Resource allocation
Resource-allocation models distribute limited resources among competing biological or medical needs.
If \(x_i\) is the amount assigned to group \(i\) and total supply is \(B\), a basic constraint is
\[\sum_i x_i\le B,\qquad x_i\ge0.\]Objective
An objective function may minimise expected infections, deaths, waiting time or ecological loss, or maximise expected benefit.
Heterogeneity
Groups can differ in risk, transmission, treatment response, accessibility and cost. These differences can make equal allocation mathematically different from allocation that optimises a chosen outcome.
Beyond mathematics
Ethical, legal and fairness considerations cannot be replaced by an optimisation objective and must be included explicitly in real decisions.
Key idea. Resource allocation converts scarcity into a constrained decision problem, but the objective itself reflects values as well as mathematics.