Problems in Supply Chain Location and Inventory under Uncertainty
Bibliographic record
Abstract
We study three problems on supply chain location and inventory under uncertainty. In Chapter 2, we study the inventory purchasing and allocation problem in a movie rental chain under demand uncertainty. We formulate this problem as a newsvendor-like problem with multiple rental opportunities. We study several demand and return forecasting models based on comparable films using iterative maximum likelihood estimation and Bayesian estimation via Markov chain Monte Carlo simulation. Test results on data from a large movie rental firm reveal systematic under-buying of movies purchased through revenue sharing contracts and over-buying of movies purchased through standard ones. For the movies considered, the model estimates an increase in the average profit per title for new movies by 15.5% and 2.5% for revenue sharing and standard titles, respectively. We discuss the implications of revenue sharing on the profitability of both the rental firm and the studio.\n\nIn Chapter 3, we focus on the effect of travel time uncertainty on the location of facilities that provide service within a given coverage radius on the transportation network. Three models - expected covering, robust covering and expected p-robust covering - are studied; each appropriate for different types of facilities. Exact and approximate algorithms are developed. The models are used to analyze the location of fire stations in the city of Toronto. Using real traffic data we show that the current system design is quite far from optimality and provide recommendations for improving the performance. \n\nIn Chapter 4, we continue our analysis in Chapter 3 to study the trade-off between adding new facilities versus relocating some existing facilities. We consider a multi-objective problem that aims at minimizing the number of facility relocations while maximizing expected and worst case network coverage. Exact and approximate algorithms are developed to solve three variations of the problem and find expected--worst case trade-off curves for any given number of relocations. The models are used to analyze the addition of four new fire stations to the city of Toronto. Our results suggest that the benefit of adding four new stations is achievable, at a lower cost, by relocating 4-5 stations.
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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 | 0.007 | 0.027 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.002 | 0.006 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.006 | 0.009 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.006 | 0.004 |
| Insufficient payload (model declined to judge) | 0.007 | 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".