DOI: https://doi.org/10.15588/1607-3274-2018-3-7

### TWO METHODS FOR CONSTRUCTION OF SUBOPTIMISTIC AND SUBPESSIMISTIC SOLUTIONS OF THE INTERVAL PROBLEM OF MIXED-BOOLEAN PROGRAMMING

К. Sh. Mamedov, N. O. Mammadli

#### Abstract

Context. The interval problem of mixed Boolean programming having numerous economic applications is considered. The
object of the study was a model of the integer programming.
Objective. Development of methods for constructing suboptimistic and subpessimistic solutions of the mixed Boolean
programming interval problem. Two methods for constructing suboptimistic and subpessimistic solutions of mixed Boolean programming problems with interval initial data are introduced. These methods are based on some economic interpretation of the model considered.
Method. Two methods for constructing suboptimistic and subpessimistic solutions of mixed Boolean programming problems
with interval initial data are introduced. These methods are based on some economic interpretation of the considered model. In the
first method a criterion of selecting unknowns for assigning values, which is based on the principle of profit maximum for each unit
of expenditure is introduced. Since the coefficients of the problem are intervals, two strategies are chosen: optimistic and pessimistic.
In the optimistic strategy, the idea of choosing unknowns is used, which corresponds to the maximum ratio of the corresponding
maximum profit to the minimum expenditure. And in the pessimistic strategy, the idea of maximum ratio of the minimum profit to
the maximum expenditure is used. In the second method, the concept of a non-linearly increasing penalty (price) for using a unit of
the remaining resources is introduced, that on the right side is bounded. Taking into account the principles of the above first and
second methods, using this concept of penalty (price), methods for constructing suboptimistic and subpessimistic solutions have been
developed.
Results. The algorithms for constructing suboptimistic and subpessimistic solutions to the interval problem of mixed Boolean
programming are developed.
Conclusions. A software package was developed for constructing suboptimistic and subpessimistic solutions to the interval problem
of mixed Boolean programming. A number of computational experiments have been carried out over random problems of various
dimensions.

#### Keywords

an interval problem of mixed Boolean programming; optimistic; pessimistic; sub-optimistic and sub-pessimistic solutions; upper and lower bounds; errors; experiments.

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