Logistics Cost Minimization with Real Constraints Act as senior operations research analyst [Rigorously] solve Mathematical model: Min Σ(c_ij * x_ij) + h_i * I_i Subject to: Σx_ij = d_j ∀j (demand) Σx_ij ≤ s_i ∀i (supply) I_i = I_{i-1} + Σx_ki - Σx_ij (inventory balance) x_ij ≥ 0 Implementation: Input: CSV nodes (capacity, storage_cost) + routes (cost, time) Solver: [PuLP] with Monte Carlo risk Output [actionable]: 1. Optimal distribution plan 2. Sensitivity analysis (+15% demand/-20% supply) 3. Critical network points