scholarly journals THE OPTIMAL PRINCIPLE OF BELLMAN IN THE PROBLEM OF OPTIMAL MEANS DISTRIBUTION BETWEEN ENTERPRISES FOR THE EXPANSION OF PRODUCTION

2019 ◽  
pp. 132-138 ◽  
Author(s):  
A. Tarasenko ◽  
I. Egorova
Keyword(s):  
Dynamic Programming ◽  
Nonlinear Programming ◽  
Optimal Solution ◽  
Optimal Distribution ◽  
Optimality Principle ◽  
Numerical Example ◽  
Maximum Profit ◽  
Cost Forecasting ◽  
Method Of Dynamic Programming ◽  
Minimum Costs

The method of dynamic programming has been considered, which is used in solving multiple problems in economics, on the example of using Bellman’s optimality principle for solving nonlinear programming problems. On a specific numerical example, the features of the solution have been shown in detail with all the calculations. The problem of optimal distribution of funds among enterprises for the expansion of production has been formulated, which would give the maximum total increase in output. The solution of the task has been presented in the case, when the number of enterprises is 3. It has been shown, that the Bellman optimality principle allows you solve applied problems of cost forecasting with obtaining the optimal solution-maximum profit at minimum costs.

scholarly journals Hierarchic Optimization of Resource the Resources Allocation among the Units of Aviation Company

2018 ◽  
Vol 6 (1) ◽  
pp. 22-29
Author(s):  
Olga Girvica
Keyword(s):  
Dynamic Programming ◽  
Programming Language ◽  
Resource Distribution ◽  
Limited Resource ◽  
Resources Allocation ◽  
Special Program ◽  
The Real ◽  
Maximum Profit ◽  
Optimal Resource ◽  
Method Of Dynamic Programming

Abstract This paper deals with the problem of optimal resource distribution in optimal way among the units of an aviation company. This task could be solved by using the method of dynamic programming. Using Mathcad 14 programming language, there was created a special program that allows to make corresponding calculations. The solution of the real task for an aviation company is observed in this paper as a numerical sample of limited resource distribution between the units of the company in order to get the maximum profit.

scholarly journals One task of routing jobs in high radiation conditions

2021 ◽  
Vol 58 ◽  
pp. 94-126
Author(s):  
A.G. Chentsov ◽  
A.A. Chentsov ◽  
A.N. Sesekin
Keyword(s):  
Dynamic Programming ◽  
Numerical Solution ◽  
Model Problem ◽  
Optimal Solution ◽  
High Radiation ◽  
Dose Load ◽  
Route Problem ◽  
Precedence Conditions ◽  
Sequential Bypass ◽  
Radiation Conditions

The problem of sequential bypass of megalopolises is investigated, focused on the problem of dismantling a system of radiation hazardous objects under constraints in the form of precedence conditions. The radiation impact on the performers is assessed by the doses received during movements and during the performance of dismantling works. The route problem of minimizing the dose load of workers carrying out dismantling in one or another sequence of operations is considered. The procedure for constructing an optimal solution using a variant of dynamic programming is investigated. On this basis, an algorithm is built, implemented on a PC. Examples of the numerical solution of a model problem for the minimum dose load are given.

Optimizing Series Repairable Systems with Imperfect Repair

2013 ◽  
pp. 83-93
Author(s):  
Mohammed Hajeeh
Keyword(s):  
Mathematical Model ◽  
Closed Form ◽  
Optimal Solution ◽  
Closed Form Expression ◽  
Repairable Systems ◽  
Nonlinear Mathematical Model ◽  
Repair Rate ◽  
Imperfect Repair ◽  
Repair Models ◽  
Minimum Costs

Repairable systems are either repaired perfectly to a state of as good as new or imperfectly. In this work, a system which undergoes imperfect repair is investigated. A nonlinear mathematical model is formulated for a system with the objective of finding the optimum failure and repair rate with the minimum costs subject to attaining a pre-specified performance level. Two imperfect repair models are examined. In the first model, the system is replaced by a new one after several failures. In the second model, the system is either replaced with a specific probability (1-p) or is imperfectly repaired after each failure with probability p. The optimal solution is presented in a closed form expression.

A Production Planning Model for Make-To-Order Companies with Capacity Constraint

2011 ◽  
Vol 201-203 ◽  
pp. 1066-1069 ◽  
Author(s):  
Hua Li Gao ◽  
Bin Dan ◽  
You Guo Jing
Keyword(s):  
Decision Making ◽  
Production Planning ◽  
Production Systems ◽  
Optimal Solution ◽  
Capacity Constraint ◽  
Planning Model ◽  
Numerical Example ◽  
Make To Order ◽  
Decision Making Model

This paper proposes a decision-making model of the planning quantity put into production for Make-To-Order (MTO) companies with capacity constraint. The low repeatability and the uncertain products eligibility-rate of the MTO production systems are fully taken into account, and an optimal solution is presented. Finally, a numerical example is given to illustrate the validity of the model.

An Optimal Power Management Strategy for Hydraulic Hybrid Output Coupled Power-Split Transmission

2009 ◽  
Author(s):  
Rajneesh Kumar ◽  
Monika Ivantysynova
Keyword(s):  
Dynamic Programming ◽  
Power Management ◽  
Control Strategy ◽  
Management Strategy ◽  
Optimal Solution ◽  
Programming Approach ◽  
Power Management Strategy ◽  
Optimal Power ◽  
Power Split ◽  
Instantaneous Optimization

Power-split drive represents a class of Continuously Variable Transmission (CVT) that combines the convenience of CVT with the high overall transmission efficiency. In its hybrid configuration, a high pressure accumulator is used to capture the braking energy that is regenerated to aid the engine power during the next propulsion event. Output coupled power split drives are particularly suited for small and medium duty vehicle applications. In this work, optimal power management strategy has been designed based on Dynamic Programming approach. Although the control strategy obtained by Dynamic Programming is non-causal, it represents the benchmark solution against which other implementable power management schemes can be compared. Another control strategy based on instantaneous optimization is also discussed where a given cost function is minimized at every instant. It results in a sub-optimal solution that is practical and implementable. Finally, Dynamic Programming results are utilized to discuss the possible improvements that can be made to the instantaneous optimization based control strategy.

scholarly journals Dynamic Programming and Hamilton–Jacobi–Bellman Equations on Time Scales

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yingjun Zhu ◽  
Guangyan Jia
Keyword(s):  
Dynamic Programming ◽  
Dynamic System ◽  
Time Scales ◽  
Discrete Time ◽  
Continuous Time ◽  
Stochastic Dynamic ◽  
Optimality Principle ◽  
Bellman Equations ◽  
Special Cases ◽  
Hamilton Jacobi Bellman

Bellman optimality principle for the stochastic dynamic system on time scales is derived, which includes the continuous time and discrete time as special cases. At the same time, the Hamilton–Jacobi–Bellman (HJB) equation on time scales is obtained. Finally, an example is employed to illustrate our main results.

Analysis of a two-dimensional stair-case warranty policy with preventive maintenance

2020 ◽  
Vol 32 (1) ◽  
pp. 51-67
Author(s):  
Jinting Wang ◽  
Sheng Zhu ◽  
Simiao Du
Keyword(s):  
Mathematical Model ◽  
Preventive Maintenance ◽  
Optimal Strategy ◽  
Optimal Solution ◽  
Two Dimensional ◽  
Rectangular Region ◽  
Numerical Example ◽  
Warranty Cost

Abstract We develop a mathematical model to study optimal preventive maintenance (PM) strategy under a two-dimensional stair-case warranty policy considering both age and usage of a product. During the warranty term, sellers implement preventive maintenance within the stair-case region of the warranty policy and upon failure a product is repaired minimally and immediately. Our objective is to find the optimal PM strategy that minimizes the seller’s cost of warranty while jointly considering the age and usage intervals of the PM policy and the level of PM executed. We also discuss how our results compare to those in a two-dimensional warranty policy with a rectangular region, and we find that the stair-case policy is preferable for sellers. An algorithm is provided to find the optimal solution and a numerical example is presented to illustrate how to find an optimal strategy with our proposed method. We show numerically that the expected total warranty cost is convex both in the age and the usage of the product under certain conditions.

scholarly journals Modified Dynamic Programming Algorithm and Its Application in Distribution of Power Plant Load

2019 ◽  
Vol 136 ◽  
pp. 01005
Author(s):  
Wanshan Wang ◽  
Peihong Wang ◽  
Yihua Dong
Keyword(s):  
Dynamic Programming ◽  
Power Plant ◽  
Thermal Power ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Step Size ◽  
Long Time ◽  
Distribution Of Power ◽  
Method Of Dynamic Programming ◽  
Method Show

Dynamic programming algorithm is the classic method in distribution of plant loads. The traditional calculation method of dynamic programming is easy to make the calculation take too long time. This paper proposes two modiefied methods of dynamic programming, namely, dynamic programming in progressive structure and dynamic programming in progressive step-size. What is more, these two methods are combined to a new hybrid method. And these three methods and conventional dynamic programming are applied to the distribution of thermal power plant load to verify. The results of modiefied methods contrast with the conventional method show the modiefied methods reduce the calculation time and alleviate the curse of dimensionality effectively, ensuring the accuracy of calculation.

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