Allotments vs spot

How it works

Background

Cargo airlines sell much of their space months ahead as allotments (block space agreements): a forwarder commits to a number of kilos on every flight at a fixed contract rate. The rest goes on the spot market, one shipment at a time, at whatever the market pays that week. Allotments steady the revenue, but they lock in a rate that can look cheap when the market jumps, and forwarders often hand back space they don't need, sometimes too late to sell again. The page simulates one weekly freighter over a 26-week season, a thousand times, for every allotment share from 0% to 100%.

The lane

One weekly freighter rotation with 100 tonnes of payload (weight only; volume and density are ignored), over a 26-week season from July to December, week 1 to week 26. A share a of the capacity, A = a × 100 t, is sold as allotments at the contract rate r. The rest, plus any allotment space released back, is sold on the spot market. The carrier takes the spot rate as given: it sells as much spot space as there is demand for, at that week's market rate.

The spot market

A market factor x follows a mean-reverting random walk with occasional jumps: x_t = φ x_t−1 + σ ε_t + J_t, with ε standard normal, σ the weekly volatility and φ the persistence (0.85 in most scenarios, 0.90 in the 2020–21 one). A shock J hits with the weekly probability shown, is up or down (up 60% of the time, 75% in 2020–21) and moves the market by 70% to 130% of the shock size, then fades as x reverts. The spot rate is S_t = S̄ (1 + p_r h_t) e^x_t, where S̄ is the typical rate, p_r the peak uplift and h_t a hump from 0 to 1 and back over weeks 15 to 25, highest in week 20. Spot demand for this flight is d × 100 t × (1 + p_d h_t) e^x_t, with 15% lognormal noise: rates and volumes rise and fall together because both follow the same market.

The forwarders

Each week the allotment holders have cargo F_t = A × n × (market level)^0.7, with 12% noise, where n is the forwarders' average cargo as a share of their allotment. When spot is cheaper than what the allotment costs them, they move part of it to the spot market: the share moved is 2 × (r_eff − S_t) / r_eff, capped at 80%, where r_eff = r × (1 − use-it-or-pay share) is the price they avoid by not using the space. So a use-it-or-pay clause both earns a fee and keeps forwarders on the allotment. They use min(A, cargo kept). Of the space they don't use, the "returned late" share (40% by default, varying week to week) is only handed back after the 72-hour cut-off.

Use-it-or-pay: the forwarder pays the chosen share of the contract rate on unused space beyond a 10% tolerance: u × r × max(0, unused − 0.1 A). Contracts differ; some waive the fee on space returned before the cut-off, which this page doesn't.

The release rules

• Hold: allotment space stays with the forwarder until departure. Anything unused flies empty.
• Release at 72 h: space the forwarder hasn't booked by the cut-off goes back on sale. Only the space returned in time can be resold, and only if there is spot demand left for it.
• Release + resell: as above, and the carrier also sells ahead the space it expects to be returned late, taken as the average late return of the previous four weeks. When forwarders turn up anyway, the extra spot cargo is offloaded, earning nothing and costing the offload cost ($1 per kg by default: rebooking, trucking and goodwill). It is the cargo version of overbooking.

Revenue and the two optima

Weekly revenue = r × allotment kilos flown + spot rate × spot kilos flown + use-it-or-pay fees − offload costs. Season revenue is the sum over 26 weeks. For each share from 0% to 100% in steps of 5%, the page runs the same 1,000 seasons (common random numbers, fixed seed), so differences between shares come from the decision, not from luck. The risk-neutral best maximises average season revenue. The risk-averse best maximises the average of the worst 10% of seasons (the conditional value at risk at 10%), a standard way to put a floor under a result. The week-by-week view shows one of the 1,000 seasons: it opens on the one whose average spot rate is the median, and "Show another season" steps through the others. Costs of flying the freighter are the same whatever the mix, so revenue is enough to compare shares.

Sources

• Kasilingam, R. (1997), "Air cargo revenue management: characteristics and complexities", European Journal of Operational Research 96(1): why cargo capacity is sold partly under allotments and why it is harder to manage than seats.
• Levin, Y., Nediak, M. and Topaloglu, H. (2012), "Cargo capacity management with allotments and spot market demand", Operations Research 60(2), 351–365: the allotment and spot problem this page simplifies.
• Littlewood, K. (1972), "Forecasting and control of passenger bookings", AGIFORS Symposium; reprinted in the Journal of Revenue and Pricing Management 4, 2005.
• Rate levels, for scale only: the base case's typical spot rate of $4.00/kg and contract rate of $3.40/kg are invented to sit in the range of the public long-haul index levels quoted in the context panel above (links there, checked 30 September 2026). They are not any lane's actual rates.

Limitations

• One flight and one direction. Real allotment decisions cover a network, with backhauls that are much weaker than the main direction, and forwarders who negotiate allotments across many flights at once.
• Weight only. Real cargo is limited by volume and by the position of pallets and containers too, and dense and light shipments are priced differently.
• The contract rate is taken as given. In practice a carrier offering a no-show penalty or a short release deadline has to accept a lower rate, and the forwarders' response to the market is a simple rule here, not a negotiation.
• The carrier takes the spot rate as it comes. A real cargo RM system also chooses which spot bookings to accept, by rate and density, against a bid price (RM 101, chapter 04).
• No express, mail, dangerous goods or other priority products, and no belly cargo on passenger flights, where the space left depends on passengers' bags.

This is a personal project and isn't affiliated with any airline.