Abstract
In practice, there are often problems, which must simultaneously optimize several criterias. This so-called multi-objective optimization problem. In the article we consider the use of the method ideal point to solve the two-objective optimization problem of production planning. The process of finding solution to the problem consists of a series of steps where using simplex method, we find the ideal point. After that for solving a scalar problems, we use the method of Lagrange multipliers
Highlights
When solving various problems in economics, social sphere, information technologies, etc. the decision often needs to be made under certainty, uncertainty and conflict circumstances
To solve the problem (1)–(4), let us use the method of ideal point [1, 3]
Aij x j bi, i 1, 2,..., m, j 1 if x j 0, j 1, 2,..., n, where a (a1, a2 ) is the ideal point, which is defined as follows: n a1 max p j x j, j 1 n a2 max rj x j j 1 on the set that is defined by the irregularities (3), (4)
Summary
Varnaliy Zahariy, Doctor of Economics Sciences, Professor, Department of Finance, Taras Shevchenko National University of Kyiv, Vasilkovskaya str., 60, Kyiv, Ukraine, 01033. Onyshchenko Svitlana, Candidate of Economic Sciences, Associate Professor, Department of Finance and Banking, Poltava National Technical Yuri Kondratyuk University, Pershotravnevyi ave., 24, Poltava, Ukraine, 36000. Technical Yuri Kondratyuk University, Pershotravnevyi ave., 24, Poltava, Ukraine, 36000. There are often problems, which must simultaneously optimize several criterias. In the article we consider the use of the method ideal point to solve the twoobjective optimization problem of production planning. Ми застосовуємо методу ідеальної точки для розв’язання двокритеріальної задачі планування виробництва. Розв’язок задачі складається з двох кроків, де за допомогою симплексного методу знаходимо ідеальну точку, а для розв’язування скаляризованої задачі, використовуємо метод множників Лагранжа. Ключові слова: метод ідеальної точки, двокритеріальна задача, скаляризована задача, метод множників Лагранжа
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