be pretty satisfactory due to the strategic Geo-policy, climate, nature, and trade potentials. A linear programming for the rail transport industry (LPRTI) has been provided to suggest the ways for maximizing of the rail transport system’s profits to support the national macro economy. The outcome of this research paper assists the regional/national economies with the help of a successful railroad transportation industry everywhere in the world.
14
Content available remote Zarządzanie zadaniami pracowników w branży budowlanej
PL
Właściwa organizacja pracy polega na takim ustawieniu przebiegu pracy, aby przy najmniejszym nakładzie pracy człowieka lub urządzeń uzyskiwać maksymalne rezultaty działania. Artykuł prezentuje problem przydziału personelu, który występuje w rzeczywistej firmie świadczącej usługi budowlane. Sformułowano model matematyczny dla tego zagadnienia. Przedstawiono algorytm rozwiązujący problem alokacji personelu. Zaproponowana analiza stanowi punkt wyjścia do określenia możliwości usługowych oraz obciążenia każdego pracownika, co jest szczególnie istotne w przypadku stosowania pracy wielostanowiskowej.
EN
The proper organization of work is to set the workflow to the slightest effort of man and machine operation to obtain maximum results. The article presents the problem of the allocation personnel, that occurs in a real company that provides construction services. The mathematical model for this issue was formulated. An algorithm solving the problem of personnel allocation is presented. The proposed analysis is a starting point for determining the production capacity and load of each workstation, which is particularly important when using multi-station work.
EN
The routing and spectrum assignment problem is an NP-hard problem that receives increasing attention during the last years. Existing integer linear programming models for the problem are either very complex and suffer from tractability issues or are simplified and incomplete so that they can optimize only some objective functions. The majority of models uses edge-path formulations where variables are associated with all possible routing paths so that the number of variables grows exponentially with the size of the instance. An alternative is to use edge-node formulations that allow to devise compact models where the number of variables grows only polynomially with the size of the instance. However, all known edge-node formulations are incomplete as their feasible region is a superset of all feasible solutions of the problem and can, thus, handle only some objective functions. Our contribution is to provide the first complete edge-node formulation for the routing and spectrum assignment problem which leads to a tractable integer linear programming model. Indeed, computational results show that our complete model is competitive with incomplete models as we can solve instances of the RSA problem larger than instances known in the literature to optimality within reasonable time and w.r.t. several objective functions. We further devise some directions of future research.
16
Content available remote A Minimum set-cover problem with several constraints
EN
A lot of problems in natural language processing can be interpreted using structures from discrete mathematics. In this paper we will discuss the search query and topic finding problem using a generic context-based approach. This problem can be described as a a Minimum Set Cover Problem with several constraints. The goal is to find a minimum covering of documents with the given context for a fixed weight function. The aim of this problem reformulation is a deeper understanding of both the hierarchical problem using union and cut as well as the non-hierarchical problem using the union. We thus choose a modeling using bipartite graphs and suggest a novel reformulation using an integer linear program as well as novel graph-theoretic approaches.
PL
W artykule omawiana jest możliwość wykorzystania metod programowania liniowego w sytuacji, gdy w danym przedsiębiorstwie jest wdrożony kaskadowy model cenowy. Dzięki strukturze liniowej kaskadowego modelu pojawia się możliwość wprowadzenia metod programowania liniowego w optymalizacje procesów decyzyjnych dotyczących wyznaczania odpowiedniej ceny kontraktów. Optymalizowane są te elementy proces decyzyjnego, dla których jest możliwe zdefiniowanie poziomu ograniczeń zasobów. Funkcja celu jest zbudowana w oparciu o wartość parametru Pocket Margin zdefiniowanego w kaskadowym modelu cenowym, jako wartość wyliczająca wynik ekonomiczny dla danej transakcji. Przygotowane i wyliczone rozwiązanie programu liniowego jest wyłącznie propozycją dla kadry menadżerskiej, mająca na celu wspieranie procesu decyzyjnego dodatkowymi informacjami.
EN
The article discusses the possibility of using linear programming methods in a situation where a cascaded pricing model is implemented in a given company. Thanks to the linear structure of the cascading model, there is the possibility of introducing linear programming methods into optimization of decision-making processes concerning determining the appropriate price of contracts. These elements of the decision process are optimized for which it is possible to define the level of resource constraints. The goal function is built based on the value of the Pocket Margin parameter defined in the cascaded pricing model, as the value calculating the economic result for a given transaction. The prepared and calculated solution of the linear program is only a proposal for the managerial staff, aimed at supporting the decision-making process with additional information.
EN
The aim of the article is to present the possibilities of using selected optimization methods to planning accommodation in spa establishments. Therefore, two methods of solving problems in the field of linear programming were used. The first is the north-west angle method, and the second is the Vogel's approximation method. The methods used so far in logistics in the field of planning a production program can be effectively used also in spa services and improving the efficiency of business models of spa enterprises.
19
Content available remote A software program for optimal 1D cutting suport
EN
The paper summarizes the procedure of solving 1D optimal cutting problems, giving details of coding it using dynamic programming, knapsack problem formulation and column generation approach. Finally, the software program for optimal 1D cutting support is described, which is the open code version enabling researchers to extent its capabilities. The paper ends by giving solutions to stated problems and the description of the GUI of the program. At the end of the paper, the reference to the other paper of the authors discussing the effectiveness of the proposed solution is given, tightly connected with this paper.
PL
W artykule przedstawiono procedurę rozwiązywania zadania optymalizacji docinania 1D, włączając szczegóły zakodowania algorytmu przy użyciu programowania dynamicznego, formalizmu zadania plecakowego oraz metody generowania kolumn. W końcu, opisano program wspomagania optymalnego docinania, w postaci programu w otwartym kodzie co pozwoli badaczom na jego dalsze rozwijanie. Artykuł zawiera rozwiązania przykładowych zadań optymalizacji, jak i też opis interfejsu użytkownika. Zawarto również odnośnik do drugiego artykułu autorów, przedstawiającego efektywność zastosowanych metod.
PL
Sieci bezprzewodowe opierające się na standardzie IEEE802.15.4e-TSCH zdobywają popularność w dziedzinie Przemysłowego Internetu Rzeczy. TSCH (ang. Time Slotted Channel Hopping) pozwala na osiągnięcie wysokiego stopnia niezawodności łącza odpowiadającej zastosowaniom przemysłowym. Standard jednakże nie definiuje działania planisty, co jest obecnie tematem prac wielu ośrodków badawczych. W naszym artykule przedstawiamy rozwiązanie problemu maksymalizacji przepustowości w sieciach TSCH z założeniem zerowej domeny kolizyjnej. Celem uzyskania rozwiązania optymalnego, przydział zasobów łącza został rozwiązany jako problem programowania liniowego. Proponujemy ponadto autorski algorytm heurystyczny, harmonogramujący transmisje w sposób centralny. W pracy zaprezentowaliśmy jego działanie oraz zestawiliśmy wyniki symulacji z rozwiązaniem optymalnym.
EN
Wireless sensor networks incorporating the IEEE802.15.4e-TSCH standard are recognized as a reliable solution in the field of Industrial Internet of Things. TSCH (Time Slotted Channel Hopping) allows achieving a high degree of link reliability which corresponds to industrial applications. The standard, however, does not define how the scheduler operates. This open issue is one of the trending topic of many research centers. In our article, we put forward a solution to the problem of throughput maximization in TSCH networks assuming a zero collision domain. In our article the issue of resource allocation has been described as a linear programming problem in order to obtain an optimal solution. We also propose an original heuristic algorithm that schedules transmissions in a centralized way. A comparative study of simulation results is presented.
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