Transfer lines with multi-machine stages and non-deterministic processing time: transient performance analysis and control

Serial transfer lines with parallel machines in each stage are now a fairly common manufacturing system. However, its analysis and predictive-reactive control during transients remains mostly unexplored. This manufacturing system consists of a series of stages where in each stage a finite number of machines work concurrently. A two multi-state stage transfer line is studied in this paper. To describe the probability of one part being completed from the several machines in a stage, an equivalent multi-state, perfectly reliable machine is proposed. This multi-state model enables variance in the processing time between job completions to be captured stochastically. Based on historic data or engineering experience, an equivalent multi-state machine is simulated from the cumulative distribution function of the aggregated behavior of the parallel machines. In this paper, a serial production line with two equivalent, multi-state machines is used to analyze transient performance. Analytical closed-form expressions are derived to evaluate system transient behaviors. This system is also used with a controller to implement practical production control. Using model predictive control, system control parameter values provide decision support for managers to control short-term production. The proposed methodology can be applied to improve resource efficiency in other operation management problems.