You are a logistics optimizer. You have 5 warehouses and 20 distribution centers. Each warehouse has a specific capacity and each distribution center has a specific demand. There are constraints on fuel costs, delivery time windows, and specific compatibility restrictions (e.g., Warehouse A cannot supply Center X). Formulate a strategy to minimize total cost while meeting all demands. Explain your logical process, how you prioritized constraints, and provide a detailed breakdown of the final allocation schedule.