Revenue management for Python: the building blocks for selling fixed, perishable capacity well. Single-leg seat protection, overbooking, pricing, network bid prices and the standard performance metrics, computed from the textbook methods and validated against published worked examples.
The core has no third-party dependencies. Every result carries provenance
(library version, input hash, timestamp) and a JSON-safe to_dict().
With revmng[plot] installed, each method also has a chart in a clean, neutral style:
pip install revmngimport revmng
# Two-class seat protection (Littlewood's rule)
revmng.littlewood(fare_high=1000, fare_low=400, mean_high=50, sd_high=18)
# -> protect this many seats for the high fare; sell the low fare below it
# Multi-class nested booking limits (EMSR-b, the industry-standard heuristic)
a = revmng.emsr_b(
[(1000, 30, 12), (700, 40, 15), (400, 60, 20)], # (fare, demand mean, sd)
capacity=120,
)
a.booking_limits_int # nested whole-seat booking limits
print(a.summary())
# Overbooking: balance the cost of bumping against the cost of empty seats
o = revmng.overbooking_limit(100, no_show_rate=0.12,
denied_cost=400, spoilage_cost=180)
o.authorization_limit # how many reservations to accept
# Pricing: the newsvendor stocking quantity and the profit-maximising price
revmng.newsvendor(price=10, cost=4, demand_mean=100, demand_sd=30).optimal_quantity
revmng.optimal_price(revmng.LinearDemand(intercept=100, slope=2), unit_cost=10)
# Score booking limits against perfect-hindsight and no-control benchmarks
revmng.revenue_opportunity([1000, 800, 600, 200], [25, 30, 20, 50], capacity=100,
booking_limits=[100, 70, 45, 32]).rom
# Exact optimal protection levels (and the expected revenue EMSR leaves behind)
opt = revmng.optimal_protection_levels(
[(1000, 30, 12), (700, 40, 15), (400, 60, 20)], capacity=120)
opt.expected_revenue
# Should we take this group? (displacement analysis)
cost = revmng.group_displacement(group_size=30, capacity=100,
demand=[70, 95, 85], value_per_unit=70)
revmng.evaluate_group(group_rate=60, units=90, displacement_cost=cost,
variable_cost=50).accept
# Should we accept this multi-night stay? (length-of-stay bid-price control)
revmng.evaluate_stay({"Mon": 80, "Tue": 120, "Wed": 90},
["Mon", "Tue", "Wed"], total_rate=320).acceptNetwork bid prices need SciPy and the charts need matplotlib:
pip install "revmng[network]" # bid_prices via the deterministic LP
pip install "revmng[plot]" # booking-limit, overbooking and ROM chartsfrom revmng import Product
n = revmng.bid_prices(
[Product(fare=200, uses={"AB": 1}, demand=60),
Product(fare=300, uses={"AB": 1, "BC": 1}, demand=40)],
capacities={"AB": 100, "BC": 100},
)
n.bid_prices # marginal value of each resource
n.accept(fare=250, uses={"AB": 1, "BC": 1})| Area | Functions |
|---|---|
| Single-leg capacity control | littlewood, emsr_a, emsr_b |
| Exact optimal control | optimal_protection_levels, policy_revenue |
| Overbooking | overbooking_limit (service level and cost based) |
| Pricing | newsvendor, optimal_price (LinearDemand, ConstantElasticityDemand) |
| Group evaluation | evaluate_group, group_displacement |
| Length-of-stay | evaluate_stay |
| Performance metrics | revpar, adr, occupancy, yield_, load_factor, rasm, casm, spill, spoilage |
| Revenue opportunity | revenue_opportunity, nested_revenue |
| Network (needs SciPy) | bid_prices, Product |
| Charts (needs matplotlib) | booking_limit_chart, emsr_curve, overbooking_cost_curve, price_curve, newsvendor_curve, revenue_opportunity_chart, bid_price_chart |
optimal_protection_levels computes the exact optimal nested protection levels
by dynamic programming (the policy the EMSR heuristics approximate) and reports
the optimal expected revenue; policy_revenue scores any policy against it.
Group and length-of-stay decisions share one idea: accept a request when its
contribution covers the opportunity cost of the capacity it displaces (a
marginal seat value or a sum of nightly bid prices).
Demand for the capacity-control methods is assumed normal and independent, with the classic low-before-high booking assumption. EMSR-a and EMSR-b are heuristics; for two classes both reduce to Littlewood's optimal rule.
revmng computes decisions from the demand you supply. It does not forecast demand, estimate willingness-to-pay, or unconstrain censored bookings, and it does not connect to any reservation, property-management or distribution system. Those belong upstream; keeping them out is what lets every result here be reproduced and audited.
The methods are checked against published and hand-derived worked examples (see
tests/validation_cases.json):
| Method | Source | Result |
|---|---|---|
| Littlewood booking limits | Phillips, Pricing and Revenue Optimization (2005), Ex. 9.2 | 25 / 50 / 76 reproduced |
| Revenue opportunity metric | Phillips (2005), Ex. 9.7 | perfect 66000, no-control 46000, realized 59200, ROM 66% |
| EMSR-b (two classes) | Belobaba (1989) | equals Littlewood's optimal rule |
| EMSR-b (three classes) | Belobaba (1989) formula, arithmetic shown | protection 23.71 / 70.83, limits 97 / 50 |
| Optimal control (DP) | Talluri and van Ryzin (2004) | matches Littlewood for two classes; expected revenue at least EMSR-b's |
| Group displacement | standard displacement analysis, arithmetic shown | 40 displaced room-nights, cost 2800, break-even rate 81.11 |
| Length-of-stay bid price | Talluri and van Ryzin (2004), arithmetic shown | 290 hurdle, accept at rate 320 |
| Newsvendor quantity | critical-fractile rule | reproduced |
| Overbooking (service level) | deterministic no-show formula | reproduced |
A clean multi-class EMSR-b worked example with both inputs and outputs is hard to
find in the open literature, so the heuristics are also cross-checked two
independent ways (tests/test_crosscheck.py): their protection levels match a
separate SciPy implementation of the same formulas to 1e-9, and over many random
instances EMSR-b never exceeds revmng's exact dynamic program and stays within
about 0.5% of it, matching Belobaba's reported near-optimality.
- K. Littlewood, "Forecasting and control of passenger bookings" (1972).
- P. Belobaba, "Application of a probabilistic decision model to airline seat inventory control," Operations Research (1989). EMSR-a and EMSR-b.
- K. Talluri and G. van Ryzin, The Theory and Practice of Revenue Management (2004).
- R. Phillips, Pricing and Revenue Optimization (2005).
revmng-mcp exposes these revenue-management decisions and charts to AI agents over the Model Context Protocol.
MIT. Written and maintained by Atakan Arikan, MSc Student at Tsinghua University and Politecnico di Milano.