A Stochastic Deteriorated Single Product Inventory System Sustaining in Heterogeneous Environments with Restricted Compulsory Waiting Period in reordering

Abstract Environmental influence on replenishing items in the inventory management within supply chain management is a more challenging, crucial and practical study, which is offering valuable recommendations for investors, suppliers, and retailers in the diverged economic market spectrum. The contribution of this article is as follows: the article delves for the study of dynamics of a stochastic perishable product inventory system which fluctuates in two distinct environments, incorporating a compulsory waiting period (CWP) while replenishing items. The CWP initiates immediately after each replenishment and extends for a random duration which follows an exponential distribution. The system waits for CWP to expire, even if the inventory becomes depleted due to demand or item deterioration. Variable demands occur in each environment, independently following which are following Poisson distributions. The maximum capacity of the inventory system is S units. The system evolves in two different environments, with the duration of stay in each environment being a random variable following an exponential distribution. The perishability rate of items in each environment are independent and exponentially distributed. The study identifies three-state stochastic processes, forming a discrete state Markov chain, and derives steady-state probabilities, average total cost, and profit. Additionally, various performance metrics are identified and evaluated, including the mean number of items in the inventory, mean number of demands satisfied events, mean number of replenishment events, mean number of deterioration events, mean number of lost demands in the environments one and two, mean number of times the system switches between environments, and mean number of times the system fluctuates between CWP and Non-CWP. Conducting sensitivity analysis alongside a numerical illustration reveals the impact of environmental influences, restricted CWP, demand rates, and deterioration rates on arriving at the average profit and cost of the system. In the realm of supply chain management, this article offers guidance to retailers navigating such scenarios, aiding in designing and planning their businesses through informed decision-making processes to achieve desirable profit.