预算优先资费推荐（BFTR）：无过度收费的电信套餐推荐完整算法框架
Budget-First Tariff Recommendation (BFTR): A Complete Algorithmic Framework for Telecom Plan Recommendation without Overcharging
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中文总结 AI 辅助
本文提出BFTR算法框架，整合八种预算优先策略，含两种原创混合方法，可保证零过度收费，在974名客户数据集上验证了其有效性与运营可行性。
中文摘要 AI 辅助
电信运营商传统上提供预定义的资费网格，迫使用户从有限的套餐中进行选择。本文提出BFTR（预算优先资费推荐，Budget-First Tariff Recommendation），这是一个整合了八种预算优先策略的完整算法框架，其中包括两种原创混合方法：递归混合（条件插值）和优先背包混合（priority knapsack）。与现有通过上调价格以保证最低利润率的方法不同，BFTR通过系统性地将最终价格与目录参考价格对齐，保证不存在过度收费。我们对每种策略进行了数学形式化，证明了对于任何正预算都存在可行方案，并且证明了所有不使用带修正的插值的策略的价格偏差（附加费）为零。我们在十个维度上将BFTR与十种主要现有资费模型进行了详细的对比分析。在基于尼日利亚MTN市场的974名客户数据集上的实验表明：（i）递归混合对客户而言是最优的（100%预算被使用，29.9GB流量，效用值0.946，0%过度收费）；（ii）分段策略提供最高流量（39.7GB）且0%过度收费；（iii）幂律策略实现了出色的权衡（99.9%预算，38.1GB，0%过度收费）。所有策略均实现零附加费，验证了理论保证。对权重参数α（0.2-流量优先，0.5-平衡，0.8-预算优先）的敏感性分析显示，效用排名逻辑合理演变。执行时间（<10毫秒）和极低的失败率（鲁棒策略为0%）证实了该系统的运营可行性。对无过度收费的形式化证明构成了重大理论贡献。
英文摘要
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.
