Optimal lot sizing for an unreliable production system under partial backlogging and at most two failures in a production cycle

The paper considers an economic manufacturing quantity problem for an unreliable manufacturing system where the machine is subject to random failure and at most two failures can occur in a production cycle. Upon first failure, the repair action is started immediately and the demand is met first from the on-hand inventory. The shortages, if occur due to longer repair time, are backlogged partially by resuming the production run after machine repair. While backlogging, if failure occurs again then the accumulated shortages until completion of the second repair are assumed to be lost. The model is formulated under general failure and general repair time distributions. Some characteristics of the model with exponential failure and exponential/constant repair times are studied. The optimal lot sizing policies are derived and the sensitivity of some model parameters is examined with the help of numerical examples.