# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2021036

## Inventory replenishment policies for two successive generations price-sensitive technology products

 1 Department of Management Studies, BITS Pilani, Pilani Campus, Rajasthan, India 2 Department of Management Studies and Department of Mathematics, BITS Pilani, Pilani Campus, Rajasthan, India

* Corresponding author: Gaurav Nagpal

Received  May 2020 Revised  November 2020 Published  March 2021

The high technology products come in generations, where the demand for newer technology generations is strongly influenced by the installed base of earlier generations (such as computers, cameras, notebooks, etc). However, the effect of technology substitution on inventory replenishment policies has received little attention in the supply chain literature. In the hi-technology market, consumers' purchasing capability, the utility of a product along with the entry of the advanced generation product influence the market expansion/contraction of the products. In this study, the impact of parallel diffusion of two successive generations' products on inventory policies of the monopolist has been analysed. The demand models have been characterised by considering the life-cycle dynamics for a P-type inventory system. The purpose of this paper is to develop a model for joint pricing and replenishment of technology generation products. The model has been solved by using a genetic algorithm technique. The impact of yearly price drop and the price sensitivity of demand on the profit margins vis-à-vis on replenishment policies has also been studied. The paper also brings forward the dynamics of the launch of newer generations and the pricing strategies on optimal inventory replenishment policies. Numerical illustrations have also been covered in the paper.

Citation: Gaurav Nagpal, Udayan Chanda, Nitant Upasani. Inventory replenishment policies for two successive generations price-sensitive technology products. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021036
##### References:

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##### References:
The behavior of the price of the technology products with the time elapsed after the launch for different values of annual % price drop "$\Upsilon$"
The P Model of inventory management before the launch of the second generation
The P Model of inventory management in the $m^{th}$ planning horizon with $n$ replenishments before the launch of first-generation
Influence of diffusion rate of second generation product on phase-out timing of 1st generation
Influence of price elasticity of demand on the diffusion pattern and revenues
Tabular review of existing literature on multi-item inventory modeling under price-dependent demand
Optimal number of replenishments ($n_1$ and $n_2$, both of them, say equal n, ) in pooled logistics determined by minimizing the sum of holding cost and carrying costs for each planning horizon (All the costs are in Mn INR)
Total Revenue, Profits and Opportunity Loss for two generations scenario (The Revenue and Profit figure are in Mn INR)
Total Profit values $T{P_{{m^{',{n_1}{n_2}*}}}}$ for different values of yearly price drop % with the change in $\beta$ (The Profit figures are in Mn INR)
Total Profit values $T{P_{{m^{',{n_1}{n_{{2_*}}}}}}}$ for different planning horizons with different values of price sensitivity $\beta$ (The Profit figures are in Mn INR
Comparison of the replenishment dynamics: Joint vs Dis-joint for both the generations of products (The Profit figures are in Mn INR)
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