OPTIMAL PRODUCTION?SALES STRATEGIES FOR A COMPANY AT CHANGING MARKET PRICE

In this paper we consider a monopoly producing a consumer good of high demand. Its market price depends on the volume of the produced goods described by the Cobb-Douglas production function. A production-sales activity of the firm is modeled by a nonlinear differential equation with two bounded cont...

Full description

Main Authors: Grigorieva, Ellina V., Khailov, Evgenii N.
Format: Artículo
Language: Inglés
Published: 2015
Subjects:
Online Access: http://revistas.ucr.ac.cr/index.php/matematica/article/view/17557
http://hdl.handle.net/10669/13065
id RepoKERWA13065
recordtype dspace
spelling RepoKERWA130652017-08-08T18:50:29Z OPTIMAL PRODUCTION?SALES STRATEGIES FOR A COMPANY AT CHANGING MARKET PRICE ESTRATEGIAS O?PTIMAS DE VENTAS Y PRODUCCIO?N PARA UNA COMPAN?I?A EN UN MERCADO CON PRECIOS CAMBIANTES Grigorieva, Ellina V. Khailov, Evgenii N. modelo de control microecono?mico no lineal estrategia de produccio?n y ventas principio del ma?ximo de Pontryagin sistema hamiltoniano In this paper we consider a monopoly producing a consumer good of high demand. Its market price depends on the volume of the produced goods described by the Cobb-Douglas production function. A production-sales activity of the firm is modeled by a nonlinear differential equation with two bounded controls: the share of the profit obtained from sales that the company reinvests into expanding own production, and the amount of short-term loans taken from a bank for the same purpose. The problem of maximizing discounted total profit on a given time interval is stated and solved. In order to find the optimal production and sales strategies for the company, the Pontryagin maximum principle is used. In order to investigate the arising two-point boundary value problem for the maximum principle, an analysis of the corresponding Hamiltonian system is applied. Based on a qualitative analysis of this system, we found that depending on the initial conditions and parameters of the model, both, singular and bang- bang controls can be optimal. Economic analysis of the optimal solutions is discussed. En este arti?culo consideramos un monopolio produciendo un producto de consumo de gran demanda. Su precio de mercado depende del volumen de produccio?n descrito por la funcio?n de produccio?n de Cobb-Douglas. Una actividad de produccio?n y ventas de la firma es modelada por una ecuacio?n diferencial no lineal con dos controles de frontera: la participacio?n en el resultado de las ventas que la compan?i?a reinvierte para expandir su propia produccio?n, y el monto de los pre?stamos a corto plazo adquiridos del sistema bancario con el mismo propo?sito. Se plantea y resuelve el problema de maximizar la ganancia total descontada en un intervalo de tiempo dado. Para encontrar las estrategias o?ptimas de produccio?n y ventas para la compan?i?a, se usa el principio del ma?ximo de Pontryagin. Para investigar el problema de valores de dos puntos de frontera que aparece para el principio del ma?ximo, se aplica un ana?lisis del sistema hamiltoniano correspondiente. Basado en un ana?lisis cualitativo del sistema, encontramos que dependiendo de las condiciones iniciales y los para?metros del modelo, tanto el control singular como el bang-bang pueden ser o?ptimos. Se discute un ana?lisis econo?mico de las soluciones o?ptimas. 2015-05-19T19:12:58Z 2015-05-19T19:12:58Z 2015-01-01 00:00:00 2015-05-19T19:12:58Z info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://revistas.ucr.ac.cr/index.php/matematica/article/view/17557 http://hdl.handle.net/10669/13065 10.15517/rmta.v22i1.17557 en Revista de Matem?tica: Teor?a y Aplicaciones Vol. 22 N?m. 1 2015 89-112 application/pdf
institution Universidad de Costa Rica
collection Repositorio KERWA
language Inglés
topic modelo de control microecono?mico no lineal
estrategia de produccio?n y ventas
principio del ma?ximo de Pontryagin
sistema hamiltoniano
spellingShingle modelo de control microecono?mico no lineal
estrategia de produccio?n y ventas
principio del ma?ximo de Pontryagin
sistema hamiltoniano
Grigorieva, Ellina V.
Khailov, Evgenii N.
OPTIMAL PRODUCTION?SALES STRATEGIES FOR A COMPANY AT CHANGING MARKET PRICE
description In this paper we consider a monopoly producing a consumer good of high demand. Its market price depends on the volume of the produced goods described by the Cobb-Douglas production function. A production-sales activity of the firm is modeled by a nonlinear differential equation with two bounded controls: the share of the profit obtained from sales that the company reinvests into expanding own production, and the amount of short-term loans taken from a bank for the same purpose. The problem of maximizing discounted total profit on a given time interval is stated and solved. In order to find the optimal production and sales strategies for the company, the Pontryagin maximum principle is used. In order to investigate the arising two-point boundary value problem for the maximum principle, an analysis of the corresponding Hamiltonian system is applied. Based on a qualitative analysis of this system, we found that depending on the initial conditions and parameters of the model, both, singular and bang- bang controls can be optimal. Economic analysis of the optimal solutions is discussed.
format Artículo
author Grigorieva, Ellina V.
Khailov, Evgenii N.
author_sort Grigorieva, Ellina V.
title OPTIMAL PRODUCTION?SALES STRATEGIES FOR A COMPANY AT CHANGING MARKET PRICE
title_short OPTIMAL PRODUCTION?SALES STRATEGIES FOR A COMPANY AT CHANGING MARKET PRICE
title_full OPTIMAL PRODUCTION?SALES STRATEGIES FOR A COMPANY AT CHANGING MARKET PRICE
title_fullStr OPTIMAL PRODUCTION?SALES STRATEGIES FOR A COMPANY AT CHANGING MARKET PRICE
title_full_unstemmed OPTIMAL PRODUCTION?SALES STRATEGIES FOR A COMPANY AT CHANGING MARKET PRICE
title_sort optimal production?sales strategies for a company at changing market price
publishDate 2015
url http://revistas.ucr.ac.cr/index.php/matematica/article/view/17557
http://hdl.handle.net/10669/13065
_version_ 1650733859616063488
score 11.754696