Modeling and optimization of multilevel marketing operations
Bibliographic record
Abstract
Abstract This paper models the resource allocation problem arising in multilevel marketing (i.e., network) operations. The supervisor of a network of salespersons has a limited resource (her own time). She must decide on the (i) optimal number of “direct contacts” to recruit, train and develop; (ii) optimal number of lower levels she should be responsible for helping to hire, train and develop their own direct contacts, and (iii) optimal allocation of her time at each level in the network. We use tools from branching processes and find general results for the probability distribution of the number of lower level contacts with non‐identical distributions for any given number of initial contacts. Using these results, we present an optimization model for contacts with different characteristics and determine the optimal number of initial contacts, the number of lower levels and the supervisor's optimal effort at each level using tools from nonlinear programming, in particular, Kuhn‐Tucker conditions and Lagrangian duality. We generalize our models, (i) to allow for the randomness of time spent by the supervisor; and (ii) the possibility of supervisor generating her own direct sales. Several examples illustrate our findings.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 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".