Allocation and Scheduling of Resource Allocation Systems via Variable Timed Petri Nets

This paper aims to present a unified optimization for resource allocation and scheduling in resource allocation systems. In contrast to traditional two-stage methods, which optimize scheduling and resource allocation independently, this study combines the two to produce globally optimal solutions within practical limitations. In order to describe various resource categories and their disparate quantity needs, a variable timed Petri net is created, in which the arc weights and time delays are determined by resource types. The problem is formulated as a budget-constrained makespan minimization model, with constraints linearized if possible. To handle an inherent non-linear constraint, an iterative mixed integer linear programming approach is developed to obtain optimal resource allocation and scheduling strategies. Extensive computational experiments verify that the proposed framework effectively determines optimal resource type and quantity configurations along with scheduling strategies, jointly minimizing makespan under budget constraints and demonstrating practical efficiency and applicability.