Abstract
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.
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