A Markov–modulated deteriorating inventory model with price–dependent demand: optimal markdown and cycle policies
摘要
This paper develops a Markov–modulated deteriorating inventory model with price–dependent demand, where both demand intensity and deterioration dynamics evolve according to a stochastic environment modeled by a continuous–time Markov chain. Unlike classical deterministic formulations, the proposed framework captures random fluctuations in market conditions and storage quality, allowing a more realistic representation of inventory systems for perishable and time–sensitive products. A finite replenishment cycle with an endogenous markdown policy is considered, and the expected inventory dynamics are described through a coupled system of differential equations driven by the Markovian environment. Based on this structure, an explicit expected average total profit function is constructed and optimized with respect to the markdown time and the replenishment cycle length. Due to the analytical intractability of the resulting objective function, global optimization methods are employed. A detailed numerical study for a two–state environment shows that pricing and replenishment decisions jointly determine the structure of the optimal policy. The results emphasize that higher selling prices lead to delayed markdowns and longer replenishment cycles, while increased deterioration intensities significantly shorten optimal cycles and reduce profitability. In contrast, cost parameters primarily shift the profit level without substantially affecting the optimal policy. These findings highlight the dominant role of revenue–driven decisions and stochastic environmental effects in shaping optimal inventory strategies for deteriorating items.