Robotic cells with parallel machines: throughput maximization in constant travel-time cells

We present a general analysis of the problem of sequencing operations in bufferless robotic cell flow shops with parallel machines. Our focus will be cells that produce identical parts. The objective is to find a cyclic sequence of robot moves that maximizes the steady state throughput. Parallel machines are used in the industry to increase throughput, most typically at bottleneck processes having larger processing times. Efficient use of parallel machines requires that several parts be processed in one cycle of robot movements. We analyze such cycles for constant travel-time robotic cells. The number of cycles that produce several parts is very large, so we focus on a subclass called blocked cycles. In this class, we find a dominating subclass called LCM Cycles. The results and the analysis in this paper offer practitioners (i) guidelines to determine whether parallel machines will be cost-effective for a given implementation, (ii) a simple formula for determining how many copies of each machine are required to meet a particular throughput rate, and (iii) an optimal sequence of robot moves for a cell with parallel machines under a certain common condition on the processing times.