On the Stochastic Non-sequential Production-planning Problem
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Stochastic modelling
A widely used heuristic for solving stochastic optimization problems is to use a deterministic rolling horizon procedure, which has been modified to handle uncertainty (e.g. buffer stocks, schedule slack). This approach has been criticized for its use of a deterministic approximation of a stochastic problem, which is the major motivation for stochastic programming. We recast this debate by identifying both deterministic and stochastic approaches as policies for solving a stochastic base model, which may be a simulator or the real world. Stochastic lookahead models (stochastic programming) require a range of approximations to keep the problem tractable. By contrast, so-called deterministic models are actually parametrically modified cost function approximations which use parametric adjustments to the objective function and/or the constraints. These parameters are then optimized in a stochastic base model which does not require making any of the types of simplifications required by stochastic programming. We formalize this strategy and describe a gradient-based stochastic search strategy to optimize the parameters.
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Stochastic Approximation
Time horizon
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Most models for chemical production planning are based on deterministic programming approaches without considering uncertainty. This paper presents a two-stage stochastic programming model for chemical production planning optimization with management of purchase and inventory under economic uncertainties including prices of raw materials, product prices and demands, and uses the Monte Carlo sampling method to solve it. The expected profit is maximized taking into account raw materials costs, inventory costs, operating costs and costs of lost demand under economic uncertainties, while the production planning and purchase scheme are optimized simultaneously. The proposed model is validated by a real chemical enterprise based on GIOCIMS (Graphical I/O Chemical Industry Modeling System). The results indicate that the two-stage stochastic programming model can suggest a solution with higher expected profit and lower risk than the one suggested by deterministic programming model.
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Although stochastic programming is probably the most effective framework for handling decision problems that involve uncertain variables, it is always a costly task to formulate the stochastic model that accurately embodies our knowledge of these variables. In practice, this might require one to collect a large amount of observations, to consult with experts of the specialized field of practice, or to make simplifying assumptions about the underlying system. When none of these options seem feasible, a common heuristic has been to simply seek the solution of a version of the problem where each uncertain variable takes on its expected value otherwise known as the solution of the mean value problem. In this paper, we show that when 1 the stochastic program takes the form of a two-stage mixed-integer stochastic linear programs, and 2 the uncertainty is limited to the objective function, the solution of the mean value problem is in fact robust with respect to the selection of a stochastic model. We also propose tractable methods that will bound the actual value of stochastic modeling: i.e., how much improvement can be achieved by investing more efforts in the resolution of the stochastic model. Our framework is applied to an airline fleet composition problem. In the three cases that are considered, our results indicate that resolving the stochastic model can not lead to more than a 7% improvement of expected profits, thus providing arguments against the need to develop these more sophisticated models.
Stochastic modelling
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Expected value
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A widely used heuristic for solving stochastic optimization problems is to use a deterministic rolling horizon procedure, which has been modified to handle uncertainty (e.g. buffer stocks, schedule slack). This approach has been criticized for its use of a deterministic approximation of a stochastic problem, which is the major motivation for stochastic programming. We recast this debate by identifying both deterministic and stochastic approaches as policies for solving a stochastic base model, which may be a simulator or the real world. Stochastic lookahead models (stochastic programming) require a range of approximations to keep the problem tractable. By contrast, so-called deterministic models are actually parametrically modified cost function approximations which use parametric adjustments to the objective function and/or the constraints. These parameters are then optimized in a stochastic base model which does not require making any of the types of simplifications required by stochastic programming. We formalize this strategy and describe a gradient-based stochastic search strategy to optimize the parameters.
Stochastic modelling
Stochastic Approximation
Time horizon
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Stochastic modelling
Energy market
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Бұл зерттеужұмысындaКaно моделітурaлы жәнеоғaн қaтыстытолықмәліметберілгенжәнеуниверситетстуденттерінебaғыттaлғaн қолдaнбaлы (кейстік)зерттеужүргізілген.АхметЯссaуи университетініңстуденттеріүшін Кaно моделіқолдaнылғaн, олaрдың жоғaры білімберусaпaсынa қоятынмaңыздытaлaптaры, яғнисaпaлық қaжеттіліктері,олaрдың мaңыздылығытурaлы жәнесaпaлық қaжеттіліктерінеқaтыстыөз университетінқaлaй бaғaлaйтындығытурaлы сұрaқтaр қойылғaн. Осы зерттеудіңмaқсaты АхметЯсaуи университетіндетуризмменеджментіжәнеқaржы бaкaлaвриaт бaғдaрлaмaлaрыныңсaпaсынa қaтыстыстуденттердіңқaжеттіліктерінaнықтaу, студенттердіңқaнaғaттaну, қaнaғaттaнбaу дәрежелерінбелгілеу,білімберусaпaсын aнықтaу мен жетілдіружолдaрын тaлдaу болыптaбылaды. Осы мaқсaтқaжетуүшін, ең aлдыменКaно сaуaлнaмaсы түзіліп,116 студенткеқолдaнылдыжәнебілімберугежәнеоның сaпaсынa қaтыстыстуденттердіңтaлaптaры мен қaжеттіліктерітоптықжұмыстaрaрқылыaнықтaлды. Екіншіден,бұл aнықтaлғaн тaлaптaр мен қaжеттіліктерКaно бaғaлaу кестесіменжіктелді.Осылaйшa, сaпa тaлaптaры төрт сaнaтқa бөлінді:болуытиіс, бір өлшемді,тaртымдыжәнебейтaрaп.Соңындa,қaнaғaттaну мен қaнaғaттaнбaудың мәндеріесептелдіжәнестуденттердіңқaнaғaттaну мен қaнaғaттaнбaу деңгейлерінжоғaрылaту мен төмендетудеосытaлaптaр мен қaжеттіліктердіңрөліaйқын aнықтaлды.Түйінсөздер:сaпa, сaпaлық қaжеттіліктер,білімберусaпaсы, Кaно моделі.
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Risk and uncertainty in the complex systems chance-constrained stochastic programming two-stage stochastic programming problems multistage stochastic programming problems game approach to stochastic programming problems existence of solution and its optimality in stochastic programming problems methods for solving infinite and semi-infinite programming problems optimization of fuzzy sets optimization of nonlinear programming problems with nonuniquely defined variables optimization problems in function spaces.
Robust Optimization
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This chapter reviews the main ideas behind dynamic programming, stochastic programming, and robust optimization, and illustrates the techniques with examples. It provides taxonomy of methods for optimization when the input parameters are uncertain. Dynamic programming solves a large multistage optimization problem sequentially, starting at the last stage and proceeding backward, thus keeping track only of the optimal paths from any given time period onward. The stochastic programming can be used to address the presence of uncertain input data in three types of optimization problems: expected value for single-stage and multistage models; models involving risk measures; and chance-constrained models. A major problem with dynamic and stochastic programming formulations is that in practice it is often difficult to obtain detailed information about the probability distributions of the uncertainties in the model. Robust optimization formulations can be used also in multistage settings to replace dynamic programming or stochastic programming algorithms.
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