A markovian model for economic production lot size of a process with imperfect production and machine failures

In this paper, a single-machine single-product manufacturing system is considered;the system is assumed to operate under constant production rate that exceeds customerdemand rate, customer demand rate is constant and certain. The machine is not perfectand is prone to failure, upon which it needs repair. The machine is also not perfectlyefficient and it manufactures non-confirming and imperfect items. The possibility offailure and imperfect production are combined and modeled into a single model. Themachine times-to-failure, the repair time, and the item manufactured being nonconfirmingare random. When the machine is under repair, the demand is backordered tilla maximum backorder level is reached and after that the demand is considered to be lost.The state of the system changes in discrete time and the process is modeled as aMarkov chain which is used to find the cost model. The Economic ManufacturingQuantity of a machine which is prone to failure and also may manufacture nonconfirmingitems is derived. Modeling the process in a Markov chain is very beneficial inincorporating backorders and failures into the process.The results clearly indicate that the total cost is convex with respect to the maximuminventory and the total cost increases when the probability for the machine not to faildecreases. The results also show that the repair success has an effect on the total cost. The total cost is higher when the probability of repair success is low than when the probabilityis high.