A stochastic optimization approach for the supply vessel planning problem under uncertain demand
Bibliographic record
Abstract
This paper presents a two-stage stochastic programming with recourse methodology to solve the Supply Vessel Planning Problem with Stochastic Demands (SVPPSD), a problem arising in offshore logistics and which generalizes the Periodic Vehicle Routing Problem with Stochastic Demands and Time Windows. In the SVPPSD, a fleet of vessels is used to deliver a regular supply of commodities to a set of offshore installations to ensure continuous production, with each installation requiring one or more visits per week and having stochastic demands. Both the onshore depot where the product to be distributed is kept and the offshore installations have time windows, and voyages are allowed to span more than one day. A solution to the SVPPSD consists in the identification of an optimal fleet of vessels and the corresponding weekly schedule. As a solution methodology, we embed a discrete-event simulation engine within a genetic search procedure to approximate the cost of recourse and arrive at the minimized expected cost solution. We make comparisons with two alternative approaches: an expected value problem with upscaled demand, and a chance-constrained algorithm. While alternative methodologies yield robust schedules, robustness is achieved mainly through an increase in fleet size. In contrast, a two-stage stochastic programming with recourse algorithm, by accounting for the cost of recourse in the search phase, and exploring a wider solution space, allows arriving at robust schedules with a smaller fleet size, thereby yielding significant cost savings. For the tested problem instances, the proposed algorithm leads to savings of approximately 10 to 15 million USD per year.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".