task-assignment-problem

What it does

Guides an AI agent to solve assignment and resource allocation problems, matching workers to tasks or tasks to resources to optimize objectives like minimizing cost or maximizing throughput. It covers several problem types (LAP, unbalanced, GAP, QAP, multi-objective) and provides concrete algorithmic approaches and examples.

How it works

• It starts with an initial assessment of the problem structure, objectives, constraints, and data availability.
• It outlines different Problem Types and their characteristics, including the Linear Assignment Problem, Bottleneck, Unbalanced, Generalized Assignment Problem, Quadratic Assignment Problem, and Multi-Objective Assignment.
• It provides mathematical formulations for Linear Assignment Problem and Generalized Assignment Problem, including decision variables, parameters, objective, and constraints.
• It presents specific algorithms:
  • Hungarian Algorithm for LAP, including a Python example using SciPy's linear_sum_assignment and a sample cost matrix and worker/task lists.
  • Greedy Assignment heuristic as a fast alternative with a simple implementation.
  • GAP solution via a heuristic MILP approach using PuLP, with an example that builds a model, defines variables, constraints, and solves it.
• It describes Advanced Techniques such as Skills-Based Assignment and Dynamic Task Assignment with corresponding code sketches and explanations for handling constraints like skills, one-to-one mappings, and real-time task arrival.
• It includes example code blocks for each method, showing how to set up costs, tasks, workers, and constraints, and how to extract assignments and totals.

When to use it

Use when you need to optimally or near-optimally match workers to tasks, resources to jobs, or other one-to-one or constrained many-to-one allocations, especially when the user mentions Hungarian algorithm, assignment optimization, worker-task assignment, job allocation, resource assignment, or matching problem. For scheduling or routing tasks, follow related skills (workforce-scheduling, picker-routing-optimization).

What it can touch

• It references and uses tool/functionality such as Python code, numpy, scipy.optimize.linear_sum_assignment, PuLP, PULP_CBC_CMD, and pandas in examples. It also uses standard Python control structures and dictionary/data structures for costs, tasks, and workers.

Caveats

• License is MIT (as declared). The skill provides example code and heuristics that may be suboptimal for large or highly complex instances. Real deployments should validate model assumptions and scalability. It emphasizes that some solutions (e.g., greedy) are not optimal, and that GAP solutions rely on MILP solvers which may have performance considerations on larger datasets.