Pricing and revenue management · intercity coach
Managing fares and capacity on a coach route
Advance discounts can reduce departure contribution when they displace full-fare passengers. Decisions on fare availability and additional services require a demand forecast for each departure, including the passengers likely to book later.
Seat allocation and departure costs
In this illustrative coach service, advance discounts increase expected contribution on an off-peak departure and reduce it on a busy departure. Each coach has 50 seats, a $43 standard fare, $3 of servicing cost per passenger, and a $900 departure cost. Before any discount, the busy service attracts demand from 32 advance purchasers and 30 late purchasers. Since demand already exceeds capacity, a promotion changes the passenger mix without increasing the number of passengers who travel.
For a departure the operator has already committed to run, an additional passenger costs $3 to service. If that passenger takes a seat that would otherwise sell at full fare, the operator also forgoes the contribution from the later sale. An average cost per seat obscures this opportunity cost because it assigns the same cost to seats with different prospects of selling. An additional departure, by contrast, incurs a separate operating cost that must be recovered from the passengers the new service adds.
The calculations use departure contribution, defined as ticket revenue less passenger servicing and departure costs. Company overhead and vehicle capital costs are excluded. This measure allows the operator to assess a promotion across the full booking window and compare an additional departure with the existing schedule.
Advance discounts on a capacity-constrained departure
A 20% advance discount reduces the fare to $34.40. Under the assumed advance-demand elasticity of minus 1.6, early bookings increase from 32.0 to 45.7. Total passengers remain at 50, while late bookings decline from 18.0 to 4.3. The additional advance customers replace full-fare customers because both groups compete for the same seats.
Departure contribution declines from $1,100 to $706.72. The chart attributes the change to additional early sales valued at the original fare, the fare reduction across all advance bookings, and the revenue lost on displaced late sales. At the original fare, the additional early sales and displaced late sales have equal values and cancel. The $393.28 reduction in contribution therefore equals the discount across the enlarged advance segment. Passenger servicing costs remain unchanged because passenger volume remains unchanged. A measure of advance conversion or advance-segment revenue would omit the lost late sales and could support a promotion that reduces total departure revenue.
Contribution effect of a busy-service discount
A 20% advance discount on a 50-seat departure with open inventory. Starting and ending values show total departure contribution.
View chart data · $
| Component | $ |
|---|---|
| No discount | 1,100 |
| Additional early sales | 590.41 |
| Advance fare reduction | -393.28 |
| Displaced late sales | -590.41 |
| Passenger costs | 0 |
| 20% discount | 706.72 |
Discounts on services with unused capacity
The off-peak departure initially has 18 advance and 12 late passengers. At a 36% advance discount, expected advance passengers increase to 36.8 and total passengers reach 48.8. Contribution increases from $300 to $481.37 because the contribution from additional passengers exceeds the fare reduction granted to customers who would have booked without the promotion.
Further discounts reduce contribution as the coach approaches capacity. At a 38% discount, contribution declines to $468.03 because some additional advance sales displace late passengers. At 40%, contribution falls to $398.93. Estimating demand response without applying the seat limit would miss this decline. The operator needs the expected late bookings as well as the advance-demand curve to estimate the revenue forgone through displacement.
The 36% discount produces the highest contribution on the tested grid, which uses two-percentage-point intervals. Its performance depends on the assumed demand response and unused capacity. Applying it to the busy departure with open inventory reduces contribution to $326. The off-peak result consequently supports a promotion restricted to departures with sufficient unsold capacity and limited later demand. It provides no basis for applying the discount across the route.
Departure contribution at different advance discounts
Busy and off-peak demand, with open inventory or seats reserved for late bookings. Contribution deducts passenger servicing and one departure cost.
View chart data · $
| Advance discount (%) | Busy, open inventory | Busy, 30 late seats protected | Off-peak, open inventory |
|---|---|---|---|
| 0 | 1,100 | 1,100 | 300 |
| 2 | 1,071.58 | 1,082.8 | 307.67 |
| 4 | 1,041.25 | 1,065.6 | 315.55 |
| 6 | 1,008.85 | 1,048.4 | 323.66 |
| 8 | 974.21 | 1,031.2 | 332 |
| 10 | 937.13 | 1,014 | 340.59 |
| 12 | 897.41 | 996.8 | 349.45 |
| 14 | 854.78 | 979.6 | 358.57 |
| 16 | 809 | 962.4 | 367.98 |
| 18 | 759.76 | 945.2 | 377.69 |
| 20 | 706.72 | 928 | 387.71 |
| 22 | 649.51 | 910.8 | 398.07 |
| 24 | 587.7 | 893.6 | 408.77 |
| 26 | 541 | 876.4 | 419.84 |
| 28 | 498 | 859.2 | 431.29 |
| 30 | 455 | 842 | 443.15 |
| 32 | 412 | 824.8 | 455.43 |
| 34 | 369 | 807.6 | 468.17 |
| 36 | 326 | 790.4 | 481.37 |
| 38 | 283 | 773.2 | 468.03 |
| 40 | 240 | 756 | 398.93 |
Allocating seats to later demand
Reserving 30 seats for late demand limits the busy departure to 20 advance sales. At a 20% discount, contribution is $928, an improvement of $221.28 over the $706.72 under open inventory. Seat protection preserves more full-fare revenue, although contribution remains below the $1,100 earned without a discount. Although reserving seats reduces the loss from the promotion, maintaining the standard fare produces the highest contribution in this scenario.
A reserve can also forgo a discounted sale without securing a later customer. At the 20% discount, an advance passenger contributes $31.40 after servicing, compared with $40 from a full-fare passenger. If the alternatives are a certain advance sale or a single possible later sale, reserving the seat yields greater expected contribution only when the probability of a later sale exceeds 78.5%. The calculation assumes no subsequent opportunity to resell the seat and no other difference between the passengers. As departure approaches, the operator should revise the reserve against the remaining demand forecast. The assumed allocation of 30 seats is justified only to the extent that the forecast supports those later bookings.
Demand required for an additional departure
Adding a departure changes the cost and capacity calculation. With a 15% advance discount and higher-fare late demand protected, reference demand would produce 71.5 passengers if sufficient capacity were available. A second coach permits 21.5 additional passengers and generates $721.43 of incremental contribution before its operating cost. At a $900 departure cost, the additional service reduces total contribution by $178.57. Existing excess demand is therefore insufficient to justify the proposed service at that cost.
At 1.1 times reference demand, the added capacity generates $961.32 before the second departure cost and increases contribution by $61.32 after that cost. Break-even occurs at approximately 1.074 times reference demand. The cost ceiling in the chart gives the maximum operating expenditure the additional passenger contribution can recover at each demand level. The calculation compares the full capacity alternatives with the same fare policy and protection of late demand in both cases.
The expected gain at 1.1 times reference demand is sensitive to a small forecasting error. Losing two incremental advance passengers reduces contribution by $67.10 and eliminates the $61.32 gain. The calculation also assumes passengers will accept either departure time. If a proposed timetable divides existing demand between services without attracting the expected additional passengers, the operator incurs the second departure cost with less incremental revenue. Approval therefore requires a demand estimate for the proposed departure time, including the transfer of passengers from the original service. The pooled-capacity result alone cannot establish that estimate.
Break-even operating cost for an additional departure
A 15% advance discount, with higher-fare late demand protected in both capacity alternatives. Additional service increases contribution when its operating cost is below the curve.
View chart data · $
| Demand versus reference (x) | Break-even operating cost | $900 departure cost |
|---|---|---|
| 0.8 | 241.64 | 900 |
| 0.9 | 481.53 | 900 |
| 1 | 721.43 | 900 |
| 1.1 | 961.32 | 900 |
| 1.2 | 1,201.21 | 900 |
| 1.3 | 1,441.1 | 900 |
| 1.4 | 1,677.5 | 900 |
| 1.5 | 1,677.5 | 900 |
| 1.6 | 1,677.5 | 900 |
| 1.7 | 1,683.95 | 900 |
| 1.8 | 1,703.3 | 900 |
| 1.9 | 1,722.65 | 900 |
| 2 | 1,742 | 900 |
| 2.1 | 1,761.35 | 900 |
| 2.2 | 1,780.7 | 900 |
Full original scenario grid
| Second departure cost ($) / Demand versus reference | 0.8x | 0.9x | 1.0x | 1.1x | 1.2x | 1.3x | 1.4x | 1.5x | 1.6x | 1.7x | 1.8x | 1.9x | 2.0x | 2.1x | 2.2x |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 600 | -358.36 | -118.47 | 121.43 | 361.32 | 601.21 | 841.1 | 1,077.5 | 1,077.5 | 1,077.5 | 1,083.95 | 1,103.3 | 1,122.65 | 1,142 | 1,161.35 | 1,180.7 |
| 700 | -458.36 | -218.47 | 21.43 | 261.32 | 501.21 | 741.1 | 977.5 | 977.5 | 977.5 | 983.95 | 1,003.3 | 1,022.65 | 1,042 | 1,061.35 | 1,080.7 |
| 800 | -558.36 | -318.47 | -78.57 | 161.32 | 401.21 | 641.1 | 877.5 | 877.5 | 877.5 | 883.95 | 903.3 | 922.65 | 942 | 961.35 | 980.7 |
| 900 | -658.36 | -418.47 | -178.57 | 61.32 | 301.21 | 541.1 | 777.5 | 777.5 | 777.5 | 783.95 | 803.3 | 822.65 | 842 | 861.35 | 880.7 |
| 1000 | -758.36 | -518.47 | -278.57 | -38.68 | 201.21 | 441.1 | 677.5 | 677.5 | 677.5 | 683.95 | 703.3 | 722.65 | 742 | 761.35 | 780.7 |
| 1100 | -858.36 | -618.47 | -378.57 | -138.68 | 101.21 | 341.1 | 577.5 | 577.5 | 577.5 | 583.95 | 603.3 | 622.65 | 642 | 661.35 | 680.7 |
| 1200 | -958.36 | -718.47 | -478.57 | -238.68 | 1.21 | 241.1 | 477.5 | 477.5 | 477.5 | 483.95 | 503.3 | 522.65 | 542 | 561.35 | 580.7 |
| 1300 | -1,058.36 | -818.47 | -578.57 | -338.68 | -98.79 | 141.1 | 377.5 | 377.5 | 377.5 | 383.95 | 403.3 | 422.65 | 442 | 461.35 | 480.7 |
| 1400 | -1,158.36 | -918.47 | -678.57 | -438.68 | -198.79 | 41.1 | 277.5 | 277.5 | 277.5 | 283.95 | 303.3 | 322.65 | 342 | 361.35 | 380.7 |
Booking evidence for fare and timetable decisions
The operator needs a booking history for each departure that records fare availability, changes to seat limits, and the time at which the service sold out. Sales after a fare closes or a service reaches capacity are constrained by availability. Treating recorded sales as the full level of demand understates demand by excluding customers who were unable to book and can distort both the late-seat reserve and the demand forecast for another departure.
Fare decisions should use the latest estimate of remaining demand. When late demand weakens on a committed departure, a discounted booking can add contribution after servicing cost. When full-fare demand remains probable, restricting advance availability preserves seats for those passengers. The case for an additional departure requires a further comparison of incremental passenger revenue and servicing costs with the cost of operating the proposed schedule. For the illustrated expansion at 1.1 times reference demand, the $61.32 expected gain makes the timetable assumption material to approval.
The assumptions and exclusions below define the worked scenario.
Model notes and assumptions
- One departure has 50 seats; undiscounted fare is $43 for both segments.
- Busy reference demand is 32 advance and 30 late passengers; off-peak demand is 18 advance and 12 late passengers. Fractional expected passengers are allowed.
- Advance demand follows constant elasticity of -1.6 against the $43 reference fare; late demand and fare do not change.
- One departure costs $900; passenger servicing costs $3 per passenger. The full scenario grid varies the incremental second-departure cost from $600 to $1,400.
- Protected-seat scenarios reserve up to forecast late demand. Capacity comparison assumes perfect demand foresight and passenger acceptance of either departure.
All numerical inputs are assumptions, not measured client results or externally verified market facts.
No demand uncertainty, no-shows, competitor response, taxes, depot overhead, vehicle capital charge, or schedule-specific demand penalty. Contribution is not company net profit.
The analysis covers one route. A network estimate would require route-level demand, service costs and fare policies.