The Use of Boundary Values of Variables in Solving Problems of Optimal Production Planning

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Year:
2022
Type of Publication:
Article
Keywords:
Axial Boundary Point, Objective Function, Hyperplane, Tangency Point, Integer, Second Order Surface, Optimal Solution, Suboptimal Solution, Boundary Value, Polyhedral Set
Authors:
A. Shapiro
Journal:
IJISM
Volume:
10
Number:
1
Pages:
11-16
Month:
January
ISSN:
2347-9051
Abstract:
In the problem of optimal production planning, a subset of the vertices of the polyhedron of the conditions of the problem lying on the coordinate axes is distinguished. Surfaces of the second order containing these vertices are considered. The point of tangency between the surface and the hyperplane parallel to the hyperplane of the objective function is taken as a solution to the problem. Also considered are issues related to obtaining an integer solution to the problem. Necessary and sufficient conditions for the variables to be integer are indicated. An algorithm for obtaining a suboptimal integer solution is proposed. The influence of the size of the boundary values of the variables in the optimal solution on the amount of profit is investigated. The factors of a possible increase in profit are indicated.

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