The vendor resource allocation problem is a typical NP-hard problem, and finding efficient solutions has always been a challenge in both academia and industry. This paper proposes a neural network-based deterministic annealing algorithm to address this problem. The algorithm consists of two main parts: a globally convergent iterative process and a convergence path composed of minima of barrier functions. The paper proves that, as the barrier factor decreases from a sufficiently large real number to 0, a high-quality approximate solution to the problem can be obtained along a series of convergence paths composed of minima of barrier functions. Simulation results demonstrate the superiority of the proposed algorithm compared to existing methods.