On an Applied Problem of Mixed Programming and an Efficient Algorithm for the Optimal Choice of Alternatives and Resource Management

Abstract

Applied management tasks solved by a subdivision of a light industry enterprise, the main activity of which is the organization of effective planning of clothing production and marketing, are in the article set and formalized. The main problems to be solved in this case were: — selection of an effective assortment from a variety of alternatives and production volumes, based on the structure and size of demand; — determination of the volume of purchases of raw materials and components; — volumes and delivery schedules for the entire assortment list being formed. Substantial and formal formulations of a set of problems of the milp class (mixed linear programming) of choosing the optimal production assortment, taking into account demand factors, restrictions on resources and the structure of the assortment, determining production volumes in dynamics, are given. A decompositional algorithm for searching for optimal solutions to a set of tasks has been developed and implemented in software. The final result of the work is the formation of the best compositions of collections and the dynamics of the volume of commodity production of goods in relation to the enterprise of the garment industry. At the end of the paper, the performance statistics of the program that implements the proposed algorithm for finding optimal solutions to a set of control problems are given, as well as a general assessment of the effectiveness of the developed toolkit on real data.