RT info:eu-repo/semantics/article
T1 Profitability index maximization in an inventory model with a price- and stock-dependent demand rate in a power-form
A1 Pando Fernández, Valentín
A1 San José Nieto, Luis Augusto
A1 Sicilia Rodríguez, Joaquín
A1 Alcaide López de Pablo, David
K1 Inventory control - Mathematical models
K1 Gestión de existencias - Modelos matemáticos
K1 Gestión de existencias
K1 Industrial Management
K1 Administracion de empresas
K1 Profit
K1 Applied mathematics
K1 Price- and stock-dependent demand
K1 Demanda dependiente del precio y de las existencias
K1 12 Matemáticas
AB 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.
PB MDPI
SN 2227-7390
YR 2021
FD 2021
LK https://uvadoc.uva.es/handle/10324/59733
UL https://uvadoc.uva.es/handle/10324/59733
LA eng
NO Mathematics, 2021, Vol. 9, Nº. 10, 1157
NO Producción Científica
DS UVaDOC
RD 15-jun-2024