ИСТИНА

In this article, a new practical problem is proposed, as well as algorithms for solving the one-dimensional bin packing problem. The generalization of this problem is one of the most fundamental problems of combinatorial optimization and has been widely studied for decades. Our formulation for this problem takes into account not only the different weights of products and separability but the difference in their types. An objective function is formulated that minimizes the sum of the components with weights responsible for different characteristics of product distribution. Parameter generation of the problem is based on data that approximate the real one. In order to compare the algorithms 168 test instances were generated. In addition they were solved optimally using the Gurobi solver with a time limit of 1 hour. The algorithms proposed are based on the separation of the set of subjects under consideration on the basis of divisibility. Also, the proposed algorithms have been tested on a large family of generated instances with the number of bins from 100 to 1000 ones.