Budget-First Tariff Recommendation (BFTR): A Complete Algorithmic Framework for Telecom Plan Recommendation without Overcharging

Telecom operators traditionally offer predefined tariff grids, forcing users to choose from a limited set of plans. This paper proposes BFTR (Budget-First Tariff Recommendation), a complete algorithmic framework integrating eight Budget-First strategies, including two original hybrid approaches: Recursive Hybrid (conditional interpolation) and Knapsack-First Hybrid (priority knapsack). Unlike existing approaches that adjust prices upward to guarantee a minimum margin, BFTR guarantees the absence of overcharging by systematically aligning the final price with the catalog reference price. We mathematically formalize each strategy, prove the existence of an offer for any positive budget, and prove that the price deviation (surcharge) is zero for all strategies that do not use interpolation with correction. A detailed comparative analysis confronts BFTR to ten main existing tariff models on ten dimensions. Experiments on a dataset of 974 customers inspired by the Nigerian MTN market show that: (i) Recursive Hybrid is optimal for the customer (100% budget used, 29.9 GB volume, utility 0.946, 0% overcharging), (ii) Piecewise offers the highest volume (39.7 GB) with 0% overcharging, (iii) Power Law provides an excellent compromise (99.9% budget, 38.1 GB, 0% overcharging). All strategies achieve a zero surcharge, confirming the theoretical guarantees. A sensitivity analysis on the weighting parameter alpha (0.2 - volume priority, 0.5 - balance, 0.8 - budget priority) shows that utility rankings evolve logically. Execution times (< 10 ms) and very low failure rates (0% for robust strategies) confirm the operational viability of the system. The formal proof of the absence of overcharging constitutes a major theoretical contribution.