Appointment Scheduling with Multiple Providers and Stochastic Service Times
Bibliographic record
Abstract
In many appointment scheduling systems with multiple providers, customers are assigned appointment times but they are not assigned a specific provider in advance – that is, customers can be seen by any available provider. This type of system is common in a variety of service sectors, such as healthcare, banking, and legal counseling. The majority of the existing literature assumes constant service times or does not consider customer no-shows, which are unrealistic assumptions in many situations. In this paper, we overcome this shortcoming by developing an appointment scheduling model that considers stochastic service times along with customer no-shows for multiple-provider systems with identical providers. The objective is to minimize the weighted sum of customers’ waiting time, and providers’ idle time and overtime. We model this problem as a time-inhomogeneous Discrete-Time Markov Chain process. We use analytical results to reduce the space of optimal schedule candidates, and we employ machine learning techniques to detect patterns among optimal or near-optimal schedules. We then develop an effective heuristic method which provides schedules that perform better than the ones generated by existing models. We test our heuristic both on simulated data and a real-world application. As the real-world application, we collaborate with a local counseling center to implement the schedules suggested by our method. Results from this field experiment reveal an average schedule cost reduction of 16% per day, with a maximum reduction of 40% per day.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 | 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) | 0.004 | 0.001 |
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".