scholarly journals The problem solution of the uniform distribution of resources by the dynamic programming method

2016 ◽  
Vol 6 (3) ◽  
pp. 248-254
Author(s):  
Коновальчук ◽  
Evgeniy Konovalchuk ◽  
Коновалов ◽  
Oleg Konovalov ◽  
Сербулов ◽  
...  
Keyword(s):  
Dynamic Programming ◽  
Quadratic Programming ◽  
Utility Function ◽  
Uniform Distribution ◽  
Fixed Number ◽  
Dynamic Programming Method ◽  
Problem Solution ◽  
Absolute Minimum ◽  
Integer Quadratic Programming ◽  
Distribution Of Resources

The solution of two problems is considered for this purpose in the article: the achievements of a conditional minimum and the achievement of an absolute minimum according to the devel-oped algorithms. At the same time the problem solution of achieving the conditional minimum is reduced to theproblem of integer quadratic programming and the problem of achieving the abso-lute minimum – to minimization of the utility function in the field of the set restrictions and to the search of the fixed number of variables.

scholarly journals Single-Manufacturer Multi-Retailer Supply Chain Models with Discrete Stochastic Demand

2021 ◽  
Vol 13 (15) ◽  
pp. 8271
Author(s):  
Yaqing Xu ◽  
Jiang Zhang ◽  
Zihao Chen ◽  
Yihua Wei
Keyword(s):  
Dynamic Programming ◽  
Supply Chain ◽  
Computational Complexity ◽  
Stackelberg Game ◽  
Programming Model ◽  
Dynamic Programming Method ◽  
Game Model ◽  
Chain Model ◽  
Stochastic Demands ◽  
Demand Models

Although there are highly discrete stochastic demands in practical supply chain problems, they are seldom considered in the research on supply chain systems, especially the single-manufacturer multi-retailer supply chain systems. There are no significant differences between continuous and discrete demand supply chain models, but the solutions for discrete random demand models are more challenging and difficult. This paper studies a supply chain system of a single manufacturer and multiple retailers with discrete stochastic demands. Each retailer faces a random discrete demand, and the manufacturer utilizes different wholesale prices to influence each retailer’s ordering decision. Both Make-To-Order and Make-To-Stock scenarios are considered. For each scenario, the corresponding Stackelberg game model is constructed respectively. By proving a series of theorems, we transfer the solution of the game model into non-linear integer programming model, which can be easily solved by a dynamic programming method. However, with the increase in the number of retailers and the production capacity of manufacturers, the computational complexity of dynamic programming drastically increases due to the Dimension Barrier. Therefore, the Fast Fourier Transform (FFT) approach is introduced, which significantly reduces the computational complexity of solving the supply chain model.

scholarly journals Initializing the EM Algorithm for Univariate Gaussian, Multi-Component, Heteroscedastic Mixture Models by Dynamic Programming Partitions

2018 ◽  
Vol 15 (03) ◽  
pp. 1850012 ◽  
Author(s):  
Andrzej Polanski ◽  
Michal Marczyk ◽  
Monika Pietrowska ◽  
Piotr Widlak ◽  
Joanna Polanska
Keyword(s):  
Dynamic Programming ◽  
Mixture Models ◽  
Recursive Algorithm ◽  
Dynamic Programming Method ◽  
Mixture Distributions ◽  
Gaussian Mixtures ◽  
Scoring Functions ◽  
Initial Values ◽  
The Em Algorithm

Setting initial values of parameters of mixture distributions estimated by using the EM recursive algorithm is very important to the overall quality of estimation. None of the existing methods are suitable for heteroscedastic mixtures with a large number of components. We present relevant novel methodology of estimating the initial values of parameters of univariate, heteroscedastic Gaussian mixtures, on the basis of dynamic programming partitioning of the range of observations into bins. We evaluate variants of the dynamic programming method corresponding to different scoring functions for partitioning. We demonstrate the superior efficiency of the proposed method compared to existing techniques for both simulated and real datasets.

scholarly journals Multi-Robot Searching using Game-Theory Based Approach

10.5772/6232 ◽  
2008 ◽  
Vol 5 (4) ◽  
pp. 44 ◽  
Author(s):  
Yan Meng
Keyword(s):  
Game Theory ◽  
Dynamic Programming ◽  
Utility Function ◽  
Real Time ◽  
Dynamic Environment ◽  
Equilibrium Solutions ◽  
Strategy Equilibrium ◽  
The Game Theory ◽  
Target Searching ◽  
Multi Robot

This paper proposes a game-theory based approach in a multi–target searching using a multi-robot system in a dynamic environment. It is assumed that a rough priori probability map of the targets' distribution within the environment is given. To consider the interaction between the robots, a dynamic-programming equation is proposed to estimate the utility function for each robot. Based on this utility function, a cooperative nonzero-sum game is generated, where both pure Nash Equilibrium and mixed-strategy Equilibrium solutions are presented to achieve an optimal overall robot behaviors. A special consideration has been taken to improve the real-time performance of the game-theory based approach. Several mechanisms, such as event-driven discretization, one-step dynamic programming, and decision buffer, have been proposed to reduce the computational complexity. The main advantage of the algorithm lies in its real-time capabilities whilst being efficient and robust to dynamic environments.

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