A (10/7)-Approximation Algorithm for an Optimum Cyclic Solution in Additive Travel-Time Robotic Cells

This paper considers the problem of scheduling operations in bufferless robotic cells that produce identical parts. Finding a cyclic solution that minimizes the long-run average time to produce a part has long been a fundamental open problem. Most research has been focused on finding an optimal 1-unit cyclic solution. However, it is known that an optimal multi-unit cyclic solution can be better than an optimal 1-unit cyclic solution for cells with four or more machines. For additive travel-time cells, we present a linear-time algorithm that produces a cyclic solution whose per unit cycle time is within a factor of 10/7 of the optimum. This result improves the current best 3/2-approximation guarantee