Multiple Part-Type Production in Robotic Cells: Equivalence of Two Real-World Models

We address the scheduling of operations in a robotic cell that produces multiple part-types. The objective is to obtain a cyclic schedule-a sequence of robot moves and an ordering of the parts-that minimizes the long-run average time to produce a part or, equivalently, maximizes the throughput. We consider two different models that are currently used in practice. The first is a single-gripper cell with a unit-capacity output buffer at each machine. The second is a bufferless dual-gripper cell. We focus our analysis on a widely used class of cyclic solutions, referred to as CRM cycles. The main outcome of our analysis is the equivalence of the two models (i.e., the maximum throughput is the same for both models) under conditions that are common in practice. The equivalence is established in two steps: (i) identification of a subset of dominating cyclic solutions for each model, and (ii) provision of a one-to-one mapping between these dominating cycles such that corresponding cycles have the same throughput. We also analyze the computational complexity of the throughput maximization problem for the two models. The enhanced capabilities (i. e., output buffers and dual gripper) of both models were motivated by a need to improve the throughput. However, the costs of acquiring these capabilities differ significantly. Our discussions with operations managers at a Dallas-area robotic cell manufacturer revealed that the total cost of designing and programming the robot's control mechanism for a cell with output buffers is about 20% less than that for a dual-gripper cell. The equivalence of the two models is, therefore, somewhat surprising and has significant practical implications. For cells that operationalize CRM cycles, the use of output buffers instead of a dual gripper can result in considerable savings without compromising throughput.