title: ÐÐ¾Ð´ÐµÐ»Ð¸ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾ Ð½Ð°Ð·Ð½Ð°ÑÐµÐ½Ð¸ÑÑ Ð¸ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ ÐµÐµ ÑÐµÑÐµÐ½Ð¸Ñ Ð´Ð»Ñ Ð½Ð¾Ð²Ð¾Ð³Ð¾ Ð¿Ð¾Ð´Ñ Ð¾Ð´Ð° ÑÐµÑÑÑÑÐ½Ð¾Ð³Ð¾ Ð¿Ð»Ð°Ð½Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Models of the assignment problem and algorithms for its solution for a new approach to resource planning
Creators: name: Ð£Ð»ÑÑÐ½Ð¾Ð², ÐÐ¼Ð¸ÑÑÐ¸Ð¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2025
Subjects: ÑÐµÑÑÑÑÐ½Ð¾Ðµ Ð¿Ð»Ð°Ð½Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð·Ð°Ð´Ð°ÑÐ° Ð¾ Ð½Ð°Ð·Ð½Ð°ÑÐµÐ½Ð¸ÑÑ
Ð¿Ð»Ð°Ð½Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÑÑÐ´Ð¾Ð²ÑÑ ÑÐµÑÑÑÑÐ¾Ð²
Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸Ð·Ð°ÑÐ¸Ñ
resource planning
appointment problem
labor resource planning
automation

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¿ÑÐ¾Ð±Ð»ÐµÐ¼Ð°ÑÐ¸ÐºÐµ Ð¿ÑÐ¾ÑÐµÑÑÐ° Ð¿Ð»Ð°Ð½Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÑÐ´Ð¾Ð²ÑÑ ÑÐµÑÑÑÑÐ¾Ð², Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÐµÐ¹ ÐµÐ³Ð¾ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸ÐµÐ¼ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¾Ð½Ð½ÑÑ ÑÐ¸ÑÑÐµÐ¼ Ð¸ Ð²Ð½ÐµÐ´ÑÐµÐ½Ð¸ÐµÐ¼ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð°Ð¿Ð¿Ð°ÑÐ°ÑÐ°, Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑÐµÐ³Ð¾ Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸ Ð½Ð°Ð·Ð½Ð°ÑÐ°ÑÑ ÑÐ¾ÑÑÑÐ´Ð½Ð¸ÐºÐ¾Ð² Ð½Ð° Ð·Ð°Ð´Ð°ÑÐ¸. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1) Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ðµ Ð½Ð¾Ð²Ð¾Ð³Ð¾ Ð¿Ð¾Ð´ÑÐ¾Ð´Ð° Ðº Ð¿Ð»Ð°Ð½Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÑÐ´Ð¾Ð²ÑÑ ÑÐµÑÑÑÑÐ¾Ð²; 2) ÑÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾ Ð½Ð°Ð·Ð½Ð°ÑÐµÐ½Ð¸ÑÑ Ð¸ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐµÑÐµÐ½Ð¸Ñ ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¸ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ Ð·Ð°Ð´Ð°Ñ Ð¾ Ð½Ð°Ð·Ð½Ð°ÑÐµÐ½Ð¸ÑÑ; 3) ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° ÑÐµÑÐµÐ½Ð¸Ñ Ð´Ð»Ñ Ð²ÑÐ±ÑÐ°Ð½Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾ Ð½Ð°Ð·Ð½Ð°ÑÐµÐ½Ð¸ÑÑ, ÐµÐ³Ð¾ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÑ ÑÑÐµÐ´ÑÑÐ²; 4) ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° ÐºÐ¾Ð½ÑÐµÐ¿ÑÐ¸Ð¸ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ Ð´Ð»Ñ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ ÑÑÑÐ´Ð¾Ð²ÑÐ¼Ð¸ ÑÐµÑÑÑÑÐ°Ð¼Ð¸, Ð² ÐºÐ¾ÑÐ¾ÑÑÑ Ð±ÑÐ´ÐµÑ Ð²ÑÑÑÐ¾ÐµÐ½Ð¾ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½Ð¾Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ. Ð Ð°Ð±Ð¾ÑÐ° Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð° Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐµÐ°Ð»ÑÐ½ÑÑ Ð·Ð°Ð´Ð°Ñ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ, ÑÑÑÐµÑÑÐ²ÑÑÑÐ¸Ñ Ð² ÐºÐ¾Ð¼Ð¿Ð°Ð½Ð¸Ð¸ Ð¸Ð· ÑÑÐµÑÑ Ð¸Ð½ÑÐµÐ»Ð»ÐµÐºÑÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð±Ð¸Ð·Ð½ÐµÑÐ°. ÐÐ¾ Ð²ÑÐµÐ¼Ñ Ð½Ð°Ð¿Ð¸ÑÐ°Ð½Ð¸Ñ ÑÐ°Ð±Ð¾ÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð»Ð¸ÑÑ ÑÐ¸Ð½ÑÐµÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð´Ð°Ð½Ð½ÑÐµ, ÐºÐ¾ÑÐ¾ÑÑÐµ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸ÑÑ Ð´Ð»Ñ Ð±Ð¾Ð»ÑÑÐ¸Ð½ÑÑÐ²Ð° ÐºÐ¾Ð¼Ð¿Ð°Ð½Ð¸Ð¹, Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÑÑÐ¸Ñ Ð¸Ð½ÑÐµÐ»Ð»ÐµÐºÑÑÐ°Ð»ÑÐ½ÑÐµ ÑÑÐ»ÑÐ³Ð¸. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¿Ð¾Ð´ÑÐ¾Ð±Ð½Ð¾ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð° Ð¿ÑÐ¾Ð±Ð»ÐµÐ¼Ð°ÑÐ¸ÐºÐ° Ð¿ÑÐ¾ÑÐµÑÑÐ° Ð¿Ð»Ð°Ð½Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÑÐ´Ð¾Ð²ÑÑ ÑÐµÑÑÑÑÐ¾Ð², Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÐ¹ Ð²Ð°ÑÐ¸Ð°Ð½Ñ Ð±Ð¸Ð·Ð½ÐµÑ-Ð¿ÑÐ¾ÑÐµÑÑÐ° ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÐ¾ÑÑÑÐ´Ð½Ð¸ÐºÐ¾Ð² Ð¼ÐµÐ¶Ð´Ñ Ð·Ð°Ð´Ð°ÑÐ°Ð¼Ð¸ Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸ÐµÐ¼ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ, ÑÐ°ÑÑÐ¸ÑÐ½Ð¾ Ð²ÐºÐ»ÑÑÐ°ÑÑÐµÐ¹ Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð½Ð°Ð·Ð½Ð°ÑÐµÐ½Ð¸Ðµ ÑÐ¾ÑÑÑÐ´Ð½Ð¸ÐºÐ¾Ð² Ð½Ð° Ð·Ð°Ð´Ð°ÑÐ¸. ÐÐ»Ñ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ ÑÐ°ÐºÐ¾Ð³Ð¾ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð¿ÑÐ¾Ð²ÐµÐ´ÑÐ½ ÑÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾ Ð½Ð°Ð·Ð½Ð°ÑÐµÐ½Ð¸ÑÑ. ÐÐ°Ð¸Ð±Ð¾Ð»ÐµÐµ Ð¿Ð¾Ð´ÑÐ¾Ð´ÑÑÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð°, Ð¸ Ð´Ð»Ñ ÐµÑ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼. Ð ÐµÑÐµÐ½Ð¸Ðµ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾ Ð½Ð°Ð·Ð½Ð°ÑÐµÐ½Ð¸ÑÑ ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ð¾ Ð½Ð° ÑÐ·ÑÐºÐµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Python Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸ÐµÐ¼ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸ PuLP. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÐ°Ð±Ð¾ÑÑ Ð¼Ð¾Ð³ÑÑ Ð±ÑÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ñ Ð´Ð»Ñ Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð½Ð°Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ ÑÐ¾ÑÑÑÐ´Ð½Ð¸ÐºÐ¾Ð² Ð½Ð° Ð·Ð°Ð´Ð°ÑÐ¸.
description: This work is devoted to the problems of the process of planning labor resources, the possibilities of its optimization using information systems, and the introduction of a mathematical apparatus that allows to automatically assign employees to tasks. The research set the following goals: 1) description of a new approach to planning labor resources; 2) comparative analysis of assignment problem models, and methods for solving classical and modified assignment problems; 3) development of an algorithm for solving the assignment problem for the selected model, its implementation using software development tools; 4) development of the concept of an information system for human resource management, into which the developed software solution will be embedded. The work was carried on the basis of real management tasks existing in the company from the field of intellectual business. During the writing of the work, synthetic data were used that can be applied to most companies providing intellectual services. The work describes in detail the problems of the workforce planning process, proposes an optimized version of the business process for allocating employees between tasks using an information system that partially includes automatic assignment of employees to tasks. To implement such an algorithm, a comparative analysis of assignment problem models was carried out. The most suitable model has been modified, and an algorithm has been developed to implement it. The solution to the modified assignment problem is implemented in the Python programming language using the PuLP library. The results of the work can be used for automatically assignment employees to tasks.