Last-Mile Dispatch Feasibility and Window Spec

Role: Lead Routing Algorithms and Logistics Systems Architect

Context

• Delivery network: {{carrier_network}}
• Urban delivery zone: {{delivery_zone_profile}}
• Scheduled drop density: {{daily_stop_density}}
• Average stem distance from hub: {{average_stem_distance_km}}
• Traffic delay factor: {{traffic_congestion_multiplier}}
• Maximum driver shift duration: {{driver_shift_limit_hours}}

Task

Produce an urban delivery feasibility specification containing mathematical models to validate route viability, stop-density feasibility, and time-window compliance for {{carrier_network}} in {{delivery_zone_profile}}.

Method

1. Formulate the total route transit time equation including stem distance via {{average_stem_distance_km}} and inter-stop travel time.
2. Incorporate {{traffic_congestion_multiplier}} as a non-linear coefficient applied across dynamic peak delivery intervals.
3. Model on-site stop service time as a function of drop density using {{daily_stop_density}}.
4. Formulate the cumulative shift duration equation and enforce the boundary condition bounded by {{driver_shift_limit_hours}}.
5. Define the mathematical feasibility score ($0.0 \le S \le 1.0$) balancing total drops against strict delivery time windows.
6. Formulate the time-window penalty penalty function for early arrival wait times and late delivery violations.
7. Specify the exact mathematical threshold criteria that automatically flags a planned route as infeasible.

Constraints

• All time calculations MUST be standard minute/hour units with consistent velocity terms (km/h).
• The feasibility criteria MUST NOT allow total route duration to exceed {{driver_shift_limit_hours}} under any congestion scenario.
• You MUST explicitly include dwell time per package distinct from vehicle transit time.
• Avoid heuristic pseudo-code; formulate clear algebraic equations and boolean acceptance rules.

Output format

• Section 1: Route Duration & Transit Time Equations (stem time, inter-stop transit, traffic adjusted)
• Section 2: Shift Bounding & Feasibility Logic (drop capacity formulas, boundary constraints)
• Section 3: Time-Window Violation Functions (cost equations for delays and idle waits)
• Total length: 450-700 words.

Self-review

• Confirm stem distance calculations properly account for both outbound and return journeys.
• Verify that the shift limit constraint creates an impossible-to-dispatch boundary when violated.
• Check that all variable terms are clearly defined with their respective metric units.