title: Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÐ°ÑÑÐµÑÐ° ÑÑÐ¾Ð¸Ð¼Ð¾ÑÑÐ¸ Ð½Ð°Ð»Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð´ÐµÐ½ÐµÐ¶Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÐ°ÑÐµÐ½Ð¸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: Construction of the mathematical model for calculating the cash circulation cost
Creators: name: ÐÐ°Ð±Ð·Ð°Ð»Ð¸Ð»Ð¾Ð², ÐÑÑÑÑ
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: 2021
Subjects: ÑÐ¸ÑÑÐµÐ¼Ð° Ð¼Ð°ÑÑÐ¾Ð²Ð¾Ð³Ð¾ Ð¾Ð±ÑÐ»ÑÐ¶Ð¸Ð²Ð°Ð½Ð¸Ñ
ÑÐ»ÑÑÐ°Ð¹Ð½ÑÐµ Ð¿ÑÐ¾ÑÐµÑÑÑ
Ð¿ÑÐ¾ÑÐµÑÑÑ ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ñ Ð¸ Ð³Ð¸Ð±ÐµÐ»Ð¸
Ð²ÐµÑÐ²ÑÑÐµÐµÑÑ ÑÐ»ÑÑÐ°Ð¹Ð½Ð¾Ðµ Ð±Ð»ÑÐ¶Ð´Ð°Ð½Ð¸Ðµ
Ð½Ð°Ð»Ð¸ÑÐ½Ð¾Ðµ Ð´ÐµÐ½ÐµÐ¶Ð½Ð¾Ðµ Ð¾Ð±ÑÐ°ÑÐµÐ½Ð¸Ðµ
queueing system
random process
birth and death processes
branching random walk
cash circulation

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÐ°ÑÑÐµÑÐ° ÑÑÐ¾Ð¸Ð¼Ð¾ÑÑÐ¸ Ð½Ð°Ð»Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð´ÐµÐ½ÐµÐ¶Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÐ°ÑÐµÐ½Ð¸Ñ. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ: 1. Ð¤Ð¾ÑÐ¼Ð°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð½Ð°Ð»Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð´ÐµÐ½ÐµÐ¶Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÐ°ÑÐµÐ½Ð¸Ñ; 2. ÐÐ¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸; 3. Ð ÐµÑÐµÐ½Ð¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸, ÑÑÐ¾ÑÐ¼ÑÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¹ Ð½Ð° Ð±Ð°Ð·Ðµ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð½Ð¾Ð¹ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¾Ð´Ð½Ð° Ð¸Ð· ÑÐ°Ð·Ð½Ð¾Ð²Ð¸Ð´Ð½Ð¾ÑÑÐµÐ¹ Ð¿ÑÐ¾ÑÐµÑÑÐ¾Ð² ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ñ Ð¸ Ð³Ð¸Ð±ÐµÐ»Ð¸ Ì¶ Ð²ÐµÑÐ²ÑÑÐµÐµÑÑ ÑÐ»ÑÑÐ°Ð¹Ð½Ð¾Ðµ Ð±Ð»ÑÐ¶Ð´Ð°Ð½Ð¸Ðµ Ð¿ÑÐ¸Ð¼ÐµÐ½ÑÐµÑÑÑ Ð´Ð»Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð½Ð°Ð»Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð´ÐµÐ½ÐµÐ¶Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÐ°ÑÐµÐ½Ð¸Ñ. Ð Ð°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ð¾ Ð°ÑÐ¸Ð¼Ð¿ÑÐ¾ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ ÑÑÐµÐ´Ð½ÐµÐ³Ð¾ Ð¾Ð±ÑÐµÐ¼Ð° Ð½Ð°Ð»Ð¸ÑÐ½ÑÑ Ð² Ð¾Ð±Ð¾ÑÐ¾ÑÐµ. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑÑÑÑ ÑÐµÐ°Ð»ÑÐ½ÑÐµ Ð´Ð°Ð½Ð½ÑÐµ, Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÑÑÑÐ¸Ðµ ÑÐ¾Ð±Ð¾Ð¹ ÑÑÐ°ÑÐ¸ÑÑÐ¸ÐºÑ ÑÑÑÑÐºÑÑÑÑ Ð½Ð°Ð»Ð¸ÑÐ½Ð¾Ð¹ Ð´ÐµÐ½ÐµÐ¶Ð½Ð¾Ð¹ Ð¼Ð°ÑÑÑ, Ð° ÑÐ°ÐºÐ¶Ðµ Ð´Ð°Ð½Ð½ÑÐµ Ð¾ ÑÐ°ÑÑÐ¾Ð´Ð°Ñ Ð½Ð° Ð¸Ð½ÐºÐ°ÑÑÐ°ÑÐ¸Ñ Ð½ÐµÐºÐ¾ÑÐ¾ÑÑÑ Ð¾ÑÐ³Ð°Ð½Ð¸Ð·Ð°ÑÐ¸Ð¹. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð±ÑÐ» ÑÐ´ÐµÐ»Ð°Ð½ Ð²ÑÐ²Ð¾Ð´, ÑÑÐ¾ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð²ÐµÑÐ²ÑÑÐµÐ³Ð¾ÑÑ ÑÐ»ÑÑÐ°Ð¹Ð½Ð¾Ð³Ð¾ Ð±Ð»ÑÐ¶Ð´Ð°Ð½Ð¸Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼Ð° Ð´Ð»Ñ ÑÐ°ÑÑÐµÑÐ° ÑÑÐ¾Ð¸Ð¼Ð¾ÑÑÐ¸ Ð½Ð°Ð»Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð´ÐµÐ½ÐµÐ¶Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÐ°ÑÐµÐ½Ð¸Ñ. Ð ÑÐ°ÐºÐ¶Ðµ, Ð±ÑÐ»Ð° Ð½Ð°Ð¹Ð´ÐµÐ½Ð° ÑÐ¾ÑÐ¼ÑÐ»Ð° Ð´Ð»Ñ ÑÐ°ÑÑÐµÑÐ° ÑÐ°ÑÑÐ¾Ð´Ð¾Ð² Ð½Ð° Ð¾Ð±ÑÐ»ÑÐ¶Ð¸Ð²Ð°Ð½Ð¸Ðµ Ð½Ð°Ð»Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð´ÐµÐ½ÐµÐ¶Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÐ°ÑÐµÐ½Ð¸Ñ.
description: This work is devoted to the construction of a mathematical model for calculating the cost of cash circulation. The main research tasks are: 1. Formalization of cash circulation; 2. Construction of the mathematical model; 3. Solution of the formulated problem based on the constructed mathematical model. The present work assumes the use of birth and death processes, specifically it is required to develop a model of cash circulation, using the branching random walk model. The asymptotic behavior of the average amount of cash is considered. The work uses real data, representing statistics on the structure of cash in circulation, as well as data on the costs of collection of some organizations. As a result, it was concluded that the branching random walk model is applicable to calculate the cost of cash circulation. Also, a formula for calculating the cost of cash circulation was found.