Staffing to Maximize Profit for Call Centers with Alternate Service-Level Agreements
Why this work is in the frame
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Bibliographic record
Abstract
To ensure quality from outsourced call centers, firms sign service-level agreements (SLAs). These define service measures such as what constitutes an acceptable delay or an acceptable abandonment rate. They may also dictate penalties for failing to meet agreed-upon targets. We introduce a period-based SLA that measures performance over a short duration such as a rush hour. We compare it to alternate SLAs that measure service by individual and over a long horizon. To measure the service levels for these SLAs, we develop several approximations. We approximate the probability an acceptable delay is met by generalizing the heavy-traffic quality and efficiency driven regime. We also provide a new approximation for the abandonment rate. Further, we prove a central limit theorem for the probability of meeting a service level measured by the percentage of customers acceptably served during a period. We demonstrate how an outsourced call center operating in an environment with uncertain demand and abandonment can determine its staffing policy to maximize the expected profit for these SLAs. Numerical experiments demonstrate a high degree of accuracy for the approximations and the resulting staffing levels. We indicate several salient features of the behavior of the period-based SLA.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 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