Optimal Order Selection via the Dinkelbach Method

This article study the Optimal Order Selection problem posed in the SBPO 2025 challenge, in which one must choose a subset of customer orders and warehouse aisles so as to maximize the ratio of total items picked to the number of aisles activated, under given lower and upper bounds on wave size.  A pure Dinkelbach-based approach that reformulates the fractional objective into a sequence of parametric mixed-integer programs is proposed, each solved to optimality by CPLEX.  On 35 official benchmark instances (20 from Dataset A, 15 from Dataset B), the method achieves optimal ratios on 25 cases, and respects the 10 min time limit.