A petri net-based modeling and scheduling with a branch and bound algorithm

We examine a non-cyclic scheduling problem of a timed Petri net (TPN) with a branch and bound (B&B) algorithm. There have been many approaches and algorithms for conventional scheduling problems such as job shops, resource-constrained project scheduling problems (RCPSPs), and robotized system scheduling problems. Most of these methods have focused on their effectiveness or efficiency in solving their own problems. However, they tend to ignore the issue of compatibility with other scheduling problems and the solution methods are ad hoc and hard to be used for other scheduling problems with even small changes. Petri nets have been widely used for modeling and analyzing complex discrete event dynamic systems, such as robotized manufacturing cells or other automated manufacturing systems. There are studies on scheduling cyclic Petri net models and some non-cyclic Petri net models for specific applications. In this paper, we examine a scheduling problem for non-cyclic TPNs, where there is the starting and end transitions, and the transitions do not repeat an identical firing cycle. We also allow multiple arc weights in TPNs so as to model batch processing of tasks at a resource and multiple units of a resource required for a task. We briefly explain how various scheduling constraints and objectives can be modeled by TPNs. Then, we develop an efficient B&B procedure that utilizes a dynamic branching strategy and a resource-based lower bound. We finally present examples of the B&B algorithm for an RCPSP and a single-armed cluser tool scheduling problem.