Stochastic inventory model for imperfect production processes

Production/inventory decisions for imperfect production process are considered in this paper. The process is in the in‐of‐control state when it starts a production run. However, it may shift to the out‐of‐control state at any point in time during the production cycle. The time until the shift from the in‐control state to the out‐of‐control state is modelled by a Weibull random variable with increasing hazard. It is assumed that when the process is in the out‐control state, it stays in that state until the next setup where it is brought to as‐good‐as new conditions. While in the out‐of‐control state, the process produces a fixed fraction on non‐conforming items which are scrapped with no salvage value. Unlike the existing models in the literature, the demand is stochastic and is modelled by a normal probability distribution. Two cases are considered, the first of which is for a predetermined service level case. The other case is when the service level is a decision variable. The cost function is developed and minimised to find the optimal lot size using a simple and efficient algorithm.