Dynamic hoist scheduling for multi-recipe and multi-stage production lines: A logical framework

This article studies the dynamic multi-hoist scheduling problem in a robotic cell with multi-function and parallel processing units. We consider a general case of a multi-recipe and multi-stage material handling process, which can be encountered in many manufacturing industries such as electronics, chemical, food, automotive, and steelmaking. Scheduling such a process, even for a line with a single hoist, is very complex and has been merely dealt with using exact mathematical methods. We propose a logic-based optimization model to solve the task scheduling and resource allocation problem for a line with multiple hoists. Then necessary and sufficient conditions are presented to avoid collision between the hoists. A compact formulation for these constraints is then integrated into the model. We consider the units with multi-capacity as a special case of parallel units; nevertheless, we drive a more efficient model to deal with this problem in particular. Eventually, the logical constraints are translated into a MILP model that can be solved to optimality to minimize both productivity and hoist movement. In the end, we verify the effectiveness of the proposed method by applying it to various practical problems.