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1
Content available Asset liability management for the Bank of Uganda defined benefits scheme by stochastic programming
Mukalazi Herbert, Larsson Torbjörn, Kasozi Juma, Mayambala Fred
Operations Research and Decisions
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2022
|
Vol. 32, No. 2
105--124
EN
We develop a model for asset liability management of pension funds, which is solved by stochastic programming techniques. Using data provided by the Bank of Uganda Defined Benefits Scheme, which is closed to new members, we obtain the optimal investment policies. Randomly sampled scenario trees using the mean and covariance structure of the return distribution are used for generating the coefficients of the stochastic program. Liabilities are modelled by remaining years of life expectancy and guaranteed period for monthly pension. We obtain the funding situation of the scheme at each stage, and the terminal cash injection by the sponsor required to meet all future benefit payments, in absence of contributing members.
2
Content available Stochastic programming model for production planning with stochastic aggregate demand and spreadsheet-based solution heuristics
Saadouli Nasreddine
Operations Research and Decisions
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2021
|
Vol. 31, No. 4
117--127
EN
By discretising the stochastic demand, a deterministic nonlinear programming formulation is developed. Then, a hybrid simulation-optimisation heuristic that capitalises on the nature of the problem is designed. The outcome is an evaluation problem that is efficiently solved using a spreadsheet model. The main contribution of the paper is providing production managers with a tractable formulation of the production planning problem in a stochastic environment and an efficient solution scheme. A key benefit of this approach is that it provides quick near-optimal solutions without requiring in-depth knowledge or significant investments in optimisation techniques and software.
3
Content available remote Chance constraint programming problems with parameters as exponential random variable
Sarkar Vaskar
Mathematica Applicanda
|
2021
|
Vol. 49, no. 1
15--30
EN
Robust decision making under uncertainty is deemed to be a crucial factor in many disciplines and application areas. In addition, management and measurement of risk is an important issue in almost all areas that require decisions to be made under uncertain information. Chance constrained programming (CCP) has been used for modelling and analysis of risks in a number of application domains. This paper presents a deterministic reduction of a linear and nonlinear chance constraint programming problem using simple mathematical and statistical tools, assuming the coefficients of the decision variables in the chance constraints as exponential random variables. After converting the proposed chance constraint programming problem into a deterministic problem, a standard generic package is used to find the compromise solution and a comparison with some other techniques is considered. Then MATLAB programming code is used to verify the validity of solution for the original chance constraints.
PL
Podejmowanie decyzji w warunkach niepewności jest kluczowym czynnikiem wpływającym na efektywność i opłacalność projektów w wielu dyscyplinach badawczych i działalności gospodarczej. W związku z tym, zarządzanie i pomiar ryzyka są ważną kwestią w prawie wszystkich obszarach, które wymagają podejmowania decyzji na podstawie niepewnych informacji. Programowanie ograniczone szansą (CCP) zostało wykorzystane do modelowania i analizy ryzyka w wielu dziedzinach aplikhttps://www.overleaf.com/project/5ff6f9808edae84a1313f60bacji. W artykule przedstawiono deterministyczną redukcję liniowego i nieliniowego problemu programowania z ograniczeniami losowymi z wykorzystaniem prostych narzędzi. Po przekształceniu proponowanego problemu programowania z ograniczeniami losowymi w problem deterministyczny, do dalszej analizy i wyznaczenia rozwiązania używane są standardowe metody optymalizacji. W pracy podano także porównania przy zastosowaniu innych, niż standardowe metod. Rezultaty porównano z rozwiązaniami wyjściowych problem, bez przekształcania, otrzymanych procedurami zaimplementowanymi w MATLAB.
4
Content available Decision maker's preferences modeling for multiple objective stochastic linear programming problems
Bellahcene Fatima
Operations Research and Decisions
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2019
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Vol. 29, No. 3
5--16
EN
A method has been suggested which solves a multiobjective stochastic linear programming problem with normal multivariate distributions in accordance with the minimum-risk criterion. The approach to the problem uses the concept of satisfaction functions for the explicit integration of the preferences of the decision-maker for different achievement level of each objective. Thereafter, a nonlinear deterministic equivalent problem is formulated and solved by the bisection method. Numerical examples with two and three objectives are given for illustration. The solutions obtained by this method are compared with the solutions given by other approaches.
5
Content available Application of the polyblock method to special integer chance constrained problem
Bellahcene Fatima
Operations Research and Decisions
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2019
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Vol. 29, No. 4
23--40
EN
The focus in this paper is on a special integer stochastic program with a chance constraint in which, with a given probability, a sum of independent and normally distributed random variables is bounded below. The objective is to maximize the expectation of a linear function of the random variables. The stochastic program is first reduced to an equivalent deterministic integer nonlinear program with monotonic objective and constraints functions. The resulting deterministic problem is solved using the discrete polyblock method which exploits its special structure. A numerical example is included for illustration and comparisons with LINGO, COUENNE, BONMIN and BARON solvers are performed.
6
Content available Research of traffic prediction accuracy influence on the effectiveness of trains breaking-up order control
Bardas O., Skovron I., Demchenko Y., Dorosh A., Buriak S.
Transport Problems
|
2017
|
T. 12, z. 1
151--158
EN
The article presents the research results of economic feasibility of trains’ breaking-up order control at marshalling yards. The article objective was to determine the area of rational use of trains’ breaking-up order model, formalized in the form of stochastic programming problem. As a effectiveness criterion of trains’ breaking-up order operating costs of marshalling yard were used, including the costs associated with cars’ and locomotives’ dwell time on the station and its approaches, as well as costs associated with additional shunting work. With the help of simulation modeling the dependence was obtained, describing the impact of trains’ arrival forecasting error and processed car volumes on reducing operating costs of the marshalling yards through the trains’ breaking-up order control. The studies enable us to establish the requirements for the accuracy of information support of operational planning tasks, which is necessary to achieve the desired economic effect of the trains’ breaking-up order control.
7
Teoria badań operacyjnych jako narzędzie zarządzania optymalizacyjnego
Ficoń K., Krasnodębski G.
Logistyka
|
2014
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nr 6
622--635, CD 2
PL
W pracy przedstawiono rolę i znaczenie teorii i metod badań operacyjnych w procesie zarządzania optymalizacyjnego występującego szczególnie aktywnie w zarządzaniu logistycznym. We wstępie omówiono genezę i podstawowe pojęcia i definicje badań operacyjnych. Zgodnie z zarysowaną taksonomią metod stosowanych tradycyjnie w badaniach operacyjnych zaprezentowano ich ogólną charakterystykę. W szerokim nurcie programowania matematycznego omówiono metody programowania liniowego i nieliniowego, a także heurystycznego, dynamicznego, stochastycznego i sieciowego. Na zakończenie przedstawiono podstawy teorii grafów, teorii gier, teorii masowej obsługi oraz grupę nowoczesnych metod sztucznej inteligencji należących do tzw. inteligencji obliczeniowej.
EN
The paper presents the role and importance of the theory and methods of operations research in the optimization management process occurs particularly active in the management of logistics. In the introduction discusses the origins and basic concepts and definitions of operational research. According to the taxonomy applied methods traditionally in operations research's presented their general characteristics. In the broad mainstream of mathematical programming the paper discusses methods of linear and nonlinear programming, as well as heuristic, dynamic, stochastic and network programming. At the end are discussed the fundamentals of graph theory, game theory, queuing theory, and a group of modern artificial intelligence methods belonging to the so-called computational intelligence.
8
Content available Stochastic generalized transportation problem with discrete distribution of demand
Anholcer M.
Operations Research and Decisions
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2013
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Vol. 23, No. 4
9--19
EN
The generalized transportation problem (GTP) allows us to model situations where the amount of goods leaving the supply points is not equal to the amount delivered to the destinations (this is the case, e.g. when fragile or perishable goods are transported or complaints may occur). A model of GTP with random, discretely distributed, demand has been presented. Each problem of this type can be transformed either into the form of a convex programming problem with a piecewise linear objective function, or a mixed integer LP problem. The method of solution presented uses ideas applied in the method of stepwise analysis of variables and in the equalization method.
9
Content available Algorithm for the stochastic generalized transportation problem
Anholcer M.
Operations Research and Decisions
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2012
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Vol. 22, No. 4
9--20
EN
The equalization method for the stochastic generalized transportation problem has been presented. The algorithm allows us to find the optimal solution to the problem of minimizing the expected total cost in the generalized transportation problem with random demand. After a short introduction and literature review, the algorithm is presented. It is a version of the method proposed by the author for the nonlinear generalized transportation problem. It is shown that this version of the method generates a sequence of solutions convergent to the KKT point. This guarantees the global optimality of the obtained solution, as the expected cost functions are convex and twice differentiable. The computational experiments performed for test problems of reasonable size show that the method is fast.
10
Stochastyczne prognozowanie parametrów zbiornikowych i petrofizycznych skał w oparciu o mapy atrybutów sejsmicznych i profilowania geofizyki wiertniczej - przykłady modelowań wykonanych w rejonie zrębu Ryszkowej Woli (na podstawie danych zdjęcia sejsmicznego Rudka 3D)
Gruszczyk M., Jędrys J.
Prace Naukowe Instytutu Nafty i Gazu
|
2010
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nr 170 wyd. konferencyjne
521--524
PL
Celem referatu jest przedstawienie idei stochastycznego prognozowania rozkładu facji i parametrów zbiornikowych skał, poprzez integrację danych sejsmicznych i otworowych. Istotą tej integracji jest wielowymiarowe modelowanie realizowane za pomocą metod regresji oraz sieci neuronowych. Ideę takiej analizy można sprowadzić do dwóch zasadniczych etapów. Pierwszy etap realizowany jest na małej próbie danych, której liczebność ograniczona jest do ilości zlokalizowanych na obszarze zdjęcia sejsmicznego otworów. Mając do dyspozycji zarówno dane otworowe, jak i dane sejsmiczne wyznaczamy zależności między nimi, a dokładnie między parametrami skały a atrybutami sejsmicznymi. Drugi etap realizowany jest na całości obszaru występowania horyzontu sejsmicznego, w którego sąsiedztwie policzono atrybuty sejsmiczne. Znając wartości atrybutów oraz zależności wyznaczone w pierwszym etapie, można wyznaczyć wartości parametrów skały na całym obszarze badań. Wynikiem jest model parametru, np. porowatości.
EN
The paper presents the idea of using stochastic methods to predict the patterns of the facies and rocks' reservoir parameters utilising seismic and well data integration. This is realised by multidimensional modelling. The modelling itself is performed by regression methods and neural networks. There are two main stages of this analysis. The first one is realized with the small data sample which is as numerous as the quantity of wells within the area of a seismic survey. Then we check the relations between seismic and well data which are in that case the relations between rock parameters and seismic attributes. The second stage is performed using the data from the whole area of occurrence of the seismic horizon which is devoted to attributes' calculations. Knowing the attributes' values and relations found in the first stage, we are already able to find rock parameters' values in the whole area of study. The result of the analysis is a model of the rock parameter, e.g. porosity.
11
Content available Stochastic Models in Techno-Economic Analysis of Broadband Access Networks
Olender P.
Journal of Telecommunications and Information Technology
|
2010
|
nr 2
43-51
EN
Development of networks, specially access networks, is very important and urgent task nowadays. However, it turns out that this segment of telecommunication networks is the most expensive and complicated part of this undertaking. Therefore, the thorough analyses are carried out to determine the best solution under specific circumstances before any decisions are made. This paper presents techno-economic model, which was implemented and used to carry out analyses for one of the biggest city in Poland. To take uncertainty into consideration the stochastic approach was applied providing more robust solution, therefore, improving the safety of investment. Analyses concern FTTH (fibre to the home) technology, type of generic FTTx network architecture. It uses optical fibre in local telecommunication loop, what is becoming more and more popular. Presented results show the usefulness of techno-economic surveys in planning access networks development. The appropriate choice of network parameters, such as the aggregation ratio, is essential and could significantly influence the investment profitability.
12
Content available Zastosowanie modeli programowania stochastycznego do optymalizacji struktury produkcji w gospodarstwach rolnych o różnej powierzchni
Zaród J.
Inżynieria Rolnicza
|
2010
|
R. 14, nr 7
261-268
PL
Wszystkie gospodarstwa rolne województwa zachodniopomorskiego w latach 2003-2006 podzielono na osiem grup areaowych (1-5 ha, >5-10 ha, >10-15 ha, >15-20 ha, >20-30 ha, >30-50 ha. >50-200 ha, >200 ha). Na podstawie rzeczywistych danych dla każdej grupy zbudowano dynamiczne modele optymalizacyjny ze stochastycznymi współczynnikami funkcji celu. Wyniki rozwiązań modeli są realizacją celu pracy i przedstawiają optymalną strukturę produkcji, opłacalne kierunki produkcji, największy dochód rolniczy, jaki można osiągnąć w danych warunkach oraz ryzyko realizacji zamierzeń w gospodarstwach o różnej powierzchni.
EN
All farms in the Zachodniopomorskie region in Poland between 2003 and 2006 were divided into eight size groups (1-5 ha, >5-10 ha, >10-15 ha, >15-20 ha, >20-30 ha, >30-50 ha. >50-200 ha, >200 ha). On the basis of actual data a dynamic optimization models with stochastic coefficients of the goal function were built for each of the groups. The results of the model solutions are the implementation of the goal of the work and present optimal structure of production, profitable directions of production, the highest farm income possible in given conditions and the risk of plans implementation in farms of various size.
13
Content available remote Composite semi-infinite optimization
Dentcheva D., Ruszczyński A.
Control and Cybernetics
|
2007
|
Vol. 36, no 3
633-646
EN
We consider a semi-infinite optimization problem in Banach spaces, where both the objective functional and the constraint operator are compositions of convex nonsmooth mappings and differentiable mappings. We derive necessary optimality conditions for these problems. Finally, we apply these results to non-convex stochastic optimization problems with stochastic dominance constraints, generalizing earlier results.
14
Content available remote Pomiar ryzyka finansowego w warunkach niepewności
Trzpiot G.
Badania Operacyjne i Decyzje
|
2006
|
nr 2
81-88
EN
Coping with the uncertainties of future outcomes is a fundamental theme in finance in a stochastic environment. In the field of stochastic programming, which has grown from the traditions of linear and quadratic programming, constrains on future outcomes have commonly been relaxed to the penalty expressions. Probabilistic constrains, requiring that a condition only to be satisfied up to a given probability. Objectives have usually taken the form of maximizing expected utility or minimizing expected cost. In financial optimization, where uncertainties are likewise unavoidable, approaches of stochastic programming have prevailed. An important example is constraint and objective based notion of the value-at-risk, which is closely related to probabilistic one; unfortunately it suffers from similar mathematical shortcomings. Value-at-risk suffers from financial inconsistencies, which have led to axiomatic development of coherent risk measures, so we also add the robust alternative called conditional value-at-risk. We also cope with some connection between CVaR and stochastic dominance.
PL
Zarządzanie losowymi przyszłymi stopami zwrotu jest podstawowym zadaniem finansów w otoczeniu, które ma charakter stochastyczny. W metodologii programowania stochastycznego, które wyrosło z tradycji programowania liniowego i kwadratowego, ograniczenia, co do przyszłych wartości, są często zamieniane na funkcję kary. Probabilistyczne ograniczenia w zadaniu wymagają jedynie, aby zdarzenia zachodziły z pewnym prawdopodobieństwem. Funkcja celu zazwyczaj maksymalizuje oczekiwaną użyteczność albo minimalizuje koszty. W finansach zadania optymalizacji stochastycznej mają, zatem uprzywilejowane miejsce. Ważne są zadania bazujące na optymalizacji VaR, które są podejściem probabilistycznym do zagadnienia. Rozwój aksjomatycznej teorii związanej z koherentnymi miarami ryzyka, wskazał na odporny odpowiednik VaR nazywany CVaR. W pracy omówiono związek tej miary z dominacjami stochastycznymi.
15
Content available remote Stochastic algorithms in discrete optimization with noisy values for the function
Wieczorkowski Robert
Matematyka Stosowana : matematyka dla społeczeństwa
|
1995
|
Nr 38
119--153
EN
The paper deals with stochastic methods for searching approximately global minimum of function defined on discrete set. A measure of quality of solution is defined to compare different algorithms. Simple Monte Carlo method is analysed as main algorithm for which formulas dealing with the measure of quality are derived(two cases: exact values and noisy values of function). This Monte Carlo method is used as a base in simulation experiments for comparing other stochastic algorithms. The second part of the paper analyses asymptotic properties of the generalised simulated annealing algorithms. Theory of Markov chains is used in modelling this class of algorithms. Theorems about convergence of the records of algorithms to set of optima with probability one are presented in the case of function having random noisy values. The paper also reviews known results in the field of simulated annealing type algorithms for function with randomly perturbated values.
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