Live planning model
Find where two moving cost lines cross
Represent each option with a fixed economic cost and a per-mile slope. The model solves the exact intersection, identifies a negative crossover as outside feasible distance, and separately prices the planned route.
| Cost line | DIY option | Professional option | DIY minus professional |
|---|
Current calculation process
Formula, default substitution, intermediate quantities, and check
d* = (F_pro - F_DIY) / (q_DIY - q_pro); total(d) = F + q x d
F is fixed economic cost, q is per-mile economic cost, and d is route miles. The per-mile slopes must differ; otherwise the lines are parallel and have no unique crossover.
Five-step crossover
Compare equivalent economic scope
- Define what DIY and professional service include, including packing, loading, driving, delivery, and liability choices.
- Assign distance-independent costs to each fixed line, including household time that does not grow with route miles.
- Estimate per-mile fuel, mileage, toll, lodging, driving-time, and distance-driven professional cost consistently.
- Enter the planned route distance and inspect both the algebraic crossover and planned-distance totals.
- Stress-test uncertain slopes and preserve estimates, route evidence, and the exported line ledger.
Five break-even concepts
Read the intercepts and slopes
Fixed intercept
The modeled cost at zero miles captures rental or quote minimums, supplies, and fixed labor.
Variable slope
Each additional mile changes total cost by the entered per-mile economic rate.
Unique intersection
Different slopes are required. Equal slopes produce parallel lines rather than one break-even distance.
Feasible domain
A negative algebraic crossover lies outside non-negative moving distance and does not describe a practical route.
Current-distance choice
The cheapest option at the entered route may differ from the option cheaper beyond the crossover.
Symbols and substitution
Solve the two-line equality
| Symbol | Meaning | DIY default | Professional default |
|---|---|---|---|
| F | Fixed economic cost | $1,850 | $5,100 |
| q | Per-mile economic cost | $2.15/mi | $0.62/mi |
| d | Planned distance | 1,450 mi | |
| d* | Break-even distance | solved | |
Default substitution: d* = (5,100 - 1,850) / (2.15 - 0.62). The live check substitutes d* into both cost equations and displays the residual difference.
Three diagnostic lenses
Find what drives the crossover
Fuel and lodging sensitivity
DIY slope often changes with fuel price, vehicle efficiency, tolls, overnight stops, and return travel. Test a range, not one optimistic rate.
Household labor boundary
Compare cash-only and full economic cases. If the ranking flips after time value is included, convenience is the central tradeoff.
Quote structure
A true flat or non-linear tariff may not fit one straight line. Use this model only for a justified local linear approximation.
Two crossover cases
Normal and non-feasible intersections
Long-distance route
The default DIY option starts cheaper but rises faster per mile. The family compares the 1,450-mile totals with the solved crossover and documented time assumptions.
Negative crossover
If one option has both a lower fixed cost and a lower slope, the algebraic crossing is negative. That option remains cheaper for every non-negative distance under the entered lines.
Terms
Break-even vocabulary
- Fixed cost
- Modeled economic cost independent of route miles.
- Variable rate
- Incremental economic cost assigned to each mile.
- Cost line
- Fixed cost plus variable rate multiplied by distance.
- Break-even
- Distance at which both entered cost lines are equal.
- Feasible domain
- Non-negative distances relevant to a physical move.
- Sensitivity
- How the result changes when uncertain assumptions change.
Crossover questions
Frequently asked questions
What costs belong in the DIY per-mile rate?
Fuel, mileage charges, distance-driven tolls or lodging allocation, and driving-time value can belong there if they scale reasonably with miles.
What if both per-mile rates are equal?
The cost lines are parallel. There is no unique crossover, so the calculator reports an input error.
What does a negative break-even distance mean?
The lines intersect only outside the feasible non-negative-distance domain. One entered line is cheaper for all practical distances.
Should personal time be included?
Run both cash-only and economic-cost cases. If time matters to the decision, include it explicitly and document the hourly value.
Why might a professional quote not be linear?
Weight tiers, service minimums, dates, storage, accessorial services, and tariffs can make real charges non-linear.
Does the crossover identify the better mover?
No. It compares entered cost lines only; reliability, contract terms, insurance choices, and service quality require separate review.
Limits and evidence
Straight lines simplify real moving prices
- The model assumes each option is adequately represented by one fixed amount and one constant per-mile rate.
- Minimum charges, weight tiers, seasonal rates, storage, delays, and accessorial services can create non-linear costs.
- Economic time value is subjective and should be documented.
- The route distance does not capture service quality, claims risk, physical capability, or schedule flexibility.
Evidence record: retain written estimates, rental terms, route mileage, fuel assumptions, toll and lodging plan, household labor estimate, and exported report. This is decision support, not a binding quote.
Sources and related tools
Build the cost lines from written scope
- U.S. SBA: Break-even point — fixed, variable, and crossover structure.
- FMCSA: Avoid unexpected moving costs — scope and estimate caution.