How many units should you own?

Money

The cost of owning a unit is what it costs you whether or not it is out: depreciation or finance, storage, insurance, upkeep.

How bookings arrive

Add your seasons and rental lengths, then click Find the best fleet size.

Result

Yearly profit by fleet size

Each season at the recommended fleet (Erlang B)

If demand is different from what you typed

How it is calculated

Offered load: requests per day times the average rental length, in units. Erlang B: with c units and offered load a, the share of requests turned away is B(c) from B(0) = 1 and B(c) = a·B(c−1) / (c + a·B(c−1)). It depends only on the average rental length, not on how lengths vary. Each season is computed on its own and summed, because the fleet is fixed while demand is not. Day-by-day simulation: each day draws a number of requests (Poisson, or negative binomial when clustering is above 1), each request draws a rental length from your mix and takes a free unit or is turned away. Units come back on the day after the last rental day and can go out again that day. Every fleet size sees the same simulated years from a fixed seed, one warm-up year is discarded, and the table shows the mean year and the 10th-percentile year. Profit: price × rental days − cost per rental × rentals − cost of turning a customer away × turn-aways − units × yearly cost of owning one. Recommendation: the fleet size with the highest mean profit, or the smallest size meeting your turn-away limit if that is larger. Calendar-booked rentals use the simulation; any-hour rentals use Erlang B.

Not modelled: different unit types, damage, theft or units out for repair, deposits, delivery routes and staff, taxes and financing, resale value, waiting lists or customers who come back later, and rentals that cross the year boundary (revenue is counted when a rental starts). Unverified: tested against hand-calculated Erlang values, an exact one-day-rental formula and a repeatable simulation, not on a real rental business's books. It does not tell you what to charge or which unit to buy.

Common questions

How many units should a small rental business own?

As many as still pay for themselves. Each extra unit rescues fewer requests than the one before it, because it is only needed on the few busiest days, while it costs the same to own every day of the year. The table in this tool shows the yearly profit of every fleet size from one upward and marks the size after which the next unit earns less than it costs to own.

Why not just buy enough for the busiest weekend?

Because the busiest weekend is a handful of days and the unit sits in the shed for the rest of the year. A unit needs a minimum number of rental days a year to cover its cost; the tool prints that number from your own price and costs. When the last unit you are considering would be out fewer days than that, it loses money even though every request in the peak would have been served.

What is the difference between Erlang B and the day-by-day simulation?

Erlang B is the classic formula for the share of requests turned away when every unit is busy. It assumes requests arrive at any moment and a unit is only free once it is back. The simulation books by calendar day, so a unit returned on a day can go out again that day, and it can model bookings that cluster. Calendar-booked rentals such as a tent for Saturday sit closer to the simulation; hourly or walk-up rentals sit closer to Erlang B. The tool computes both and lets you choose which drives the recommendation.

What does the booking clustering setting do?

It sets how much busier and quieter than average the days are, as a variance-to-mean ratio. At 1, requests arrive independently. At 2 or 3, a day's requests swing more widely around the average, as they do when weather, holidays or a single event drive bookings. Clustering turns away more customers at the same fleet size, so the best fleet and the bad-year figures both move.

Can I set a limit on how many customers I turn away?

Yes. Enter the largest share of requests you are willing to turn away, and the recommendation becomes the larger of the most profitable fleet and the smallest fleet that meets the limit. The result says what the limit costs you in a year, so you can see the price of the promise before making it.

What does it not model?

It treats the units as identical and the demand as figures you type. It does not model different unit types, damage or theft, units out of service for repair, deposits, delivery routing, staff, taxes, financing or the resale value of a unit. The yearly cost of owning a unit is a number you supply, so include depreciation, storage, insurance and upkeep in it.

Is my data uploaded?

No. Everything runs in your browser from the figures you type, nothing is sent to a server, there are no accounts, and it works offline after the page loads.