Dynamic Capacity Expansion for a Service Firm with Capacity Deterioration and Supply Uncertainty
Bibliographic record
Abstract
Motivated by the challenges faced by the telecom industry during the past decade, in this paper we study a dynamic capacity expansion problem for service firms. There is a random demand for the firm's capacity in each period: the demand in excess of the capacity is lost, and revenue is generated for the fulfilled demand. At the beginning of each period, the firm might increase its capacity through purchasing equipment for immediate delivery, which is constrained by a random supply limit, or it might sign a future contract for equipment delivery in the following period. We assume that the firm's capacity might partially become obsolete due to natural deterioration or technology innovation. We aim at characterizing optimal capacity expansion strategies and comparing the profit functions as well as the optimal control policies of different options. Specifically, we show that the optimal capacity expansion policy for the current period is determined by a base-stock policy. Compared with the case where no future contracts are available, the optimal control parameters of capacity expansion are always smaller. We further show that when the obsolescence rate is deterministic, the optimal policy for capacity expansion through future contracts is also a base-stock type. The results are extended to the cases with stochastically dependent capacity supply limits and stochastically dependent demand processes, which establish the robustness of the optimal policy in various market conditions.
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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 | 0.002 | 0.007 |
| 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 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 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".