Customer Acquisition and Retention: A Fluid Approach for Staffing
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We investigate the trade‐off between acquisition and retention efforts when customers are sensitive to the quality of service they receive, that is, whether they get timely access to a company's resources when requested. We model the problem as a multi‐class queueing network with new and returning customers, time‐dependent arrivals, and abandonment. We derive its fluid approximation; a system of ordinary linear differential equations with continuous, piecewise smooth, right‐hand sides. Based on the fluid model, we propose a novel approach to determine optimal stationary staffing levels for new and returning customer queues in anticipation of future time‐varying dynamics. Using system accessibility as a proxy for service quality and staffing levels as a proxy for investment, we demonstrate how to apply our approach to two families of time‐varying arrival functions motivated by real‐world applications: an advertising campaign and a clinical setting. In a numerical study, we demonstrate that our approach creates staffing policies that maximize throughput while balancing acquisition and retention efforts more effectively (i.e., equitable abandonment from each customer class) than commonly used near‐stationary methods such as variants of square‐root staffing policies. Our model confirms that acquisition and retention efforts are intimately linked; this has been found in empirical studies but not captured in the operations literature. We suggest that in time‐varying environments, focusing on either alone is not sufficient to maintain high levels of throughput and service quality.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it