Mathematical Model

Integer Linear Programming formulation

The platform follows the Generalized Assignment Problem structure for Maintenance, Operations, and Administration: assign each task once, respect capacity, ensure role competency compatibility, and minimize the highest employee workload.

Formal notation

Minimize Z = Wmax

Subject to:
Σi xij = 1, for every task j
Σj hj xij ≤ Ci, for every employee i
Σj hj xij ≤ Wmax, for every employee i
xij ≤ eligibilityij
xij ≤ allowedij
xij ∈ {0,1}

Website implementation

The static website implements the model as a browser-based branch-and-bound search. It evaluates feasible employee-task combinations and scores assignments by maximum workload, workload spread, and cross-team penalty.

For larger real deployments, the same interface can be connected to Python PuLP, OR-Tools, Excel Solver, or a backend optimization API.