A dynamic method for the production lot sizing with machine failures

This paper presents a dynamic method to deal with two economic lot sizing models with exponential machine failures. Its main difference from the static method is that the machine failure is separately treated from the perspective of failure realisation. The optimal lot size is derived through the equation between the incurred average cost and the marginal cost, which has to be performed for each lot due to the random failures. In the first no-resumption model, the simulation shows that two methods have the similar performance as the lot number increases. For the resumable model, we propose a zero-inventory resumption policy that always resumes the production after each machine failure but delays the resumption until the on-hand inventory is depleted. The simulation result indicates that the new policy by the dynamic method outperforms the initial abort/resume policy, and it also shows the convergence as the production continues.