Reachability Tree-Based Optimization Algorithm for Cyclic Scheduling of Timed Petri Nets

Abstract

Timed Petri nets (TPNs) have been widely used for modeling discrete-event systems of diverse manufacturing and service industries. In this article, we introduce a reachability tree-based optimization algorithm to optimize cyclic schedules of TPNs. In particular, we focus on a special class of cyclic schedules that are referred to as one-cyclic schedules, i.e., the algorithm efficiently finds the optimal one-cyclic transition firing schedule of a TPN. The proposed scheduling method can be robustly applied and extended to a number of different scheduling models since the methodology is not bounded to a specific domain. To enhance the computational performance, we establish a set of transition ordering constraints that can reduce the tree size during the search procedure. We evaluate the computational efficiency of the suggested algorithm by examining robotized manufacturing systems where one-cyclic schedules are popularly being used. It is numerically shown that the proposed algorithm is computationally more efficient than the previously studied Petri net-based optimization methods. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Resource scheduling is one of the most important managerial issues in diverse industrial systems. An optimal scheduling method for a certain industrial system is often locally developed by utilizing domain-specific operational properties. Although such domain-dependent knowledge can contribute to enhancing the computational efficiency of an optimization method, such an approach has a weak point that the method might not be applicable to scheduling problems of different industrial fields. Our motivation is to develop an algorithm for optimizing steady-state schedules that can be robustly applied for various types of discrete-event systems. The algorithm is developed on the basis of the Petri net modeling framework as it is widely being used for describing cyclic behaviors of diverse manufacturing systems, service systems, and social systems. It is experimentally shown that the proposed algorithm is computationally efficient compared with the existing cyclic scheduling methods.