RateHighwayPROJECT APOGEEMenu
Harrison Schmitt during EVA on the lunar surface, Apollo 17.

Designation NB-05 · Lab notebookCar rental only

Length of rent as an instrument.

This notebook studies how rental durations shape fleet availability across the week. It is more than a discount schedule. This is research, not a product.

AS17-134-20384 · Schmitt EVAApollo 17, 13 December 1972. NASA. Public domain.

Notebook · not a stay-through list

Length of rent (LOR) is a standard car rental measure. Short rentals have more fixed cost per day. Long rentals may receive a volume discount. An average can hide the difference between a one-day and a seven-day rental. Stay-through rules can reject a short rental that would block a longer, higher-value rental. This notebook asks a broader question: how should the mix of rental lengths shape fleet availability across the whole week?

A rental is an interval

Utilization is not only a count on the pickup day. A rental that started Monday still uses a car on Thursday. RateHighway already compares peak and average utilization across a rental. This notebook asks whether rental lengths can actively shape the utilization pattern U(t) instead of being treated only as steps in a discount schedule.

A one-day online travel agency (OTA) rental on Friday may block a more valuable weekend rental. A weekly rental may cover days with weak demand and contribute more than several short rentals sold too cheaply. The goal is to choose which rental periods to accept, and in what proportions, before the week is filled.

RateMonitor already separates LOR segments. Related locations can follow a parent, and each rental length can have its own price floor and ceiling. The research must go beyond a more detailed discount table. The operator should be able to see how each rental length changes availability on the days it occupies.

Not a ladder

A discount ladder assumes that longer rentals should follow one price schedule. But a one-day downtown rental and a weekly airport rental can come from different demand patterns while using the same cars. Each rental also has a pickup and return location. The mix of rental lengths is therefore a flow through time and locations, not only a list of discounts.

If nearly all demand in a fleet pool has the same rental length, this method may add no value. In that case, RateMonitor should continue to use the rules configured by the operator. The laboratory should not create a product to solve a problem that is not present.

A direction, not a paper

The mathematics we are exploring

Represent utilization as a function of time. Represent each rental as an interval across the days it occupies. Choose the mix of rental lengths to shape availability across the week, not only to move down a discount table.

U : [0, T] → [0, 1] utilization as a function of time A rental i is a strip 1_{[s_i, s_i + ℓ_i)} U(t) = (1 / K_t) ∑_i 1_{[s_i, s_i+ℓ_i)}(t) λ ∈ Δ^{|LOR|} is a mix of lengths, not a ladder d(ℓ) = d_1 − α(ℓ − 1) the thing we are not doing Choose λ (and accept/reject by ℓ) to shape U(·): max_{λ, a} J(r, U[λ, a], λ) s.t. U(t) ≤ 1 stay-through, one-way incidence, melt-by-type a_ℓ ∈ {accept, reject, bid} at each lead The week is tiled by intervals. Filling days and then reading the mix off the wreckage is the broken order of sequential RM. Peak vs average over a duration is already a query in the house. Choosing the mix of strips is the further awareness.

U(t)

Utilization on every day, including the days inside each rental period. It is more complete than a count taken only on pickup dates.

λ

The mix of rental lengths, connected to the joint rate-and-utilization score in notebook NB-01. It is not a column of discounts.

1_{[s, s+ℓ)}

One rental from start time s for length ℓ. A one-way rental begins and ends at different locations, so the model must include the fleet network.

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

All notebooks → · The week as one object →