Last-Mile Route Split and Overtime Trade-Off Evaluation

Role: Principal Last-Mile Dispatch Mathematician specializing in urban logistics algorithms and labor optimization.

Context

• Target Distribution Zone: {{delivery_zone_code}}
• Parcel Throughput: {{daily_parcel_volume}}
• Roster Capacity: {{active_courier_count}}
• Labor Cost Matrix: {{hourly_wage_and_overtime_rates}}
• Route Transit Overhead: {{average_stem_time_minutes}}
• Target Productivity: {{target_stops_per_hour}}

Task

Formulate an analytical trade-off assessment evaluating whether to absorb overtime on current routes or activate an incremental route wave for peak delivery volumes in {{delivery_zone_code}}.

Method

1. Calculate total expected on-duty hours using {{daily_parcel_volume}} and {{target_stops_per_hour}}.
2. Factor fixed stem time per vehicle from {{average_stem_time_minutes}} across active fleet size.
3. Model regular hours versus overtime exposure across {{active_courier_count}} couriers.
4. Compute total marginal labor expense using {{hourly_wage_and_overtime_rates}} under the overtime scenario.
5. Calculate incremental vehicle dispatch fixed cost plus base driver wages for adding supplementary routes.
6. Derive the mathematical cost indifference point where adding a route is cheaper than cumulative overtime.
7. Assess delivery failure probability and late-window breach risk under both configurations.

Constraints

• MUST provide an explicit break-even parcel volume threshold.
• MUST NOT exceed maximum statutory daily driver hours in any modeled scenario.
• All cost comparisons must separate vehicle asset depreciation from driver payroll.
• Keep actionable recommendations prioritized by lowest total cost to serve.

Output format

• Scenario Summary & Recommendation (under 120 words)
• Mathematical Indifference Model (Parameters, Overtime Path Cost, Additional Route Path Cost, Net Difference)
• Risk & Sensitivity Analysis (2 distinct scenarios)
• Actionable Dispatch Decision Rule

Self-review

• Did I incorporate {{average_stem_time_minutes}} in the route cycle math?
• Is the overtime vs new route break-even point unambiguously calculated?
• Does the output strictly adhere to the designated section headers?