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

Ghislain Dorian Tchuente Mondjo

arXiv:2608.18723v1cs.CLcs.AI

TL;DR

Rigid telecom tariff grids limit personalized plan choice, while existing models may raise prices to protect margins. BFTR formalizes budget-first strategies with a no-overcharging guarantee, and experiments confirm zero surcharge across strategies while revealing distinct volume, utility, and budget-use trade-offs.

  • Problem

    Rigid telecom tariff grids limit personalized choice, while adapting recommender systems to telecom remains constrained by margin requirements and catalog complexity.

  • Method

    BFTR formalizes eight budget-first strategies, including two hybrids, and proves offer existence for positive budgets and no overcharging for composition and interpolation strategies.

  • Results

    All strategies achieve zero surcharge; HYB-REC reaches 0.946 utility with 100% budget use, PIECE maximizes volume at 39.7 GB, and POWERLAW uses 99.9% of budget with 38.1 GB.

  • Takeaways & Limitations

    BFTR provides a transparent, verifiable framework for personalized telecom tariffs with price integrity and strategy-dependent trade-offs between utility, volume, and budget capture.

Abstract

from arXiv · show

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.

I. INTRODUCTION · II. STATE OF THE ART: ECONOMIC MODELS IN TELECOM

BFTR addresses rigid telecom tariffs by letting customers specify a monthly budget and select algorithmic strategies that construct optimized plans without overcharging. The paper formalizes BFTR’s guarantees and compares them with ten established tariff systems and their economic properties.

  • I. INTRODUCTION: Rigid tariff grids cause customer frustration, overage costs, and high churn, while limiting digital inclusion in emerging markets with lower and more volatile incomes.BFTR responds to this problem through customer-directed, budget-first recommendation.
  • I. INTRODUCTION: BFTR lets customers state a monthly budget, choose among algorithmic strategies, and receive a dynamically constructed optimized plan.Available strategies include direct selection, interpolation, knapsack, regression, and hybrids.
  • I. INTRODUCTION: BFTR’s central guarantee is that the charged price never exceeds the catalog reference price, replacing margin assurance with price compliance.This directly addresses regulatory concerns about overcharging.
  • I. INTRODUCTION: Eight Budget–First strategies are mathematically formalized, including two original hybrids, alongside existence and no-overcharging proofs.The existence result covers any positive budget, while the price guarantee is formally established for composition and interpolation strategies.
  • I. INTRODUCTION: The evaluation covers 974 customers and includes sensitivity analysis across three α levels, execution-time comparisons, failure rates, and operator margin metrics.The margin measures are average margin and margin threshold attainment rate.
  • II. STATE OF THE ART: ECONOMIC MODELS IN TELECOM: The state of the art presents ten widespread tariff systems using formal definitions, real operator examples, and analyses of their economic properties.The reviewed models include prepaid, postpaid, plan selection, freemium, rollover, family sharing, data lending, and overage billing.
  • II. STATE OF THE ART: ECONOMIC MODELS IN TELECOM: Prepaid provides strict budget control through qmax = ⌊C/τ⌋, whereas postpaid charges P = Pbase + δ · max(0, qreal −Q) after consumption.Prepaid may require frequent recharges, while postpaid introduces consumption-dependent price uncertainty.
  • II. STATE OF THE ART: ECONOMIC MODELS IN TELECOM: Alternative models trade flexibility across tiers, time, groups, and users, while overage billing applies δ ≫τ beyond quota and is a major source of churn.Freemium offers free entry but abrupt paid transitions; rollover smooths inter-temporal variations; sharing mutualizes risk; lending depends on members’ balances.

III. FORMALIZATION OF THE BFTR MODEL … C. Budget–First Strategies

BFTR formalizes budget-first recommendation through utility-based plan selection, interpolation, regression, and knapsack composition while defining reference prices and surcharge to enforce no overcharging. The presented strategies align final prices with catalog or budget references, with interpolation constrained to valid catalog thresholds.

  • A. Notations and Economic Model: α = 0.5 gives equal weight to budget adequacy and needs coverage in the utility function.Sensitivity analysis evaluates α = 0.2, 0.5, and 0.8.
  • A. Notations and Economic Model: The final system removes component catalog C, so KNAP and hybrid strategies use only plans from catalog F.The change avoids artificial price discrepancies and was validated experimentally.
  • B. Operational Constraints and Definitions: A reference price is the sum of composing-plan prices, while interpolation and mixed offers use budget bu as their reference price.The budget reference reflects the requirement to use the entire budget without markup.
  • B. Operational Constraints and Definitions: An offer is overcharged when surcharge s(O) > 5%, using 5% as the regulatory tolerance threshold.Surcharge is defined as the relative difference between final and reference prices.
  • C. Budget–First Strategies: SELECT scans plans once, retaining the highest-utility plan priced within bu, with complexity O(k).Its final and reference prices are identical, so the surcharge is zero.
  • C. Budget–First Strategies: INTERP creates a virtual offer with price exactly bu by linearly combining consecutive-plan volumes.It sorts in O(k log k), searches the containing interval in O(log k), and returns failure outside [pmin, pmax].
  • C. Budget–First Strategies: REGR predicts volume from budget and average consumption, then selects the closest catalog plan without exceeding bu.Inference is O(1), the model is trained beforehand, and the surcharge is zero because final and reference prices match.
  • C. Budget–First Strategies: KNAP greedily adds plans by descending volume/price ratio under bu in O(k log k), without adjusting price upward.Its final price equals the selected plans’ price sum, which is also the reference price; therefore, it never generates overcharging.

D. Advanced Strategies

Advanced strategies use learned predictive models to estimate plan prices from data volume, with PIECE and POW providing distinct inference mechanisms. For both methods, BFTR’s final-price correction guarantees no positive overcharging.

  • D. Advanced Strategies: Predictive strategies estimate plan price P from volume d and require prior training on historical data.Calibrated models are presented later in Section VI-A.
  • D. Advanced Strategies: PIECE partitions the volume axis into L intervals, fits a linear regression on each, and infers price in O(log L) or O(1) time.Cross-validation selects breakpoints, while least squares estimates segment coefficients.
  • D. Advanced Strategies: POW models price as P = a · d^b + c, fits parameters using non-linear least squares, and performs inference in O(1).The fitting procedure uses the Levenberg–Marquardt algorithm to capture economies of scale.
  • D. Advanced Strategies: PIECE and POW set final price to min(estimated price, budget) and recompute cost on the generated volume, ensuring zero or negative surcharge.Therefore, neither method produces positive overcharging.

E. Hybrid Strategies

The two hybrid strategies combine knapsack selection with interpolation differently: HYB-REC favors interpolation within the catalog range, while HYB-KF prioritizes knapsack and interpolates any eligible remainder. Both guarantee zero overcharging when remainder interpolation is allowed.

  • Recursive Hybrid: HYB-REC returns interpolation when p_min ≤ b ≤ p_max, otherwise applying knapsack before interpolating an eligible remainder.If the budget lies within the catalog range, interpolation ensures 100% utilization; outside that range, the algorithm computes the knapsack remainder and interpolates it only when p_min ≤ br ≤ p_max.
  • Knapsack–First Hybrid: HYB-KF prioritizes knapsack, then returns a composite offer by interpolating the remainder when br > 0 and p_min ≤ br ≤ p_max.Otherwise, it returns the knapsack offer alone, while central budgets can still produce composite offers.
  • No Overcharging: 0% surcharge is guaranteed for HYB-REC and HYB-KF when interpolation of the remainder is allowed.The knapsack and interpolation components individually avoid overcharging, and their union’s final price equals the original budget.

F. Typology of Strategies: Composition vs. Generation · IV. COMPARATIVE ANALYSIS: BFTR VS. TEN EXISTING SYSTEMS · A. Detailed Score Explanations (with Justifications and Examples)

BFTR divides its eight strategies into composition and generation families, then compares them with ten existing tariff models across ten dimensions. The comparison emphasizes budget control, personalization, small-budget adaptation, and zero overage, alongside operational and customer-retention advantages.

  • F. Typology of Strategies: Composition vs. Generation: Composition strategies assemble predefined catalog plans, while generation strategies create virtual offers through interpolation, regression, piecewise modeling, or power laws.KNAP, HYB–KF, and parts of HYB–REC are composition strategies; SELECT is classified with generation strategies despite selecting an existing plan unchanged.
  • F. Typology of Strategies: Composition vs. Generation: High granularity and total absence of overcharging characterize composition strategies, whereas generation strategies enable perfect budget utilization or fine usage-profile adaptation.The passage attributes these benefits to catalog assembly and virtual-offer construction, respectively.
  • IV. COMPARATIVE ANALYSIS: BFTR VS. TEN EXISTING SYSTEMS: Ten key dimensions organize the comparison between BFTR and ten existing tariff models.Table I summarizes the comparison, using green for advantages, yellow for average performance, and red for major drawbacks.
  • A. Detailed Score Explanations (with Justifications and Examples): BFTR (Total) lets users set a cap and builds an offer at that price or less, with no overage; examples are 15C or 14.50C.Interpolation can produce 15C from a 15C budget, while knapsack can produce 14.50C; BFTR also receives “None” for surprise risk and overage handling.
  • A. Detailed Score Explanations (with Justifications and Examples): BFTR (Maximal) personalization uses a la carte assembly, exemplified by 3 GB + 200 min + roaming, while its small-budget adaptation is Yes.The paper attributes small-budget support to zero-point interpolation or a minimal offer responding to any budget.
  • A. Detailed Score Explanations (with Justifications and Examples): BFTR (Very low) customer complexity requires only a budget input and strategy choice from a clear list, while innovation incentive is Maximal through catalog additions.BFTR is also rated High for interest alignment and Medium–High for revenue predictability.
  • A. Detailed Score Explanations (with Justifications and Examples): BFTR (Very high) churn reduction follows from eliminating overages and mismatch, contrasting with lower retention ratings for several conventional models.Family and Lending are rated High, while Pay-as-you-go, Freemium, and Rollover are rated Medium.

B. Synthesis

BFTR combines user-selected tariff strategies with explicit overcharge control, positioning it as a flexible solution that guarantees no overcharging. The algorithm executes the selected strategy, validates the resulting offer against the budget, and rejects excessive overcharge.

  • Synthesis: BFTR supports strategic flexibility through user choice while guaranteeing no overcharging.The framework is presented as outperforming other systems on key dimensions through this combination.
  • Synthesis: The algorithm dispatches recommendations across selection, interpolation, regression, knapsack, piecewise, power-law, and two hybrid strategies.Recursive Hybrid and Knapsack-First Hybrid are invoked as HYB-REC and HYB-KF.
  • Synthesis: If no offer exists or the selected offer exceeds budget b, BFTR replaces it with the minimal offer.This check occurs after the selected strategy has been executed.
  • Synthesis: BFTR computes the catalog reference price and rejects the offer when its surcharge exceeds threshold τ.The surcharge is calculated as (p(O) − pref)/pref × 100 before the rejection decision.

V. ARCHITECTURE AND USER STRATEGY CHOICE

BFTR uses a modular pipeline in which operator parameters, user data, and a user-selected strategy drive offer generation followed by overcharge control. Its strategy-dependent execution remains fast, with catalog-based complexity and a worked HYB-REC example producing zero surcharge.

  • Architecture and strategy choice: BFTR accepts operator parameters and user data, including the catalog, business rules R, profitability thresholds, budget bu, consumption history Hu, and one of eight strategies.The user-selected strategy belongs to either the composition family—KNAP, HYB-KF, HYB-REC—or the generation family—SELECT, INTERP, REGR, PIECE, POW.
  • Architecture and strategy choice: The core BFTR algorithm executes the selected strategy and then applies overcharge control using rules R, thresholds pmin and pmax, and overcharge threshold τ.This control phase verifies the generated offer against the system’s overcharge conditions.
  • Computational complexity: O(k) for SELECT, O(log k) for INTERP, O(1) for REGR, PIECE, POW, O(k log k) for KNAP, and O(k log k + log k) for hybrids.The overall BFTR complexity is dominated by the chosen strategy.
  • Computational complexity: Below 1 millisecond, response time remains with k ≤100 plans, while overcharge control runs in O(|O|) = O(k).Experimental measurements confirmed the sub-millisecond response time, and the control phase is described as negligible.
  • Execution example: 9,000 NGN budget with HYB-REC produced an interpolated 31.2 GB offer and zero surcharge in 0.52 ms.Because 9,000 NGN lies within the 636–23,569 NGN catalog interval, the system interpolated between the 5 GB, 2,378 NGN plan and the 10 GB, 3,799 NGN plan; the reference price equaled the budget.

VI. EXPERIMENTS · A. Advanced Model Training · B. Experimental Setup •

The experiments trained Piecewise and Power Law price models on real MTN Nigeria data, then evaluated BFTR using synthetic customers, a six-plan catalog, randomized budgets, and a defined overcharge threshold. Model performance was assessed on a 20% test set using R2 and MAE.

  • A. Advanced Model Training: Piecewise and Power Law were trained on 21 distinct MTN Nigeria plans and 974 customers, predicting plan price from volume in GB.The target variable was plan price, and volume in GB was the explanatory variable.
  • A. Advanced Model Training: Piecewise used cross-validated breakpoints at 5 GB and 200 GB, fitting least-squares linear regressions within each segment.The resulting segments covered d ≤5 GB, 5 < d ≤200 GB, and d > 200 GB.
  • A. Advanced Model Training: Power Law used non-linear least squares with the Levenberg–Marquardt algorithm to fit P = a · d^b + c.This specifies the model form and estimation method used for training.
  • A. Advanced Model Training: R2 = 0.9147 and MAE = 2,476 NGN were reported for one model, while R2 = 0.8464 and MAE = 3,400 NGN were reported for the other on a 20% test set.The passage reports these results respectively for the two trained models.
  • B. Experimental Setup •: The evaluation used 974 synthetic customers inspired by MTN Nigeria, six plans spanning 1.5–100 GB and 636–23,569 NGN, and budgets B = P_plan × U(0.8, 1.2).The catalog defined the evaluated volume and price ranges, while budgets varied around plan prices.
  • B. Experimental Setup •: Each of the six catalog plans had a unique ID from 1 to 6, with volumes, prices, and margins used to construct offers.Table II presented the catalog attributes and the identifiers used in the offer-composition table.
  • B. Experimental Setup •: The experiments set the overcharge threshold to τ = 5%.This threshold defined the tolerated overcharge level in the experimental setup.
  • B. Experimental Setup •: The experimental environment used an Intel Core i7-1165G7 @ 2.80 GHz, 16 GB RAM, and Python 3.10.These hardware and software specifications characterized the reported execution environment.

C. Evaluation Metrics · D. Budget–First Results (α = 0.5) · E. Detailed Offer Analysis for Representative Budgets

The evaluation uses budget utilization, offered volume, utility, surcharge, overcharging, loss, execution, failure, and margin metrics. At α = 0.5, HYB-REC maximizes budget use and utility, PIECEWISE maximizes volume, and all strategies achieve zero surcharge across representative budgets.

  • C. Evaluation Metrics: Budget used measures effective-price utilization of the initial budget, while volume offered measures included data in gigabytes and utility combines budget adequacy with historical-needs coverage.A utility of 1.0 represents a perfectly adapted offer.
  • C. Evaluation Metrics: Surcharge is the final-price difference from the reference price, overcharging counts cases above 5%, and total loss is unspent budget.Execution time averages CPU time over 1,000 calls; failure rate counts invalid offers before fallback.
  • C. Evaluation Metrics: Average margin measures operator profitability, while margin threshold attainment measures offers reaching the predefined 20% margin threshold.These metrics assess profitability while respecting the non-overcharging constraint.
  • D. Budget–First Results (α = 0.5): 0% overcharging is achieved by every strategy, confirming the theoretical zero-surcharge guarantee.HYB-KFcorr reduces budget utilization to 97.1% and produces an average loss of 119 NGN per customer while preserving its average margin and threshold attainment.
  • E. Detailed Offer Analysis for Representative Budgets: Representative offers are reported for budgets of 5,000, 10,000, 15,000, 20,000, and 25,000 NGN with plan composition, price, volume, cost, surcharge, and loss.Composition notation distinguishes repeated catalog plans, interpolation, mixed compositions, and two-plan offers.
  • E. Detailed Offer Analysis for Representative Budgets: For mixed HYB-KF and HYB-REC offers, the reference price is the original budget, so selected plans plus interpolated remainder equal the budget and surcharge equals 0%.Composition, interpolation, and generation offers use distinct reference-price rules based on catalog prices, the budget, or uncapped estimated prices.
  • E. Detailed Offer Analysis for Representative Budgets: 0.00% surcharge appears in every row of Table IV, confirming the zero-surcharge outcome for the representative budgets.The loss column records budget not spent by the customer and therefore not captured by the operator.

F. Execution Times … 2) Operator-Oriented Margin Metrics:

BFTR strategies are computationally viable, but robustness and profitability consistency vary across methods. HYB-REC leads customer-oriented performance and utility, while PIECEWISE favors volume and POWERLAW balances budget use with volume despite inconsistent margins.

  • F. Execution Times: < 0.1 ms: PIECE and POW are the fastest strategies, while all strategies remain below 5 ms for real-time production use.KNAP takes 2 ms because it sorts and selects plans.
  • G. Robustness: Failure and Fallback Rates: 17.8%: INTERP has the highest failure rate outside the catalog interval, versus 9.4% for SELECT, KNAP, and hybrids below 636 NGN.PIECE, POW, and REGR never fail because they use robust parametric methods.
  • H. Sensitivity Analysis on Parameter α: α = 0.2: PIECEWISE is best with utility 0.857 because it offers the highest volume, 39.7 GB.The sensitivity analysis evaluates α = 0.2 for volume priority, α = 0.5 for balance, and α = 0.8 for budget priority.
  • H. Sensitivity Analysis on Parameter α: α = 0.5: HYB-REC becomes optimal with utility 0.946, and α = 0.8: it dominates with utility 0.978 by using 100% of the budget.These settings represent balance and budget priority, respectively.
  • 1) Customer Performance:: 100% budget utilization: HYB-REC achieves the best volume, 29.9 GB, and the highest utility, 0.946, through direct interpolation combined with KNAP for out-of-range budgets.POWERLAW uses 99.9% of the budget, offers 38.1 GB, incurs near-zero loss of 6.4 NGN, and has 0% overcharging.
  • 2) Operator-Oriented Margin Metrics:: 100%: HYB-REC, INTERP, KNAP, REGR, and SELECT achieve the 20% margin threshold for every offer.PIECE reaches the threshold in 62.1% of cases, indicating occasional thin margins.
  • 2) Operator-Oriented Margin Metrics:: 74.9%: POWERLAW offers achieve the 20% margin threshold, despite its extremely high average margin, leaving about 25% below 20%.This demonstrates why profitability consistency should be assessed alongside average margin.

3) No Overcharging: … VII. CONCLUSION AND PERSPECTIVES

BFTR aligns final prices with catalog reference prices, yielding zero overcharging across its strategies while supporting robust, fast, and objective-sensitive recommendations. Experiments validate the framework’s customer, volume, budget, transparency, and regulatory advantages, with extensions proposed for future work.

  • 3) No Overcharging:: 0% average surcharge and 0% overcharging confirm that every recommended offer’s final price equals its reference price.For composition strategies, the reference price sums catalog plan prices; for generation strategies, it is the budget or estimated price.
  • 3) No Overcharging:: p(O) = pref(O) guarantees s(O) = 0% for composition, interpolation, and hybrid offers, whose construction remains verifiable through catalog-plan decomposition.Hybrid offers combine catalog plans with an interpolated remainder, without applying a price markup.
  • 4) Hybrid Comparison:: HYB-REC outperforms HYB-KF by directly interpolating the total budget, while HYB-KFcorr reduces utilization without improving margin or surcharge.Both HYB-REC and HYB-KF achieve zero surcharge.
  • 5) Complexity and Validity:: < 5 ms execution and 0% average surcharge for composition and pure interpolation strategies support production viability.The no-overcharging guarantee is explicitly verified for these strategy classes.
  • 6) Catalog Size Impact:: 17% of out-of-range budgets cause INTERP failure with only 6 plans, whereas hybrid and KNAP strategies remain robust through composite offers.Hybrid and KNAP strategies create offers from existing plans.
  • J. Final Recommendations:: HYB-REC is recommended for maximum customer satisfaction, PIECE for robust non-overcharging, and HYB-REC, KNAP, REGR, or SELECT when 100% threshold attainment is prioritized.Tuning α adapts recommendations to different user profiles; margin reliability favors the listed 100%-attainment strategies over PIECE and POWERLAW.
  • VII. CONCLUSION AND PERSPECTIVES:: 0.946 utility with 100% budget utilization makes HYB-REC the customer-oriented leader; PIECE reaches 39.7 GB volume, while POWERLAW provides a volume-budget compromise.All strategies achieve zero surcharge, and catalog IDs make offer decomposition fully verifiable.
  • VII. CONCLUSION AND PERSPECTIVES:: 0% failure and < 2 ms execution characterize composition strategies, while low α favors volume-prioritizing strategies and high α favors budget-capturing ones.The formal no-overcharging proof for composition and interpolation strategies is identified as a major theoretical contribution.
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