Staffing Call Centers with Uncertain Demand Forecasts: A Chance-Constrained Optimization Approach
Bibliographic record
Abstract
We consider the problem of staffing call centers with multiple customer classes and agent types operating under quality-of-service (QoS) constraints and demand rate uncertainty. We introduce a formulation of the staffing problem that requires that the QoS constraints are met with high probability with respect to the uncertainty in the demand rate. We contrast this chance-constrained formulation with the average-performance constraints that have been used so far in the literature. We then propose a two-step solution for the staffing problem under chance constraints. In the first step, we introduce a random static planning problem (RSPP) and discuss how it can be solved using two different methods. The RSPP provides us with a first-order (or fluid) approximation for the true optimal staffing levels and a staffing frontier. In the second step, we solve a finite number of staffing problems with known arrival rates—the arrival rates on the optimal staffing frontier. Hence, our formulation and solution approach has the important property that it translates the problem with uncertain demand rates to one with known arrival rates. The output of our procedure is a solution that is feasible with respect to the chance constraint and nearly optimal for large call centers.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".