### International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

###### Dynamic Demand and Pricing Inventory Model for Non-Instantaneous Deteriorating Items

Nita H. Shah
Department of Mathematics, Gujarat University, Ahmedabad-380009, Gujarat, India.

Kavita Rabari
Department of Mathematics, Gujarat University, Ahmedabad-380009, Gujarat, India.

Ekta Patel
Department of Mathematics, Gujarat University, Ahmedabad-380009, Gujarat, India.

;
Accepted on September 12, 2020

Abstract

In this model, an inventory model for deteriorating products with dynamic demand is developed under time-dependent selling price. The selling price is supposed to be a time-dependent function of initial price of the products and the permissible discount rate at the time of deterioration. The object is sold with the constant rate in the absence of deterioration and is the exponential function of discount rate at the time; deterioration takes place. Here, the demand not only dependent on the selling price but also on the cumulative demand that represents the saturation and diffusion effect. First, an inventory model is formulated to characterize the profit function. The Classical optimization algorithm is used to solve the optimization problem. The objective is to maximize the total profit of the retailers with respect to the initial selling price and cycle time. Concavity of the objective function is discussed through graphs. At last, a sensitivity analysis is performed by changing inventory parameters and their impact on the decision variables i.e. (initial price, cycle time) together with the profit function.

Keywords- Dynamic demand rate, Deterioration rate, Time-dependent selling price, Variable holding cost, Discount.

Citation

Shah, N. H., Rabari, K., & Patel, E. (2021). Dynamic Demand and Pricing Inventory Model for Non-Instantaneous Deteriorating Items. International Journal of Mathematical, Engineering and Management Sciences, 6(2), 510-521. https://doi.org/10.33889/IJMEMS.2021.6.2.031.

Conflict of Interest

The authors do not have any conflict of interest.

Acknowledgements

Second author (kavita rabari) is funded by a Junior Research Fellowship from the Council of Scientific & Industrial Research having (file no.-09/070(0067)/2019-EMR-I) and all the authors are thankful to DST-FIST file # MSI-097 for their technical support to the Department of Mathematics, Gujarat University. Ekta Patel would like to extend sincere thanks to the Education Department, Gujarat State for providing scholarship under ScHeme of Developing High quality research.

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