Optimal lot sizing in an unreliable two-stage serial production–inventory system

This paper deals with a two-stage lot sizing problem in an unreliable production environment in which the machine at the first stage (stage 1) is failure-prone while the machine at the final stage (stage 2) is failure-free. The process goods are obtained in batches by manufacturing and are transferred continuously from stage 1 to stage 2 where the finished goods are produced and then shipped out to customers. If the machine at stage 1 breaks down then the production of the interrupted lot is not resumed. Instead, a new production cycle is initiated after machine repair. The model is formulated assuming that the production rate of the machine at stage 1 is greater than that at stage 2 and the time to machine failure and repair time are arbitrarily distributed. Specific formulation of the model under exponential failure and exponential repair time distributions is derived and a procedure for finding the optimal production policy is presented. The dependence of the optimal production policy on the model parameters is also examined with numerical examples.