@article{10.11648/j.ajtas.20261505.18,
  author = {Ashish Kumar Routray and Shyam Sundar Sahoo and Swagatika Dehury and Sudhir Kumar Sahu},
  title = {Stochastic Optimal Control of Perishable Inventory Under Demand Uncertainty},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {15},
  number = {5},
  pages = {303-316},
  doi = {10.11648/j.ajtas.20261505.18},
  url = {https://doi.org/10.11648/j.ajtas.20261505.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20261505.18},
  abstract = {The deterministic optimal-control literature on perishable inventory management including the dynamic-pricing, preservation investment, and advertising framework this paper extends assumes that demand evolves along a known, smooth trajectory. Real retail environments violate this assumption: freshness-sensitive demand is buffeted by continuous stochastic fluctuation and by discrete shocks such as viral promotions, weather events, and supply disruptions. This paper develops a continuous-time stochastic optimal control model in which the stock-in-phase inventory process follows a jump diffusion stochastic differential equation combining Brownian demand noise with a compound Poisson jump component, while dynamic pricing, warehousing preservation investment, and advertising remain the retailer's control variables. We derive necessary optimality conditions via a Stochastic Maximum Principle with a backward stochastic adjoint equation, establish a verification theorem linking the adjoint process to the value function of the associated integro-partial differential Hamilton-Jacobi-Bellman (HJB) equation, and show that the linear demand or quadratic-cost structure of the problem reduces the HJB equation to a solvable system of Riccati type ordinary differential equations, yielding closed-form feedback laws for the optimal price and advertising rate. As an independent, non-parametric benchmark, we additionally solve the integro PDE HJB equation via an explicit finite-difference dynamic programming scheme; the two solution methods agree to within 0.03% across the feasible inventory range, cross-validating the analytical reduction. Numerical experiments show that the optimal expected discounted profit is monotonically decreasing in jump intensity and jump severity (pure downside risk from unhedgeable demand shocks) but weakly increasing in diffusion volatility, a consequence of the convexity of the value function in the inventory state an option-like effect specific to the risk-neutral, linear-quadratic stochastic control formulation. Monte-Carlo simulation of 3,000 sample paths confirms that a policy computed under the stochastic formulation reduces downside tail exposure relative to a deterministic-equivalent (risk-naïve) policy under otherwise identical demand realizations. The paper contributes the first stochastic maximum principle treatment of the joint pricing-preservation advertising problem for perishable goods and the first dynamic-programming cross-validation of such a solution in this literature.},
 year = {2026}
}

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TY  - JOUR
T1  - Stochastic Optimal Control of Perishable Inventory Under Demand Uncertainty
AU  - Ashish Kumar Routray
AU  - Shyam Sundar Sahoo
AU  - Swagatika Dehury
AU  - Sudhir Kumar Sahu
Y1  - 2026/10/31
PY  - 2026
N1  - https://doi.org/10.11648/j.ajtas.20261505.18
DO  - 10.11648/j.ajtas.20261505.18
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 303
EP  - 316
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20261505.18
AB  - The deterministic optimal-control literature on perishable inventory management including the dynamic-pricing, preservation investment, and advertising framework this paper extends assumes that demand evolves along a known, smooth trajectory. Real retail environments violate this assumption: freshness-sensitive demand is buffeted by continuous stochastic fluctuation and by discrete shocks such as viral promotions, weather events, and supply disruptions. This paper develops a continuous-time stochastic optimal control model in which the stock-in-phase inventory process follows a jump diffusion stochastic differential equation combining Brownian demand noise with a compound Poisson jump component, while dynamic pricing, warehousing preservation investment, and advertising remain the retailer's control variables. We derive necessary optimality conditions via a Stochastic Maximum Principle with a backward stochastic adjoint equation, establish a verification theorem linking the adjoint process to the value function of the associated integro-partial differential Hamilton-Jacobi-Bellman (HJB) equation, and show that the linear demand or quadratic-cost structure of the problem reduces the HJB equation to a solvable system of Riccati type ordinary differential equations, yielding closed-form feedback laws for the optimal price and advertising rate. As an independent, non-parametric benchmark, we additionally solve the integro PDE HJB equation via an explicit finite-difference dynamic programming scheme; the two solution methods agree to within 0.03% across the feasible inventory range, cross-validating the analytical reduction. Numerical experiments show that the optimal expected discounted profit is monotonically decreasing in jump intensity and jump severity (pure downside risk from unhedgeable demand shocks) but weakly increasing in diffusion volatility, a consequence of the convexity of the value function in the inventory state an option-like effect specific to the risk-neutral, linear-quadratic stochastic control formulation. Monte-Carlo simulation of 3,000 sample paths confirms that a policy computed under the stochastic formulation reduces downside tail exposure relative to a deterministic-equivalent (risk-naïve) policy under otherwise identical demand realizations. The paper contributes the first stochastic maximum principle treatment of the joint pricing-preservation advertising problem for perishable goods and the first dynamic-programming cross-validation of such a solution in this literature.
VL  - 15
IS  - 5
ER  - 

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