An Integer Programming Model for Multidepot Order Fulfillment

We present an integer linear programming model for order fulfillment in the food industry. Each order must be fulfilled by allocating batches stored across multiple warehouses. The model uses a utility-and-penalty scheme to prioritize fulfillment of more urgent orders and the use of older batches that are closer to each customer. The formulation also incorporates depot regionalization constraints. The model was tested on real instances with up to 700 orders and 5,000 batches and showed satisfactory performance, producing solutions within 1\% of optimal in 15 minutes or less.