Discrete time model of a two-station one-buffer serial system with inventory level-dependent operation

The paper deals with the discrete-time discrete-state modeling of two-station one-buffer serial systems in which the condition of the first station (operative/idle) is controlled according to the inventory level of the intermediate buffer. Briefly, the first station is forced to remain idle each time the buffer fills up until it empties to a predefined inventory level (referred to as restarting-inventory level). Previous works have proved that this control policy, called restart policy, is effective when outage costs (e.g., waste production) are generated each time the first station restarts production after an interruption. While the works currently available in the literature assume that the buffer has to become completely empty before allowing the first station to resume production, the proposed paper develops a new analytical Markov model in which the restarting-inventory level can be greater than zero and arbitrarily set in the range 2,N-2, where N is the buffer size. The proposed model is solved in closed form by means of a partitioning procedure and a solution technique described in detail. Then, the most important performance measures are obtained as a function of the restarting-inventory level, the buffer size and the reliability parameters of both stations. Finally, some numerical results are discussed in order to validate the model and draw some concluding remarks about the values of the restarting-inventory level which maximize the effective efficiency of the system.