Profitability index maximization in an inventory model with a price- and stock-dependent demand rate in a power-form

Autor: Joaquín Sicilia, David Alcaide-López-de-Pablo, Luis A. San-José, Valentín Pando
Jazyk: angličtina
Rok vydání: 2021
Předmět:
TheoryofComputation_MISCELLANEOUS
Scale (ratio)
Administracion de empresas
General Mathematics
0211 other engineering and technologies
02 engineering and technology
Inventory control - Mathematical models
inventory models
0502 economics and business
Computer Science (miscellaneous)
Econometrics
QA1-939
Sensitivity (control systems)
Gestión de existencias - Modelos matemáticos
Engineering (miscellaneous)
Stock (geology)
Mathematics
021103 operations research
profitability index maximization
12 Matemáticas
05 social sciences
Holding cost
Demanda dependiente del precio y de las existencias
Maximization
Investment (macroeconomics)
Applied mathematics
Price- and stock-dependent demand
Industrial Management
isoelastic price-dependent demand
Gestión de existencias
Profit
Profitability index
Scale parameter
050203 business & management
Zdroj: Mathematics
Volume 9
Issue 10
Mathematics, Vol 9, Iss 1157, p 1157 (2021)
DOI: 10.3390/math9101157
Popis: Producción Científica
This paper presents the optimal policy for an inventory model where the demand rate potentially depends on both selling price and stock level. The goal is the maximization of the profitability index, defined as the ratio income/expense. A numerical algorithm is proposed to calculate the optimal selling price. The optimal values for the depletion time, the cycle time, the maximum profitability index, and the lot size are evaluated from the selling price. The solution shows that the inventory must be replenished when the stock is depleted, i.e., the depletion time is always equal to the cycle time. The optimal policy is obtained with a suitable balance between ordering cost and holding cost. A condition that ensures the profitability of the financial investment in the inventory is established from the initial parameters. Profitability thresholds for several parameters, including the scale and the non-centrality parameters, keeping all the others fixed, are evaluated. The model with an isoelastic price-dependent demand is solved as a particular case. In this last model, all the optimal values are given in a closed form, and a sensitivity analysis is performed for several parameters, including the scale parameter. The results are illustrated with numerical examples.
Ministerio de Ciencia, Innovación y Universidades y Fondo Europeo de Desarrollo Regional (FEDER) - (project MTM2017-84150-P)
Databáze: OpenAIRE