A MIP Formulation for Multi-Bin-Size Bin Packing with Physical and Operational Constraints in E-commerce Fulfillment

In e-commerce fulfillment operations, the Storage Location Assignment Problem (SLAP) involves assigning items to bins under constraints that go beyond simple volumetric capacity. These include item dimensions and orientations, regulatory restrictions on co-storage, limits on SKU diversity and copy count, and physical placement rules within bins. Most exact SLAP formulations abstract bins as scalar capacity resources, neglecting geometric feasibility and intra-bin arrangement decisions. This paper proposes MBSBPP-SIM (Multi-Bin-Size Bin Packing Problem with Structured Intra-bin Management), a Mixed-Integer Programming (MIP) formulation that integrates geometric, regulatory, and operational constraints into a unified exact model. The model is evaluated on 28 benchmark instances from a real Latin American B2C e-commerce dataset (n ∈ {20, …, 100}) using Gurobi 13 with a 2-hour time limit. Optimality is achieved in 16 instances (57.1%), including all cases with n = 20 and n = 50, with an average MIP gap of 20.3% for the remaining instances.