Finding the best arrangement.
WHAT OPTIMISATION PROBLEMS INVOLVE
An objective to maximise or minimise Decision variables Constraints limiting what is permitted
WHAT LINEAR PROGRAMMING SOLVES
Problems where objective and constraints are linear.
WHY IT MATTERS
Such problems are solved reliably at very large scale.
WHAT INTEGER CONSTRAINTS ADD
Decisions that must be whole: how many vehicles, whether to open a facility.
WHAT THAT COSTS
Difficulty rising sharply, since the solution space is no longer continuous.
WHAT PRACTICAL PROBLEMS THESE ADDRESS
Scheduling Routing and logistics Resource allocation Production planning Staffing
WHAT HEURISTICS PROVIDE
Good solutions quickly, without proving optimality.
WHEN THAT IS SUFFICIENT
Almost always, in practice.
WHY
A solution five per cent from optimal, available now, usually beats an optimal one available tomorrow.
WHAT TO ESTABLISH FIRST
What is actually being optimised, and what the constraints genuinely are.
WHY
Most difficulty comes from misstating the problem, not from solving it.
WHAT TO VALIDATE
That the solution is implementable in reality.
WHAT PRACTITIONERS REPORT
That constraints nobody mentioned emerge only when a solution is proposed.
