RateHighwayPROJECT APOGEEMenu
Saturn V on the crawlerway leaving the Vehicle Assembly Building.

Designation NB-03 · Lab notebookCar rental only

The fleet as a network.

This notebook studies cars, locations, and one-way rentals as movement through a network. It is research, not a product.

S69-17485 · CrawlerwaySaturn 504 leaving the VAB, Kennedy Space Center, 1968–69. NASA. Public domain.

Notebook · not a shuttle scheduler

Revenue management usually prices each location. Fleet teams move cars. These groups work on different schedules and use different goals. Utilization is usually measured for one location, vehicle class, and date. This notebook asks whether pricing on Thursday at location A should also consider that the car may be missing from location B on Friday.

A strip has two ends

A rental occupies several days. A rental that started Monday still uses a car on Thursday. RateHighway already compares peak and average utilization across a rental. It also groups locations and vehicle classes when those groups are meaningful. One-way rentals are movement into or out of the operator’s network. A location full of one-way returns is different from a location full of local weekend rentals.

A child location may follow a parent location’s pricing, but this does not mean their cars move as one fleet. Empty transfers follow an operations schedule; prices follow a shopping schedule. RateMonitor applies prices, but it does not always know that accepting a one-way vehicle on Thursday changes the fleet at another location on Friday.

“This location is 92% utilized” is therefore incomplete. Which rental paths created that utilization? A car used at location A today may be unavailable at location B tomorrow. A one-way fee can help guide movement that the network needs. The research question is how to price for the fleet that will exist after the cars move.

Conservation, not a percentage

Treat locations as points in a network and one-way rentals as directed connections between them. Round trips use a car for several days at one location. Upgrades connect vehicle classes. Melt—bookings that cancel or do not arrive—removes expected rentals; walk-up demand adds rentals late. The model must respect real ownership and operating boundaries. If two locations do not share cars, they must not be treated as one pool. If almost all rentals return to the same location, a network model may add cost without adding value.

The model can also become too large to calculate or explain. It should not represent every vehicle code, hour, and franchise boundary unless those details change the decision. This notebook is not a national transfer planner. It asks whether the value of a car depends on both its location and its time, and whether RateMonitor can apply a decision based on that value while the operator remains in control.

A direction, not a paper

The mathematics we are exploring

Use a network that includes location, vehicle class, and day. Cars must be conserved as rentals and transfers move them through the network. Measure utilization as flow through the relevant group of locations. Price the fleet that will exist after the movement, not only the fleet visible now.

G = (V, E) V = stations × class × day E = round-trips ∪ one-ways ∪ empty transfers ∪ upgrades At node v ∈ V, conservation (in expectation, after melt): ∑_{e ∈ δ⁻(v)} f_e − ∑_{e ∈ δ⁺(v)} f_e + fleet_v = 0 Utilization as a current on a cut C ⊂ V: U(C) = flow(C) / capacity(C) Bid on a node — the lot you will have after cars move: b_v = ∂J / ∂fleet_v A one-way fee on edge (i → j) is a price on f_{ij}, not a recovered cost. Accepting a strip 1_{[s, s+ℓ)} at i occupies a path of days and, if one-way, a different vertex at s+ℓ. RateMonitor remains the house: it executes r inside [r̲, r̄]. The notebook asks whether r_v already sees b_w for w reachable from v on the graph of the week.

G = (V, E)

Locations are vertices. One-way rentals and transfers are flows between them. Movement beyond the owned network is represented as a boundary, not as missing data.

U(C)

Utilization for a meaningful group of locations. Utilization at one location is the simplest special case.

b_v

The additional value of one car at a specific location and time. It is valid only when the grouped locations truly share cars.

This is a research notebook. It is not an announced product or release. The operator still decides.

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