Sales Territory Optimizer

What it optimizes:

Minimize the total "cost" of all assignments, where cost = distance × account value:

min Σᵢ Σⱼ∈Cᵢ ‖xⱼ - μᵢ‖² · wⱼ

Translation: Assign valuable accounts to nearby reps. Don't make reps drive far for big deals.

Example: Account worth $100K is 5 miles from Rep A and 8 miles from Rep B.
Cost if assigned to A: 5² × $100K = $2.5M cost units
Cost if assigned to B: 8² × $100K = $6.4M cost units
→ Algorithm prefers assigning to Rep A (lower cost)

The constraint that makes it "balanced":

|Cᵢ| ≤ max_accounts_i for each rep i

Each rep has a capacity limit. Once full, accounts go to the next-nearest available rep.

Example: Rep A (capacity 20) is nearest to 25 accounts.
First 20 accounts → assigned to Rep A
Remaining 5 accounts → assigned to next-nearest rep with capacity

How it works (step by step):

1. Start: Place cluster centers at each rep's home location
2. Assign: Each account goes to the nearest rep with available capacity
3. Recenter: Move each cluster center to the average location of its assigned accounts
4. Repeat: Go back to step 2. Stop when assignments don't change (typically 5-15 iterations)

Why recentering helps: After initial assignment, Rep A's accounts might cluster in the northeast corner of their territory. Moving the "center" there means the next round might reassign some southwest accounts to a closer rep, improving overall efficiency.

Speed: O(n × k × iterations) — handles 100 accounts × 5 reps in milliseconds

The simple rule:

assign(account) = nearest rep who still has capacity

Example: Account "Acme Corp" at (40.75, -73.99)
Rep A is 3 miles away (capacity: 5 remaining) ✓
Rep B is 7 miles away (capacity: 12 remaining)
Rep C is 2 miles away (capacity: 0 remaining) ✗ full
→ Assign to Rep A (nearest with capacity)

Processing order matters:

Accounts are sorted by expected value (potential × probability) and processed highest-first:

priority = annual_potential × close_probability

Why this order? Your $200K account with 60% close rate (priority = $120K) gets first pick of reps. Your $30K account with 20% rate (priority = $6K) takes whatever capacity remains.

Step by step:

1. Sort all accounts by priority (highest value first)
2. For the top account: find the nearest rep with available capacity
3. Assign that account, reduce that rep's remaining capacity by 1
4. Repeat for next account until all assigned

Trade-offs:

Pro: Fast, intuitive, easy to explain to stakeholders.
Con: "Greedy" means it doesn't look ahead. Assigning Account #1 to Rep A might force Account #50 to go to a rep 30 miles away, when a smarter initial choice would have been better overall.

Speed: O(n × k) — extremely fast, good for real-time previews

The core concept: Power Distance

Instead of plain distance, we use "power distance" that accounts for rep capacity:

power_distance(account, rep) = distance² - weight

Higher-capacity reps get a larger weight, effectively "pulling" more accounts toward them.

Example: Account is 10 miles from Rep A (weight=50) and 8 miles from Rep B (weight=10).
Power distance to A: 10² - 50 = 100 - 50 = 50
Power distance to B: 8² - 10 = 64 - 10 = 54
→ Assign to Rep A (lower power distance), even though B is physically closer!
This happens because A has more capacity and can "pull" accounts from further away.

How weights are calculated:

weightᵢ = (rep_capacity / total_capacity) × scaling_factor

Example: 3 reps with capacities 30, 20, 10 (total = 60)
Rep A weight: (30/60) × 100 = 50
Rep B weight: (20/60) × 100 = 33
Rep C weight: (10/60) × 100 = 17
→ Rep A's territory extends further from their home base

The result: Territory "cells"

Each rep ends up with a Voronoi cell—a region where they're the "most influential" rep:

Territoryᵢ = { all locations where rep i has lowest power distance }

Visual intuition: Standard Voronoi creates equal-sized cells (like a honeycomb). Weighted Voronoi lets high-capacity reps have larger cells. The boundaries curve rather than being straight lines.

Overflow handling:

If a cell contains more accounts than the rep's capacity, excess accounts are reassigned to the next-nearest rep with space.

Properties that matter for managers:

• Creates visually clean, contiguous territories (no "Swiss cheese")
• Respects that some reps can handle more accounts than others
• Territory boundaries follow natural geographic breaks

Step 1: Calculate each rep's workload

Workload isn't just account count—it's the weighted value of assigned accounts:

Wᵢ = Σⱼ∈Cᵢ (potentialⱼ × probabilityⱼ)

Example: Rep Sarah has 3 accounts worth $100K×50%, $80K×60%, $120K×40% → W = $50K + $48K + $48K = $146K

Step 2: Measure variation using CV

The Coefficient of Variation (CV) measures spread relative to the mean:

CV = σ(W) / μ(W) = standard deviation ÷ average

Example: 4 reps with workloads $146K, $152K, $148K, $154K → mean=$150K, σ=$3.4K → CV = 0.023 (very balanced!)

Bad example: Workloads $80K, $180K, $120K, $220K → mean=$150K, σ=$60K → CV = 0.40 (poorly balanced)

Step 3: Convert to 0-100% score

Balance = max(0, 100 × (1 - CV))

CV of 0.023 → 97.7% balance score ✓ | CV of 0.40 → 60% balance score ✗

Step 1: Calculate distance to each account

We use the Haversine formula (accounts for Earth's curvature):

d = 2R × arcsin(√[sin²(Δlat/2) + cos(lat₁)cos(lat₂)sin²(Δlng/2)])

Where R = 3,959 miles (Earth's radius). This gives "as the crow flies" distance.

In practice: Real-world implementations often use actual driving distances or travel times from mapping APIs (Google Maps, HERE, etc.). Driving time accounts for highways vs. local roads, traffic patterns, and geographic barriers like rivers or mountains. A 10-mile straight-line distance might be 15 minutes on a highway or 45 minutes through city traffic—which matters a lot for territory efficiency!

Step 2: Sum distances per rep

Dᵢ = Σⱼ∈Cᵢ distance(rep_homeᵢ, accountⱼ)

Example: Rep Mike has 4 accounts at 5mi, 8mi, 12mi, 15mi from home → D = 40 miles total

Step 3: Compare to maximum allowed

Travel Score = 100 × max(0, 1 - (avg_distance / max_travel))

If max_travel = 30mi and avg account distance = 10mi → Score = 100 × (1 - 10/30) = 67%

If avg distance = 5mi → Score = 100 × (1 - 5/30) = 83% (better!)

Step 1: Calculate territory value per rep

Vᵢ = Σⱼ∈Cᵢ (potentialⱼ × probabilityⱼ)

This is the same as workload—the expected value of the territory.

Step 2: Correlate effectiveness with territory value

We want high-effectiveness reps paired with high-value territories. Pearson correlation measures this:

r = Σ(eᵢ - ē)(Vᵢ - V̄) / √[Σ(eᵢ - ē)² × Σ(Vᵢ - V̄)²]

r ranges from -1 (worst performers get best accounts) to +1 (best performers get best accounts)

Example: 3 reps with effectiveness [120%, 100%, 80%] and territory values [$200K, $150K, $100K]
→ Positive correlation! r ≈ +1.0 (perfect alignment)

Bad example: Effectiveness [120%, 100%, 80%] with values [$100K, $150K, $200K]
→ Negative correlation! r ≈ -1.0 (your worst rep got your best accounts)

Step 3: Convert to 0-100% score

Revenue = 50 × (1 + r)

r = +1 → 100% | r = 0 → 50% (random assignment) | r = -1 → 0%

Step 1: Find the territory's geographic center

Calculate the centroid (average lat/lng) of all accounts in the territory.

Step 2: Measure how spread out accounts are

dispersionᵢ = avg_distance_to_centroid / hull_radius

hull_radius = distance from centroid to the farthest account

Compact example: 5 accounts all within 2-3 miles of center → low dispersion ✓

Scattered example: 5 accounts at 1mi, 2mi, 8mi, 15mi, 20mi from center → high dispersion ✗

Step 3: Convert to 0-100% score

Compactness = 100 × (1 - avg_dispersion)

Alternative metric (for reference)

The Isoperimetric Quotient measures shape efficiency:

Q = 4πA / P²

A circle has Q=1 (most compact). A long, thin sliver has Q→0.

Weighted average of all four metrics:

Overall = w₁×Balance + w₂×Travel + w₃×Revenue + w₄×Compactness

Default: equal weights (0.25 each). Adjust via the Scoring Weights sliders based on your priorities.

Example trade-off:
Design A: Balance=95%, Travel=60%, Revenue=70%, Compactness=75% → Overall = 75%
Design B: Balance=70%, Travel=90%, Revenue=80%, Compactness=80% → Overall = 80%
Is B better? Depends on whether you prioritize fairness (choose A) or efficiency (choose B).