This paper presents a novel vendor-managed inventory (VMI) optimization model that incorporates nonlinear inverse demand functions and a global budget constraint across multiple buyers and products. Unlike traditional VMI models that rely on linear demand assumptions and unconstrained financial planning, the proposed framework captures real-world market dynamics by modeling price sensitivity using a quadratic demand structure. The objective is to maximize the total profit for the vendor by determining the optimal order quantities and replenishment cycles while respecting cost limitations. We utilize Particle Swarm Optimization (PSO) to efficiently solve the nonlinear, constrained optimization problem. Numerical experiments demonstrate the model’s ability to allocate inventory profitably across four buyers and four products under a shared budget. All buyers received optimal replenishment allocations with positive profit contributions, and the total system profit exceeded $21,000. A validation study using a simplified linear model revealed a significant reduction in profit, highlighting the necessity of modeling nonlinearity in demand. Graphical and cost breakdown analyses further illustrated the robustness and interpretability of the solution. The results confirm the effectiveness of integrating nonlinear modeling with intelligent optimization and suggest promising directions for future research in constrained supply chain design.