[數] 隨機規劃
The convexity of the models for large scale transportation networks is analyzed. It is proved that this type of models are convex stochastic programming problems.
分析了大規模運輸網絡隨機規劃模型的凸性，證明了該類模型為一隨機凸規劃問題。
In addition, the efficiency solution scheme of this problem is given, after the multiple objective stochastic programming with probabilistic constrained is discussed.
此外，提出了這種具有概率約束多目标隨機規劃問題的一種有效解模型。
Present two classes of multivalued stochastic programming models, i. e. , multivalued random chance-constrained programming model and set-valued random expected-value programming model;
建立了兩類多值隨機規劃模型：多值隨機機會約束規劃模型和多值隨機期望值規劃模型；
And then, we present an approximation method for solving this probabilistic constrained stochastic programming, and prove certain convergence of the method under some conditions.
隨後我們提出了求解這類概率約束隨機規劃的一種近似算法，并在一定的條件下證明了算法的收斂性。
In this paper we give a survey of several stochastic programming models and algorithms for unit commitment problem under uncertainty load demands.
文章給出在不确定的荷載需求下機組組合問題的一些常見的隨機規劃模型和算法的綜述。
In this paper we propose a stochastic programming model to determine the location and capacity of centralized return centers and distribution centers in reverse logistics network.
為此，本文提出了一個隨機規劃模型用于确定逆向物流網絡中集中式回收中心和分銷中心的位置和容量。
As using stochastic simulation and fuzzy simulation to resolve the problem in complex stochastic programming and fuzzy programming, the concept and method of grey simulation was advanced in .
正如解決複雜隨機規劃和模糊規劃使用隨機模拟和模糊模拟的手段一樣，本文提出了灰色模拟的概念和方法。
Transform the bilevel stochastic programming model into single-level stochastic programming model under certain confidence, and a corresponding mixed method is designed.
在一定的置信度下，将雙層規劃模型轉化為單層隨機規劃模型，并設計了相應的混合智能算法。
A stochastic programming model was established for selection of container shipping routes, and in the model uncertainty in container demands was taken into consideration.
基于海運集裝箱運輸問題特性的分析，建立了需求不确定的海運集裝箱路徑隨機規劃模型。
The other one is approaching method, i. e. getting the approximate optimal value and solution of stochastic programming through genetic algorithm based on stochastic simulation.
另一種是逼近方法，利用隨機模拟技術，通過一定的遺傳算法程式，得到隨機規劃問題的近似最優解和目标函數的近似最優值。
According to the optimal investment model with minimum-risky, we give a united stochastic programming with probabilistic constrained.
根據最小風險的投資最優問題，我們給出了一個統一的概率約束隨機規劃模型。
A genetic algorithm is used to solve this stochastic programming model.
采用遺傳算法對該隨機規劃模型進行求解。
In the light of fuzzy theory, fuzzy optimization model is changed into the stochastic programming.
利用模糊隨機理論轉化模糊優化模型，使其成為一種易求解的隨機規劃模型。
This thesis presents the combination of the stochastic programming and generalized goal programming.
在本文中 ，我們提出了雙凹規劃問題和更一般的廣義凹規劃問題 。
Uncertainty environmental; inventory control; inventory coordination; remanufacturing logistics system; stochastic programming; fuzzy programming.
不确定性；庫存控制；庫存協調；再制造物流系統；隨機規劃；模糊規劃。
Traditional short-term line maintenance scheduling is always formulated as a stochastic programming problem.
傳統方法将短期線路檢修計劃作為單重不确定性優化問題進行建模和求解。
The convergence of the optimal value and optimal solution of the stochastic programming are given as the function sequence is epi-convergence and the random variable sequence is square convergence.
主要讨論了一類隨機規劃在函數序列上圖收斂和隨機變量序列均方收斂意義下，該類隨機規劃的最優解和最優值的收斂情況。
A stochastic programming model with fuzzy chance constraint is presented which has stochastic and fuzzy parameters.
提出一類模糊機會約束的隨機期望值規劃模型，該模型同時含有隨機和模糊參數。
Based on stochastic programming, a multi objective chance constrained optimization model is developed for an illustrative coal blending problem.
在隨機規劃學的基礎上，建立了電廠優化配煤的多目标機會約束數學模型。
A stochastic programming model was established for selection of container shipping routes, Author put forward an effective way of handling uncertain data in the models.
建立需求不确定的海運集裝箱路徑隨機規劃模型，在模型中提出了處理不确定數據的有效方法。
Combined with the historical data, the model predicts the stochastic parameter using Monte-Carlo simulation method, which improved accuracy and feasibility of stochastic programming model.
模型結合曆史數據，用蒙特卡羅模拟方法來預測參數，提高了隨機規劃模型的準确性和可行性。
This paper discusses a method for two-stage stochastic programming with recourse in which the objective function is replaced by its empirical mean.
探讨了以隨機變量的子樣為條件，使用目标函數的經驗均值逼近法來求解有補償二階段問題，并分析了相關的收斂性。
In order to generate scenarios, this article applies the method of autoregression and Monte-Carlo simulation in stochastic programming models.
本文将自回歸和蒙特卡羅模拟方法運用到隨機規劃模型中，生成情景元素。
Stochastic programming is recognized as a powerful modeling paradigm for several areas of application, include DALM in financial institutions.
隨機規劃就是帶不确定性的數學規劃，能應用到很多領域，包括金融機構動态資産負債管理。
In this paper, the multiple vehicles coordinated Stochastic Vehicle Routing problem with time-constrained is (analysed. ) A kind of stochastic programming model for this problem is established.
分析了有時間約束的基于多車輛協作的隨機路徑問題。 提出了問題的隨機規劃期望值模型。
We formulated scenario based multi-objective stochastic programming model to describe the problem of capacity planning under uncertainty and applied improved Multi-Objective PSO (MOPSO) to solve it.
提出了基于場景的多目标隨機規劃模型來構建不确定市場需求環境下的能力計劃問題模型，并用改進的多目标粒子群優化算法求解。
In this paper, maximum entropy theorem is used to give an approximate computational method for the single stage stochastic programming.
基于雙隨機理論，本文提出了一類兩階段雙隨機規劃模型，并對這類模型的數學性質進行了研究。
We propose a two-stage stochastic programming model with uncertain demand.
建立了消費者需求不确定狀态下的兩階段隨機規劃模型。
隨機規劃（Stochastic Programming）是運籌學與數學優化領域的重要分支，主要用于解決包含不确定參數的決策問題。其核心思想是在建模過程中将不确定性以概率分布的形式納入目标函數或約束條件，從而設計出對隨機因素具有魯棒性的最優策略。
隨機規劃通過數學規劃方法處理多階段決策問題，其中部分參數（如需求、價格、資源供給等）具有隨機性。例如，在電力系統調度中，發電量可能受天氣影響，需預先建立不同場景下的概率模型，并優化期望成本或風險值（來源：Springer《Stochastic Programming》專著）。
典型的隨機規劃模型分為兩階段或多階段：
常用算法包括隨機分解法、Benders分解和蒙特卡洛采樣法。現代求解工具（如GAMS、PySP）結合場景生成技術，可高效處理大規模問題（來源：MathWorks優化工具箱文檔）。
Stochastic programming（隨機規劃）是一種數學優化方法，用于處理包含不确定性參數的決策問題。它結合了概率論和優化理論，通過建立多階段模型來尋找在不确定環境下最優的決策策略。以下是詳細解釋：
不确定性建模
系統參數（如需求、價格、資源量等）不是固定的，而是服從某種概率分布或可能出現的多種場景。例如，電力公司需在未知未來電價的情況下規劃發電量。
多階段決策
決策分階段進行：
目标函數
通常優化期望值，例如最小化總成本的期望，或結合風險度量（如條件風險價值CVaR）以控制極端情況。
兩階段隨機線性規劃
公式示例：
$$
begin{aligned}
min_{x} quad & c^T x + mathbb{E}[Q(x, xi)]
text{s.t.} quad & Ax leq b
& x geq 0
end{aligned}
$$
其中，$Q(x, xi)$是第二階段應對隨機變量$xi$的補救成本。
場景樹方法
将不确定性離散化為有限場景（如“高需求”“中需求”“低需求”），求解大規模線性規劃問題。
如果需要更具體的數學形式或應用案例，可以進一步探讨！
destructiveagonizecentralizequininecalixCantonacartooningcolleenmashingmultimillionairenumbersslatherweatheringboundary valueopt intriplet statevowel soundaldolaseantiphlogisticberriasianchanteydoneedrifterhemiatoniahsianghualitehydrobismutiteichthyotoxicologylusitanitelymphametioprim