A production inventory model for deteriorating items in a stochastic production process

A production inventory model is developed for deteriorating items in an uncertain production process. It is assumed that the process is subject to a random imperfection from an in-control state to an out-of-control state with an arbitrary distribution and, thus, produces some proportion of imperfect items. A total cost function based on non-constant deterioration rate and time-varying demand rate is obtained and discussed. A search algorithm which determines an optimal production run length and a minimum total cost is derived. Finally, numerical examples are proposed and sensitivity analysis of the optimal solution is carried out.