Tiers Explorer Guide
A comprehensive breakdown of the 6-tier Lexicographic Constrained Optimization (LCO) hierarchy.
What is Lexicographic Constrained Optimization?
LCO solves multiple competing objectives in strict priority order. Instead of blending all objectives into a single weighted sum (which requires arbitrary trade-off decisions), LCO optimizes each tier sequentially: once a tier's objective is achieved, its optimal value is frozen as a hard floor constraint for every subsequent tier. Lower tiers can only optimize within what higher tiers have already guaranteed.
Priority Order
Ethics → Revenue → Risk → Operations → Workforce → Sustainability
Floor Locking
Each tier's result Z_k* becomes Z_k* − ε_k, a binding lower bound for all tiers below it.
Tolerance (ε)
ε controls how strictly the floor is enforced. ε = 0 means no loss allowed vs. the tier's optimal.
How to Use the Tiers Explorer
- Click any tier in the left sidebar to view its detail panel on the right.
- Read the objective, constraints, and paper example for that tier.
- Click "Optimize & Lock Floor" to simulate floor-locking and automatically advance to the next tier.
- Repeat until all 6 tiers are locked — this mirrors the full LCO sequential solve.
The 6 Tiers — Click to Expand
Floor Locked → Next Tier
Floor Locked → Next Tier
Floor Locked → Next Tier
Floor Locked → Next Tier
Floor Locked → Next Tier
Tier Summary — At a Glance
| Tier | Name | Type | Paper Improvement |
|---|---|---|---|
| L1 | Feasibility / Ethics | Hard Constraints | All VIP & ADA guaranteed |
| L2 | Revenue / Margin | Maximize | Z₂* = $1,847 (revenue ceiling) |
| L3 | Risk / Overbooking | Minimize | −55% slack, 98.2% revenue retained |
| L4 | Operations | Minimize | −14% housekeeping turns |
| L5 | Workforce Fairness | Minimize | −25% overtime shift-hours |
| L6 | Sustainability | Minimize | −9% energy proxy |