Solving the Tree-Structured Task Allocation Problem via Group Multirole Assignment
Bibliographic record
Abstract
Task allocation is a critical phase of project management. Tree-type structures are frequently used constraints to obtain a pertinent task allocation. They can illustrate where one task may require numerous agents and when an agent can be assigned to different tasks (roles). The process of task allocation is made more complex when administrators need to satisfy sequential and fixed branch relationships between/among tasks (roles). This paper formalizes the tree-structured task allocation problem (TSTAP) with group multirole assignment (GMRA) and proves necessary conditions, the necessary and sufficient condition, as well as sufficient conditions, of TSTAP. The formalization makes it easy to find a solution with the IBM ILOG CPLEX optimization package (CPLEX). The necessary conditions improve the CPLEX solution by eliminating infeasible cases. The necessary and sufficient condition describes the solution space of TSTAP completely. Another exciting result is that the sufficient conditions can not only improve the CPLEX solution by describing a practical approximate solution space but also help decision-makers and human resource officers organize a team in order to successfully assign tasks. The proposed approach is verified by simulation experiments with respect to a real-world problem. The experimental results present the practicability of the proposed solutions in this paper. This paper was motivated by general cooperative projects whose tasks have tree-structured relationships. This can make the problem of successful multitask assignment extremely challenging. The traditional method of assignment such as the KM algorithm can no longer solve this problem. To solve the assignment problem with tree-structured relationships, an efficient many-to-many assignment with constraints is required. The proposed approach provides theoretical and technical foundations for efficient assignment of TSTA, which can not only provide a viable and effective assignment scheme for TSTA problems but also help human resource officers to formulate reasonable plans according to the relationships between/among tasks.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".