Optimal control of a stochastic production-inventory model with deteriorating items

This paper considers a stochastic optimal control of an inventory model with a deterministic rate of deteriorating items. The dynamics of the inventory model includes a perturbation by a Wiener process. The paper uses Hamilton–Jacobi–Bellman principle to find a nonlinear partial differential equation that the value function must satisfy. The partial differential equation is solved by assuming a particular form for the solution and finding three functions Q(t), M(t), and R(t) of time by substituting the assumed solution form back in the partial differential equation. The paper then proceeds to find the optimal expected production rate and the optimal expected inventory level. The paper discusses some special cases for specific parameter values and provides some numerical examples.