Last-Mile Route Density Trade-off
A parcel operation delivers 1,800 stops per day from one depot using 30 vans, each averaging 60 stops per route. Average cost per stop is $9.40, of which $4.10 is the driver and van (fixed per route) and $5.30 is variable (fuel, time, handling). Management wants to cut cost per stop by 12%. Two proposals are on the table. Proposal A: add 6 vans and drivers to reduce stops per route to 50, improving service and reducing route duration. Proposal B: consolidate to 24 vans, raising stops per route to 75, and re-sequence routes. Customer promise is a 2-day delivery window; current on-time performance is 97.5%. Fuel and driver costs are fixed per route-day regardless of stops.
1. Calculate the per-stop cost under the current operation and under Proposals A and B, and determine which proposal, if either, can hit the 12% reduction target.
Read the worked answer
Current: 1,800 stops / 30 routes = 60 stops/route. Fixed cost per route = $4.10 × 60 = $246/route-day. Variable = $5.30 × 60 = $318. Total per route = $564; per stop = $9.40. ✓
Proposal A (36 routes, 50 stops each):
- Fixed per route-day stays $246 (driver + van).
- Variable per stop stays $5.30, so variable per route = $5.30 × 50 = $265.
- Total per route = $246 + $265 = $511; per stop = $511 / 50 = $10.22.
- Change vs $9.40 = +8.7% - cost rises, not falls.
Proposal B (24 routes, 75 stops each):
- Fixed per route = $246; variable per route = $5.30 × 75 = $397.50.
- Total per route = $643.50; per stop = $643.50 / 75 = $8.58.
- Change = (9.40 − 8.58)/9.40 = −8.7%.
Target: 12% reduction means ≤ $8.27/stop. Neither proposal reaches it. B gets closest (−8.7%); A moves the wrong way because fixed route cost is spread over fewer stops.
2. Explain why Proposal A raises cost per stop despite improving service, and assess the service risk of Proposal B against the 97.5% on-time baseline.
Read the worked answer
Why A raises cost: the driver-and-van cost is fixed per route-day ($246). Adding routes adds fixed cost faster than it adds stops. With 36 routes, fixed cost totals 36 × $246 = $8,856/day vs 30 × $246 = $7,380/day - $1,476 more fixed cost for the same 1,800 stops. The variable savings from shorter routes (fewer stops each) do not offset the extra fixed cost. A is a service investment, not a cost program.
Service risk of B: raising stops per route from 60 to 75 lengthens route duration and tightens the schedule. With a 2-day promise and 97.5% on-time, there is only 2.5% slack in performance. A 25% increase in stops per route raises the probability of late stops from traffic, access delays, and end-of-route fatigue. The re-sequencing must be validated before full rollout.
Judgment: B is the only cost-improving option but carries real service risk. Pilot B on a subset of routes, measure on-time and stops-per-hour, and confirm the 97.5% holds before scaling. Do not adopt A on cost grounds; it is a service lever only.
3. Given that neither proposal reaches the 12% target, recommend a path to close the gap and state the key assumption to validate.
Read the worked answer
Gap: B reaches −8.7% ($8.58); target is $8.27. Need another ~$0.31/stop, or ~$558/day across 1,800 stops.
Path to close the gap:
- Push density further where feasible. At 80 stops/route (22.5 routes), per-stop = ($246 + $5.30×80)/80 = ($246 + $424)/80 = $8.38. At 85 stops (≈21.2 routes), ≈ $8.19. Density is the dominant lever, but returns diminish and service risk rises.
- Attack the variable component. $5.30/stop is the larger cost pool. Route optimization, fewer failed deliveries, and denser geographic clustering can reduce time and handling per stop. A 10% variable reduction at 75 stops/route gives ($246 + $357.75)/75 = $8.05/stop - hitting the target.
- Reduce failed deliveries. Each failed stop effectively doubles handling cost; improving first-attempt success directly cuts variable cost.
Key assumption to validate: that the $4.10 fixed and $5.30 variable splits hold as density changes. In reality, longer routes may raise fuel and overtime (variable), eroding B's savings. Validate with a time-and-motion pilot before committing to the 12% target. Recommended sequence: pilot B at 75 stops, measure actual variable cost and on-time, then layer variable-cost reduction to reach $8.27.