Service System Design with Immobile Servers, Stochastic Demand, and Congestion
Bibliographic record
Abstract
The service system design problem seeks to locate a set of service facilities, allocate enough capacity, and assign stochastic customer demand to each of them, so as to minimize the fixed costs of opening facilities and acquiring service capacity, as well as the variable access and waiting costs. This problem is commonly known in the location literature as the facility location problem with immobile servers, stochastic demand, and congestion. It is often set up as a network of M/M/1 queues and modeled as a nonlinear mixed-integer program (MIP). Because of the complexity of the resulting model, the current literature focuses on approximate and/or heuristic solution methods. This paper proposes a linearization based on a simple transformation and piecewise linear approximations and an exact solution method based on cutting planes. This leads to the exact solution of models with up to 100 customers, 20 potential service facilities, and 3 capacity levels.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".