Facility location with modular capacity under demand uncertainty: an industrial case study
Bibliographic record
Abstract
We investigate a facility location problem (FLP) with modular capacity under demand uncertainty arising at Hydro-Québec, the largest public utility in Canada. We propose a mathematical model to locate the facilities, determine the capacity levels and compute the number of service teams needed in each facility to satisfy the service demand of all customers. We implement a two-stage stochastic optimization (SP) framework to address the uncertainty in customer demand. We present a traditional scenario-based SP method and a linear decision rule (LDR)-based solution method. We highlight the significant reduction in the computational time provided by the latter, particularly for large instances. These gains in computational performance come at the expense of probable overly robust location decisions. To manage this possible outcome, we adapt a feedback concept found in process system controllers, and we develop two LDR robust trade-off heuristic algorithms that combine a linear decision method with the feedback mechanism. The benefits are empirically illustrated via numerical experiments and validated on an industrial case study in which we achieve a 1.37–5.20% reduction in average total costs.
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 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 | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.002 | 0.006 |
| 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 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".