Modeling waste production into two-machine–one-buffer transfer lines

This article focuses on analytical models of two-machine one-buffer Markov lines including waste production. The aim is to compute the probability of producing good parts, referred to as effective efficiency, when waste production is related to stoppages of the first machine. This problem is common in industrial fields where parts are generated by a continuous process; e.g., in high-speed beverage packaging lines. Two innovative models including waste production are presented: the WP-Basic Model extends the model of a basic two-machine-one-buffer transfer line; the WP-RP Model extends the model of a two-machine-one-buffer transfer line with a restart policy operating on the first machine (i.e., when the first machine is blocked because the buffer is filled, it is not allowed to resume production until the buffer becomes empty). The two existing models are improved by distinguishing, at any time step the first machine is operational, whether it is producing a good or a bad part. The probabilities of the system being in any feasible state are analytically derived for both the WP-Basic Model and the WP-RP Model. Then, the obtained probabilities are used to determine the performance measures of interest; i.e., waste probability and effective efficiency. Finally, some numerical results are provided to illustrate the effectiveness of the WP-Basic Model and the WP-RP Model.