Development Of A Multi-Parameter Inventory Model Incorporating Time-Varying Deterioration And Innovation Adoption Rates

Abstract

In today's highly competitive and innovation-driven market, managing inventory for perishable and technologically evolving products demands dynamic and multi-dimensional modeling approaches. This paper develops a deterministic inventory model that integrates multiple decision parameters, particularly focusing on time-varying deterioration rates and innovation-induced demand behavior. Traditional inventory models fail to account for perishability that evolves over time or demand patterns that shift due to innovation diffusion. This research bridges that gap by formulating a model that incorporates linear and exponential deterioration functions, along with innovation adoption rates governed by Bass-type diffusion behavior.

The model also allows the potential market size to expand in three distinct ways: remaining static, increasing linearly, and growing exponentially. These variations simulate real-world marketing and demographic scenarios. The resulting demand is expressed as a time-dependent function influenced by external marketing efforts (innovation) and market expansion rate.

The total inventory cost function is analytically derived and numerically optimized to determine the optimal cycle time, order quantity, and associated cost. A detailed sensitivity analysis is performed to evaluate the effects of the deterioration coefficient and innovation rate. The study uses computational tools (Python, Excel Solver) to validate the model’s behavior. The results show that higher innovation rates coupled with moderate deterioration lead to shorter replenishment cycles and lower overall costs. Conversely, accelerated deterioration necessitates frequent replenishment and inflates costs.

This work contributes to the advancement of hybrid inventory modeling under realistic and complex demand conditions. It offers practical decision-making support for inventory planners in sectors such as pharmaceuticals, FMCG, agro-products, and high-tech consumer goods.