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Managing multiple brands within a single company is an increasingly important trend in the market. This trend complicates the brand management process. We propose a formal methodology to study resource allocation in brand management systems using Petri nets. Petri nets are a graphical modeling tool that is efficient in characterizing the concurrency of dynamic systems. We focus on an important class of brand conflict problems, known as deadlocks, which are caused by resource contention among brands. Marketing mix theory is employed to identify the resources that are critical to potential deadlocks. The brand management system is modeled as a Petri net, based on which we detect and prevent potential deadlocks via formal analysis. The proposed approach can also be used to verify the deadlock-freeness of a brand management system.