A mathematical model for cyclic scheduling with assembly tasks and Work-In-Process minimization

In this paper, we deal with the cyclic scheduling problem. More precisely, we consider the cyclic job shop with assembly tasks. Such a problem is made of several jobs, each job consisting of tasks (assembly/disassembly tasks and transformation tasks) being assigned to machines in a cyclic way. This kind of scheduling problem is well fitted to medium and large production demands, since the cyclic behavior can avoid the scheduling of the whole tasks by considering only a small temporal window (cycle). Thus, cyclic scheduling is a heuristic to solve the scheduling problems whose complexity is NP-hard in the general case. Many methods have been proposed to solve the cyclic scheduling problem. Among them, we focus on the mathematical programming approach. We will propose here a mathematical model for cyclic scheduling with assembly tasks and Work-In-Process minimization, and we illustrate this approach with an example from literature.