Linear Programming Algorithms for the Deterministic Discrete Dynamic Programming Problem

1972 ◽  
pp. 563-578
Author(s):  
Y. M. I. Dirickx
Keyword(s):  
Dynamic Programming ◽  
Linear Programming ◽  
Programming Problem ◽  
Discrete Dynamic ◽  
Dynamic Programming Problem ◽  
Discrete Dynamic Programming ◽  
Programming Algorithms

scholarly journals Search for all solutions to the dynamic programming problem if their multicriteria estimates coincide

2020 ◽  
Vol 82 (1) ◽  
pp. 398-403
Author(s):  
Y. V. Bugaev ◽  
L. A. Korobova ◽  
I. Y. Shurupova
Keyword(s):  
Dynamic Programming ◽  
Programming Problem ◽  
Optimal Trajectories ◽  
Universal Method ◽  
Original Algorithm ◽  
Discrete Dynamic ◽  
Optimal Paths ◽  
All Solutions ◽  
Dynamic Programming Problem ◽  
Discrete Dynamic Programming

Among the mathematical methods used in economics, a prominent place is occupied by the dynamic programming method, with the help of which the optimal control of multi-stage processes is organized. The disadvantage of this method is the impossibility of calculating all solutions to the problem if their criteria-based estimates coincide. The fact of the existence of several optimal trajectories of a multi-step process may mean that the task is not set correctly, in the sense that the assigned criteria do not fully characterize the system under study. This means that the traditional method of dynamic programming needs to be refined in case of the existence of several optimal trajectories with the same value of the criterion. This article proposes the most general version of such refinement, namely, a multi-criteria numerical scheme is generalized. For a more visual representation of calculations and the result of the study, we will describe the discrete dynamic programming problem in terms of graph theory. In this case, it reduces to the problem of finding the optimal path on a directed graph. To solve it, a three-stage algorithm is proposed, the composition of which includes the following steps. The first stage is the construction of optimal criteria estimates for paths from the initial vertex to all the others. To perform this stage, the most universal method is the multicriteria version of the Ford – Bellman method. The second stage is the construction of a graph of optimal paths. In the original graph, arcs are selected that are part of the optimal paths. Of these, using the original algorithm, a subgraph is formed in which all paths are optimal. It is analytically proved that this algorithm gives the correct result (correct). The third stage is enumeration of all paths in the constructed subgraph. Numerical experiments showed that the proposed three-stage method works efficiently on oriented graphs of any type in a sufficiently large range of dimensions. The proposed algorithm with minimal changes can be used to solve an arbitrary discrete dynamic programming problem.

THE CALCULATION OF THE LIFETIME OF THE EQUIPMENT WITH APPLICATION OF DYNAMIC PROGRAMMING

2020 ◽  
Author(s):  
Sergey Ivanovich Makarov ◽  
◽  
Maria Vladimirovna Kurganova ◽  
Keyword(s):  
Dynamic Programming ◽  
Economic Analysis ◽  
Programming Problem ◽  
Calculation Methods ◽  
Optimal Operating ◽  
Operating Period ◽  
Equipment Replacement ◽  
Dynamic Programming Problem ◽  
Replacement Time

The dynamic programming problem for finding the optimal operating period and equipment replacement time using a combination of graphical and calculation methods of economic analysis is considered.

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