On the optimality of the sequential approach for network design problems of service operations
Bibliographic record
Abstract
Abstract We consider the problem of service network design: choosing the optimal number, locations, and service capacities of facilities, taking into account that facilities may have a finite or an infinite waiting room. Accordingly, our service measure is either the percentage of blocked customers or the percentage of customers who need to wait in line. The goal is to minimize the total cost, which consists of costs associated with traveling, blocking or queueing delay, service capacities, and operating (fixed) costs. We derive structural results when facilities are on a two‐node network, and then use them to study the problem for a general network. We prove that the cost of service capacity and the cost of blocking or queueing delay are independent of the number of opened facilities as long as all facilities are identical in terms of their design parameters c and K (or only c in the case of an infinite waiting room). We use our results to develop an efficient algorithm that solves the problem for general networks. Finally, to demonstrate the applicability of our results and tractability of our algorithm, we discuss as an example an industrial‐size problem, which considers the drive‐through operations of McDonald's in the Toronto metropolitan area.
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How this classification was reachedexpand
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 | 0.005 | 0.003 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".