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Search for a Generalized Solution to an Improper Linear Programming Problem Based on a Dedicated Maximum Feasible Constraints Subsystem.

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Title: Search for a Generalized Solution to an Improper Linear Programming Problem Based on a Dedicated Maximum Feasible Constraints Subsystem.
Authors: Noskov, S. I.1 (AUTHOR) sergey.noskov.57@mail.ru, Pashkov, D. V.1 (AUTHOR) dvp-2000@mail.ru
Source: Theoretical Foundations of Chemical Engineering. Aug2025, Vol. 59 Issue 4, p949-953. 5p.
Subject Terms: *LINEAR programming, *MIXED integer linear programming, *NUMERICAL analysis, *RESOURCE allocation, *CONSTRAINT programming, *CIRCULAR economy, *PETROCHEMICAL manufacturing
Abstract: The paper provides a brief overview of publications in which the study of some complex technical objects is carried out by presenting their mathematical models in the form of mathematical problems, specifically linear programming (LP) problems. In particular, the following are considered: a model of mixed-integer linear programming for optimal planning of multi-plant, multi-delivery, and multi-grade petrochemical production; the problem of minimizing the use of water and wastewater in the production process of the Brazilian petrochemical industry using mass integration through the use of mathematical programming; innovations in petrochemical technologies aimed both at increasing the supply of liquefied natural gas and at solving new problems, including the need for decarbonization and adaptation to the future circular economy; a methodology for optimal short-term planning of integrated oil refining and petrochemical complexes; and spatial organization of the Chinese petrochemical industry. A method is proposed for the generalized solution of an improper linear programming problem in a normal form, in which the system of constraints/inequalities is incompatible. Potential reasons for this incompatibility include errors in the mathematical model itself and its information support, as well as real contradictions of the analyzed object, which are therefore reflected in the model. At the first stage, by solving a sequence of 0-1 mixed-integer linear programming problems, a set of vectors is formed, including the numbers of joint constraints, and at the second stage, by solving linear programming problems for each of these vectors, a generalized solution to the original problem is found, preserving the maximum power of the joint subsystem of constraints. A numerical example containing two variables and ten constraints is solved. [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
Description
Abstract:The paper provides a brief overview of publications in which the study of some complex technical objects is carried out by presenting their mathematical models in the form of mathematical problems, specifically linear programming (LP) problems. In particular, the following are considered: a model of mixed-integer linear programming for optimal planning of multi-plant, multi-delivery, and multi-grade petrochemical production; the problem of minimizing the use of water and wastewater in the production process of the Brazilian petrochemical industry using mass integration through the use of mathematical programming; innovations in petrochemical technologies aimed both at increasing the supply of liquefied natural gas and at solving new problems, including the need for decarbonization and adaptation to the future circular economy; a methodology for optimal short-term planning of integrated oil refining and petrochemical complexes; and spatial organization of the Chinese petrochemical industry. A method is proposed for the generalized solution of an improper linear programming problem in a normal form, in which the system of constraints/inequalities is incompatible. Potential reasons for this incompatibility include errors in the mathematical model itself and its information support, as well as real contradictions of the analyzed object, which are therefore reflected in the model. At the first stage, by solving a sequence of 0-1 mixed-integer linear programming problems, a set of vectors is formed, including the numbers of joint constraints, and at the second stage, by solving linear programming problems for each of these vectors, a generalized solution to the original problem is found, preserving the maximum power of the joint subsystem of constraints. A numerical example containing two variables and ten constraints is solved. [ABSTRACT FROM AUTHOR]
ISSN:00405795
DOI:10.1134/S0040579525602560