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Air and sea : the point where speed pays for itself

The point where air freight pays for itself, including the costs that never appear on the quote.

Live result
Sea costs $1,256 less on this shipment and holds the lead until the shipment value passes $196,448.
  • total by air$4,327
  • total by sea$3,071
  • delay cost that ends the lead$1,256
  • chargeable weight1,002 kg
  • actual weight800 kg
The lead ends when the shipment value or the cost of a late day rises far enough.
Sea costs $1,256 less on this shipment and holds the lead until the shipment value passes $196,448.The lead ends when the shipment value or the cost of a late day rises far enough.

Cost of each mode

Sea · $3,071
Cost of each modeSea costs $1,256 less on this shipment: $4,327 by air against $3,071 by sea. That holds until the shipment value passes $196,448, or until being late costs you more than $1,256 in total; note that air is billed on 1,002 kg of volume, not the 800 kg the shipment actually weighs. Air totals $4,327: $4,208 freight, $118 capital in transit and $0 delay exposure. Sea totals $3,071: $2,400 freight, $671 capital in transit and $0.00 delay exposure.
Cost breakdown4 lines
MeasureAirSea
Freight$4,208$2,400
$118$671
Delay exposure$0$0
Total$4,327$3,071
MeasureAirSea
Value permanently in transit$11,836$67,068
What holding it costs a year$1,420$8,048
Days it is out there6 days34 days
Extra cover the spread asks for$3,245$16,223
What that cover costs a year$389$1,947

Shipping this 12 times a year leaves $67,068 permanently on the water by sea and $11,836 permanently in the air, and holding the difference costs $6,628 a year. That is the same money the capital line already prices, counted as a stock instead of as a flow, and the two agree to the cent.

A sea transit that moves by 10 days asks for $16,223 of extra cover against $3,245 for air, which is $1,557 a year of stock you hold because the slower mode is also the less dependable one.

Where the answer flips

$196,448
Total cost by shipment valueAir and sea total cost against shipment value. The two lines cross at $196,000; this shipment is at $60,000, where sea is cheaper by $1,256.total cost, $

Past $60,000 this chart is drawn from the same arithmetic and not from anything you entered. The hatched part is the model extended, not a quote.

Test a different lever3 inputs

Hold every other figure still and choose the number you can change. The equality below moves with the rest of the page.

Which input can move

Costs are equal at

$196,448

Below this value sea costs less. Above it air costs less.

From $60,000, shipment value would need to rise by $136,448 (227%) before the totals are equal.

Try either side

Date exposure

Is there a date you have to hit

If being late costs you anything, sea stops being cheaper once the exposure passes $1,256 in total. That is 1.3 days at a thousand a day.

A year of shipmentsOne shipment per month, with value moving through a smooth low to peak cycle.

Peak shipment month

300%

The low month uses $60,000. The peak reaches $240,000.

Across the year

Sea costs $5,131 less across the year. Air is cheaper for 3 of the 12 monthly shipments near the peak.

Taking the lower mode cost month by month puts the 12 shipments at $47,940, $981 below keeping all 12 by sea.

Monthly cost across a shipment value cycleMonthly air and sea cost for one shipment whose value follows the cycle shown. Air is cheaper in 3 of 12 months. Across the full year sea costs $5,131 less. Air totals $54,051 and sea totals $48,921. Taking the lower mode cost month by month totals $47,940, $981 below keeping every shipment by sea.SeaAir

Past $60,000 this chart is drawn from the same arithmetic and not from anything you entered. The hatched part is the model extended, not a quote.

MeasureAirSea
Annual total$54,051$48,921
Cheaper months3 of 129 of 12

Shipment manifest

Live inputs

Try a scenario

Cargo

$

Shown in $. The arithmetic is identical in any single currency.

kg
m³

Chargeable weight for air

1,002 kg

billed on volume: 6.0×1676.0 \times 167 kg beats the 800 kg actual

Freight quotes

$4.20/ kg

Your quote, not a market rate.

How the sea quote is priced

$
0%

A flat sea quote does not split. Price the sea leg per revenue tonne and this opens.

Transit and capital terms6 inputs
6days
34days

Port to port plus the legs either side, as you would quote it.

12%

What money costs you while it sits in a container.

2days
10days

Here is the maths

Model version
1.0

The formula, in words

  • Chargeable weight for air. Airlines bill the greater of actual weight and volumetric weight, where volumetric weight is the shipment's cubic metres times 167 kg. A light, bulky shipment is billed on the space it occupies, which is why the number above is often larger than the weight on the packing list.
  • Weight or measure for sea. Ocean freight billed by the tonne uses the greater of the shipment's tonnes and its cubic metres, where one "revenue tonne" is one tonne or one cubic metre, whichever is more.
  • Capital in transit. Money spent on goods that are moving is money you do not have. Charging it at your annual cost of capital for the days in transit puts the extra four weeks of sea on the same page as the freight quote.
  • Delay exposure. If a date has to be hit, the cost of missing it belongs in the comparison. Without it, sea always wins on cheap goods and the tool only tells you what you already believed.
  • The breakeven is the shipment value where the two totals are equal. Above it, the capital saved by arriving four weeks earlier is worth more than the extra freight.
  • The single input crossover holds every other figure still and solves the same equality for shipment value, air rate or sea cost. It describes the point where the arithmetic changes sides, not a target rate. The two side chips move the selected input about a tenth below or above that point, then round to the matching input step.
  • The distance to equality subtracts the current input from its crossover, then states the absolute difference and that difference as a share of the current input. It makes the amount of movement visible without changing any other figure. When the current input is zero, the percentage is left out.
  • The year view keeps one shipment per month and moves its value through a smooth cycle. The shipment value above is the low point. The uplift sets the peak, and the month control moves that peak through the year. Freight, transit times and any entered delay exposure stay fixed. The month-by-month total adds the lower of the two mode costs in each month. Its flexibility value is the difference from the cheaper of the two all-air or all-sea annual totals.
  • Pipeline stock reads the annual shipment value as a stock that remains in transit. Multiplying that stock by the annual capital rate reproduces the capital charge per shipment times the number of shipments.
  • Transit spread uses half the full range as sigma and the 95% inventory reading. The slower mode carries more cover when its transit also moves across a wider range.
  • The reaction order prices a base sea order with a share held back for air. It does not price the information or service that later choice buys.
Wa=max⁡(W,167B)W_a=\max(W,167B)
where WaW_a is chargeable air weight in kg, WW actual weight in kg, BB volume in cubic metres.
Ws=max⁡(B,W/1000)W_s=\max(B,W/1000)
where WsW_s is revenue tonnes.
C=Vrd365C=\frac{Vrd}{365}
where CC is capital cost, VV shipment value, rr the annual rate, dd transit days.
T=F+C+ET=F+C+E
where TT is total cost, FF freight cost, EE date exposure cost.
V∗=Fa−Fs−Er(ds−da)/365V_*=\frac{F_a-F_s-E}{r(d_s-d_a)/365}
where V∗V_* is the breakeven shipment value, FaF_a air freight, FsF_s sea freight, dsd_s sea days, dad_a air days.
ra∗=Ts−CaWar_a^*=\frac{T_s-C_a}{W_a}
where ra∗r_a^* is the equal air rate, TsT_s sea total cost, CaC_a air capital cost.
Fs∗=Ta−Cs−EF_s^*=T_a-C_s-E
where Fs∗F_s^* is the equal sea quote, TaT_a air total cost, CsC_s sea capital cost.
rs∗=Fs∗Wsr_s^*=\frac{F_s^*}{W_s}
where rs∗r_s^* is the equal sea rate.
Δx=∣x∗−x∣\Delta x=|x_*-x|
where Δx\Delta x is the flip distance, x∗x_* the equal input, xx the current input.
Δx%=Δx∣x∣×100\Delta x_{\%}=\frac{\Delta x}{|x|}\times100
where Δx%\Delta x_{\%} is the percentage distance.
s=max⁡(h,0.1x∗)s=\max(h,0.1x_*)
where ss is the side distance, hh the input step.
xs=x∗±sx_s=x_*\pm s
where xsx_s is the side sample. The side sample is rounded to the input step.
Vm=V0(1+u(1+cos⁡θ)2)V_m=V_0\left(1+\frac{u(1+\cos\theta)}{2}\right)
where VmV_m is monthly shipment value, V0V_0 base value, uu uplift, θ\theta the seasonal angle.
θ=2π(m−mp)12\theta=\frac{2\pi(m-m_p)}{12}
where mm is the month number, mpm_p the peak month.
Tm=∑mmin⁡(Ta,m,Ts,m)T_m=\sum_m\min(T_{a,m},T_{s,m})
where TmT_m is the monthly choice total, Ta,mT_{a,m} monthly air cost, Ts,mT_{s,m} monthly sea cost.
Vf=min⁡(Ta,y,Ts,y)−TmV_f=\min(T_{a,y},T_{s,y})-T_m
where VfV_f is the value of flexibility, Ta,yT_{a,y} annual air cost, Ts,yT_{s,y} annual sea cost.
Vy=VnV_y=Vn
where VyV_y is annual shipment value, nn shipments per year.
P=Vyd365P=\frac{V_y d}{365}
where PP is pipeline value.
dc=zσt2d_c=\frac{z\sigma_t}{2}
where dcd_c is cover days, zz the standard normal factor at 95%, σt\sigma_t the transit spread in days.
Vc=dcVy365V_c=\frac{d_cV_y}{365}
where VcV_c is cover value.
R=aFa+(1−a)Fs+CxR=aF_a+(1-a)F_s+C_x
where RR is reaction cost, aa the air share, CxC_x split capital cost.

A worked example

A shipment of 800 kg in 6 m³ worth $60,000. Volumetric weight is 6×167=1,0026 \times 167 = 1{,}002 kg, which beats the 800 kg actual, so air is billed on 1,002 kg. At $4.20 that is $4,208. Six days of $60,000 at 12% a year costs $118, so air totals $4,327. Sea is $2,400 flat plus 34 days of capital at $671, totalling $3,071. Sea is cheaper by $1,256. Raise the shipment value and the capital term grows faster for sea than for air, by $0.0092 per dollar of value; $1,256 divided by that is roughly $196,000, the shipment value at which the two modes cost the same.

Hold the shipment at $60,000 and solve for one quote instead. Air reaches equal cost at $2.95 per kg. On the unrounded figures, that leaves $2,952 of air freight spread across 1,002 chargeable kg. Sea reaches equal cost at a flat quote of $3,656 after allowing for its capital term. The shipment-value equality is $196,448, which is $136,448 or 227% above the current $60,000. The air-rate equality is $2.95 per kg, a fall of $1.25 or 30% from the current $4.20. The sea-quote equality is $3,656, a rise of $1,256 or 52% from the current $2,400.

For the year view, put the peak in July and set the uplift to 300%. Shipment value is $60,000 in January, $150,000 in April, $240,000 in July and $150,000 in October. Air is cheaper in June, July and August. Across all twelve monthly shipments, air totals $54,051 and sea totals $48,921, so sea costs $5,131 less for the full year. Taking the lower mode cost in each month totals $47,940, which is $981 below the all-sea annual total.

Twelve shipments worth $60,000 make $720,000 of annual value. Sea leaves $67,068.49 in transit and air leaves $11,835.62. At 12% those stocks cost $8,048.22 and $1,420.27 a year. A spread of 2 days asks for 1.64 days of air cover worth $3,244.64, while 10 days asks for 8.22 days of sea cover worth $16,223.21. Their annual holding costs differ by $1,557.43.

On the bulk consumables scenario, 42 revenue tonnes make sea freight $8,190 and 9,000 chargeable kg make air freight $27,900. Holding 20% back for air makes the split total $12,341.10 against $8,439.86 for sea, a reaction premium of $3,901.23.

What this does not model

Holding cost at destination once the goods arrive, the timing difference in when duty and VAT fall due, demurrage and detention, insurance premium differences between modes, the reliability difference between a schedule and an actual arrival, carbon, and the fact that an air booking can be made later than an ocean booking, which is often the real reason air is chosen. The year view is a smooth scenario built from the low value, peak uplift and peak month you set. It is not a demand forecast. Its month-by-month comparison excludes mode-switching work, minimum allocations, annual rate commitments, capacity availability and booking lead times. It also excludes a demand distribution, the expected value of information, a probability of arriving by a date, obsolescence and shortage exposure. The reaction premium prices only the transport and capital terms entered above.

The whole record prints. Your browser can save it as a PDF instead of printing it.

Decision-support arithmetic on figures you supply.

Related

Air and sea breakeven: the point where speed pays for itself

Shipment

Current shipment
Value
$60,000Gross
800 kgVolume
6.0 m³Chargeable
1,002 kg

Quotes as priced

Air quote
USD per kg, kg, USD: 4.20×1,002=4,2084.20 \times 1{,}002 = 4{,}208
Sea quote
USD, flat quote: 2,400=2,4002{,}400 = 2{,}400

Decision

Breakeven and current side
Breakeven
$196,448Current
$60,000 · SeaTotals and gap
Air $4,327 · Sea $3,071 · Gap $1,256

Costs outside the quotes

Separate cost lines
Capital in transit: Air $118 · Sea $671Date exposure: $0.00 · no hard dateAnnual capital rate: 12.0%Annual pipeline carrying cost: Air $1,420 · Sea $8,048

Transit spread used

Transit inputs
Air 6 days · Sea 34 days · spread 28 days · range around quotes: Air 2 days, Sea 10 days

Decision-support arithmetic on figures you supply.

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