Modeling and optimization of multilevel marketing operations
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
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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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.014 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it