Quincus

Pricing and yield

Capacity is perishable. Price it accordingly.

Cargo capacity is a two dimensional constraint, weight and volume, sold across a network of connecting resources. That makes pricing a network revenue management problem rather than a rate card lookup.

LIVE

Price a quote

$679$1159$1639$2120$2600$30801.00.80.60.40.20.0Win probabilityExpected contributionoptimumrate cardPrice ($)

At 60% utilization, the revenue optimum sits 9.9% below the rate card. Quoting the card wins less than it should and forfeits about $33 of expected contribution per quote.

Optimal price$1351
Win prob at optimum50.0%
Bid price floor$1131
Displacement$231
Expected contribution$110
Delta vs rate card$33 · 42.5%
Rate card win prob20.9%
Runs in your browser on a simplified version of the production method. Illustrative of behavior, not of production performance.

The problem class

Where the money leaks.

01

Two dimensional capacity, weight and volume.

Every acceptance consumes both. Neither one alone is a sufficient booking constraint.

02

Network displacement across connecting resources.

Taking a booking on one leg prices out capacity on the legs that connect through it.

03

Quote-level win probability.

The customer's decision is stochastic. Price setting has to account for the acceptance curve.

The method

How each quote is priced.

Bid price control
accept iffiAπi\text{accept if} \quad f \ge \sum_{i \in A} \pi_i

Each resource on the itinerary carries an opportunity cost pi, taken from the dual of the capacity constraint in the network linear program. A request is accepted only when the fare clears the sum of what that capacity is worth elsewhere. Displacement is priced explicitly rather than discovered at month end.

Conversion and expected revenue
Pr(winp,x)=11+e(β0+β1p+βx)R(p)=pPr(winp,x)\Pr(\text{win} \mid p, x) = \frac{1}{1 + e^{-(\beta_0 + \beta_1 p + \beta^\top x)}} \qquad R(p) = p \cdot \Pr(\text{win} \mid p, x)

Win probability is estimated per segment from quote and award history, conditioned on lane, commodity, customer, and lead time. The revenue optimum sits where marginal revenue meets marginal displacement cost, which is rarely where the rate card sits.

Protection levels
p2=p1Pr(D1>y)p_2 = p_1 \cdot \Pr(D_1 > y^*)

Nested booking limits protect high yield capacity from early low yield consumption. The classical result generalizes to the multi-resource case through the bid price surface above.

What this changes

What changes at the quote.

  1. 01

    Displacement priced at quote time rather than discovered at month end.

  2. 02

    Rate cards become a floor, not the answer.

  3. 03

    Yield decisions that survive audit because the opportunity cost is explicit.

Where it runs

Sectors that lean on this capability.

If your network makes decisions under uncertainty, we should talk.

We work with a small number of operators at a time. Tell us what your network is optimizing for.

Start a conversation