Determining Process Capacity: Intractability and Efficient Special Cases
Bibliographic record
Abstract
Most operations management textbooks use the following simple approximation to illustrate the computation of the capacity of a process: the capacity of each resource is first calculated by examining that resource in isolation; process capacity is then defined as the smallest among the capacities of the resources, that is, bottleneck capacity. In a recent paper, Gurvich and Van Mieghem [Gurvich I, Van Mieghem JA (2015) Collaboration and multitasking in networks: Architectures, bottlenecks, and capacity. Manufacturing Service Oper. Management 17(1):16–33.] show that, in the presence of collaboration and multitasking, this “bottleneck formula” can be significantly inaccurate, and they obtain a necessary and sufficient condition under which it correctly determines process capacity. We provide further clarity on determining process capacity by showing that it is hard to compute process capacity exactly and also to approximate it to within a reasonable factor. These results are based on a novel characterization, which we establish, of process capacity that relates it to the fractional chromatic number of the associated “collaboration graph.” An important implication is that it is unlikely that we can replace the bottleneck formula with a simple but close approximation of process capacity. On the positive side, we show that capacity can be efficiently computed for processes for which the collaboration graph is a perfect graph. From a practical viewpoint, our analysis for general processes results in a natural hierarchy of subclasses of policies that require an increasing amount of sophistication in implementation and management: while process capacity is the maximum long-term process rate achievable over all feasible policies, we provide a precise expression for the maximum process rate over policies in each subclass of this hierarchy, thus highlighting the trade-off between operational difficulty and the achievable process rate. The online appendix is available at https://doi.org/10.1287/msom.2017.0689 .
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 | 0.010 | 0.100 |
| Meta-epidemiology (narrow) | 0.003 | 0.003 |
| Meta-epidemiology (broad) | 0.003 | 0.007 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.003 | 0.008 |
| Scholarly communication | 0.006 | 0.018 |
| Open science | 0.007 | 0.008 |
| Research integrity | 0.004 | 0.009 |
| Insufficient payload (model declined to judge) | 0.012 | 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".