Mock M4 · Last-Mile Drone Delivery for a Suburb

Optimization Vehicle routing Simulation

The problem

A mid-sized e-commerce company is piloting a hybrid truck + drone delivery system in a 25 km² suburban area with ~10,000 households. A truck carries packages and drones along a planned route; drones launch from the truck, deliver a single package, and return to a nearby pickup point on the truck's continuing route. The company has hired your team to design the routing and infrastructure.

Requirements

Build a model that assigns each daily order (location, weight, time window) to either drone or truck delivery and produces a daily routing plan that minimizes a stated objective.
State your objective clearly (we'll require: minimize the sum of operational cost + a per-late-delivery penalty + a carbon cost).
Apply the model to a synthetic suburb you generate: ~500 daily orders, 60% under 2 kg (drone-eligible), 40% heavier; mix of houses and apartment complexes; one 1.5×1.5 km commercial district with a charging pad. Provide the synthetic data in an appendix.
Extend to handle:
- Weather windows: drones grounded above 25 km/h winds or in precipitation.
- Battery constraints: 5 km max round-trip per drone before swap/charge.
- No-fly zones: over schools (school hours), hospitals, and the commercial district.
Sensitivity: how does the optimal drone-fleet size change with order volume (300 → 800/day), drone-eligible package fraction (40% → 80%), and grounding-day frequency (5% → 25%)?
Letter to the company CEO: how many drones to purchase, how many trucks, and what's the projected unit economics vs. all-truck baseline?

Solution sketch

Decision model

Two-tier formulation:

Assignment tier (MIP): for each order $i$ decide truck-only or drone-eligible. Binary $x_i \in \{0,1\}$. Constraints: weight ≤ 2kg for drone, location not in no-fly zone, time window achievable.
Routing tier: solve truck VRP over truck-served orders + drone launch/recovery points. Use OR-Tools or a custom Clarke-Wright savings heuristic.

Drone-launch scheduling

For each drone-eligible order: pick a launch point on the truck's planned route within drone range of the delivery, minimize truck idle time. This is a synchronized routing problem (FSTSP — Flying Sidekick TSP). Solve heuristically: insert each drone delivery at the truck-route point that minimizes added makespan.

Objective

$\min \;\; \alpha \cdot t_{\text{truck}} + \beta \cdot E_{\text{drone}} + \gamma \cdot \sum_i (\text{late}_i)^+ + \delta \cdot \text{CO}_2$

Sensitivity results (illustrative)

Scenario	Optimal drones	Cost vs. all-truck
500 orders / 60% eligible / 10% no-fly days	6 drones / 2 trucks	−22%
800 orders / 80% eligible / 5% no-fly days	14 drones / 2 trucks	−35%
300 orders / 40% eligible / 25% no-fly days	3 drones / 2 trucks	−8%

Conclusion: the economics improve roughly linearly with eligible-order volume but degrade quickly when grounding days exceed 15–20% — climate matters more than fleet size.

Self-grading focus

Did you cleanly separate assignment from routing?
Did you handle drone–truck synchronization (not just "drones magically appear")?
Are no-fly zones encoded in the optimizer, not just a footnote?
Does the CEO letter give a concrete fleet size and break-even calculation?

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