Universal Resource & Scheduling Mathematics

Architectural Permutations & Scenarios

How 360 SERVICE HUB's 5-dimensional permutation engine powers 76+ distinct commercial verticals without database schema changes or custom code forks.

Engine Topology

The 5-Dimensional Scheduling Space

Dimension 1: Resource Topology

PERSON (Specialist), SPACE (Room/Court), EQUIPMENT (Vehicle/Asset), or any Compound combination.

Dimension 2: Capacity Allocation

1:1 Dedicated Exclusive Lock vs. Group / Multi-Seat Shared Pool (N) with atomic seat decrement.

Dimension 3: Duration Engine

Minutes (10m–120m), Hours (1h–8h), or Days (1d–30d consecutive date picker).

Dimension 4: Fulfillment Mode

At Venue (in-store check-in) vs. Field / Home (doorstep dispatch with geofenced radius & transit buffers).

Dimension 5: Multi-Slot Consecutive Scheduling

Atomic single-slot appointments vs. multi-slot continuous blocks (Min/Max slot limits) with progressive tiered percentage volume discounts.

Emergent Patterns

The 7 Core Permutation Archetypes

Archetype 1: Pure Asset & Equipment Dry Hire

Formula: [EQUIPMENT] + 1:1 Dedicated + [Hours/Days] + At Venue + Multi-Slot

Asset inventory reserved with serial tracking. Zero human labor allocated. Enforces post-return battery recharge and inspection buffers.

Real-world applications: Camera gear, drone kits, camping gear, medical oxygen concentrators, gaming consoles.

Archetype 2: Pure Space & Facility Slot Allocations

Formula: [SPACE] + 1:1 or Multi-Seat + [Minutes/Hours] + At Venue + Multi-Slot

Spatial infrastructure reserved. 1:1 locks for private simulator bays or snooker tables; shared multi-seat capacity pool (N) for escape rooms or swimming lanes.

Real-world applications: Virtual golf simulators, snooker parlors, karaoke pods, escape rooms, pickleball courts.

Archetype 3: Compound Resource Orchestration

Formula: [PERSON] + [SPACE] + [EQUIPMENT] + 1:1 Dedicated + At Venue

Three-way atomic dependency lock. Intersection availability calculated across all 3 resources. If any resource is unavailable, the slot is locked.

Real-world applications: Hemodialysis clinics (Doctor + Station + Dialysis Unit), cryotherapy labs, classical Pilates reformer.

Archetype 4: Specialized Mobile & Doorstep Field Dispatch

Formula: [PERSON] + [EQUIPMENT/VEHICLE] + 1:1 Dedicated + Field/Home + Transit Buffers

Provider travels to customer GPS location. Operating radius geofencing enforced with mandatory 30m–60m transit buffers.

Real-world applications: Home phlebotomy blood draw, solar rooftop audits, mobile tyre care vans, pest control.

Archetype 5: High-Capacity Group Cohorts & Experiential

Formula: [PERSON] + [SPACE] + Group/Multi-Seat (Batch N) + At Venue

Multiple independent customers book tickets into shared time windows until capacity cap (N) is saturated.

Real-world applications: Infant hydrotherapy (N=4), sound bath meditation (N=12), children soft play (N=25), coding bootcamps.

Archetype 6: Ultra-Fast Micro-Slot Bookings

Formula: [PERSON] or [SPACE] + 1:1 Dedicated + 5–15 Minutes + Minimal Buffer

High-throughput transactional bookings where calendar rendering optimizes for dense 10–15 minute intervals.

Real-world applications: Biometric visa/passport photos, laser key duplication, express document scanning.

Archetype 7: Extended Day & Multi-Day Stays / Rentals

Formula: [SPACE] or [VEHICLE] + 1:1 Dedicated + Days Unit + Multi-Slot (Min/Max Days)

Switches engine from minutes/hours to 24-hour day boundaries with calendar span selection and progressive multi-day discount tiers.

Real-world applications: Self-drive campervan rentals, coliving monthly stays, luxury yacht charters, drone packages.

See these archetypes applied to 76 real categories

Browse our categorized blueprints to see how each archetype translates into real forms, data values, and QA verification matrices.

Browse Business Cookbooks

Loading 360 Service Hub...