Spare engines: service level against idle days
A spare engine is an expensive asset that is idle most of the time, and a shortage grounds an aircraft. This build uses an invented fleet. Change removals, shop turn time and the service level, and see how many spares are needed, how many idle days that leaves and what the capital costs.
What this shows
- Spares needed for a service level, from the chance of engines being in the shop
- Idle spare-days a year and the capital each spare ties up
- A repair, lease or buy comparison for the next spare
- A ranking of which engine to repair first when shop slots are limited
How I use it
- Deciding how many spares to hold and what each extra one costs
- Showing the cost of a higher service level in dollars of capital
- Choosing which engine goes to the shop first
Explore the model below. It uses an invented company and invented numbers.
Explore the model
Illustrative model · Synthetic dataWide tables scroll sideways: swipe inside a table to see every column.
Sample build: spare engines for an invented airline
Quillhaven Air is an invented airline. Engines come off its aircraft, spend weeks in a repair shop and come back, and spare engines cover the gap. A spare is an expensive asset that sits idle most of the time, and a shortage grounds an aircraft. The build finds how many spares cover a service level, prices the idle days and the capital, compares repair, lease and buy for the next spare, and ranks which engine to repair first.
Invented airline and invented round numbers for illustration. Not data from any employer.
What to try
- Raise the service level toward 99.9% and watch the spares, the capital and the idle spare-days. The last few points of service cost the most.
- Lengthen the shop turn time. More engines are in the shop at once, so more spares are needed.
- Change the value of one engine. The number of spares does not move, but the capital does.
- On the Repair, lease or buy tab, move the horizon from 1 year to 10 and watch the cheapest option change.
- On the Repair order tab, cut the budget and watch a costly engine give up its slot to a cheaper one.
Shop turn time is the days one removed engine spends in the shop. Service level is the share of days on which no aircraft waits for an engine. Idle spare-days are the spares held beyond the average number in the shop, times 365.
Engines in the shop, average
4.0
Removals times shop days, over 365
Spares needed
8
Cover 97.9% of days
Capital tied up
$58.4M
$7.3M in each spare
Idle spare-days a year
1,460
4.0 idle spares, times 365
Carrying cost per idle day
$2,000
Engine value at 10.0%, over 365
Cost of idle days a year
$2.92M
Of $5.84M for the whole pool
The number of engines in the shop changes from day to day around its average. Each bar is the chance that exactly that many are in the shop. Teal bars are covered by the spares held. Magenta bars are not, so an aircraft would wait for an engine. The service level is the share of days that land on a teal bar.
8 spares cover 97.9% of days. With 7 spares the cover would be 94.9%, short of the 95.0% target.
| Engines in the shop | Chance | This many or fewer | Covered |
|---|---|---|---|
| 0 | 1.8% | 1.8% | Yes |
| 1 | 7.3% | 9.2% | Yes |
| 2 | 14.7% | 23.8% | Yes |
| 3 | 19.5% | 43.3% | Yes |
| 4 | 19.5% | 62.9% | Yes |
| 5 | 15.6% | 78.5% | Yes |
| 6 | 10.4% | 88.9% | Yes |
| 7 | 6.0% | 94.9% | Yes |
| 8 | 3.0% | 97.9% | Yes |
| 9 | 1.3% | 99.2% | No |
| 10 | 0.5% | 99.7% | No |
| 11 | 0.2% | 99.9% | No |
| 12 | 0.1% | 100.0% | No |
Spares needed at common service levels
| Service level | Spares | Capital tied up | Idle spare-days a year |
|---|---|---|---|
| 80.0% | 6 | $43,800,000 | 730 |
| 90.0% | 7 | $51,100,000 | 1,095 |
| 95.0% | 8 | $58,400,000 | 1,460 |
| 99.0% | 9 | $65,700,000 | 1,825 |
| 99.9% | 11 | $80,300,000 | 2,555 |
Each extra spare lifts the service level by less than the one before it, and once the spares pass the average number in the shop each one adds another 365 idle spare-days. That is the trade: the last points of service are the most expensive ones. The first spares up to that average add no idle spare-days.
| Spares | Service level | Added by this spare | Idle spare-days a year | Capital tied up | Cost of idle days a year |
|---|---|---|---|---|---|
| 4 | 62.9% | +19.5 points | 0 | $29,200,000 | $0 |
| 5 | 78.5% | +15.6 points | 365 | $36,500,000 | $730,000 |
| 6 | 88.9% | +10.4 points | 730 | $43,800,000 | $1,460,000 |
| 7 | 94.9% | +6.0 points | 1,095 | $51,100,000 | $2,190,000 |
| 8 | 97.9% | +3.0 points | 1,460 | $58,400,000 | $2,920,000 |
| 9 | 99.2% | +1.3 points | 1,825 | $65,700,000 | $3,650,000 |
| 10 | 99.7% | +0.5 points | 2,190 | $73,000,000 | $4,380,000 |
| 11 | 99.9% | +0.2 points | 2,555 | $80,300,000 | $5,110,000 |
| 12 | 100.0% | +0.1 points | 2,920 | $87,600,000 | $5,840,000 |
The shaded row is the number of spares the target calls for. Cost of idle days is the idle spare-days times the carrying cost for one spare for one day.
Idle spare-days use the average shop count. On a day when more engines are in the shop than there are spares, no spare sits idle, so counting those days the shelf holds 4.03 spares on average, against 4.00 from the simple rule.
The next spare can come three ways. Repair means sending an engine we already own through the shop. Lease means renting one. Buy means purchasing a serviceable engine. Each is costed on the same terms: the cash paid, discounted at the cost of capital.
Cheapest over 5 years: Repair our own engine
| Item | Repair our own engine | Lease one | Buy one |
|---|---|---|---|
| Paid on day one | $6,000,000 | $0 | $7,300,000 |
| Paid at the end of each year | $73,000 | $1,051,200 | $73,000 |
| Received at the end of the horizon | $4,380,000 | $0 | $4,380,000 |
| Net cash, not discounted | $1,985,000 | $5,256,000 | $3,285,000 |
| Present value of net cost | $3,557,092 | $3,984,875 | $4,857,092 |
| Same cost spread evenly per year | $938,352 | $1,051,200 | $1,281,289 |
| Days until in service | 73 | 30 | 60 |
For repair, day one is the shop visit plus $2,500,000, the price the engine would fetch unrepaired, which we give up by keeping it. Owned engines cost 1.0% of their value a year to hold (insurance, storage and records) and resell at 60% of their value at the end, repaired or bought. Rent and holding costs are paid at the end of each year. Cash cost does not decide on its own: a repair waits for a shop slot, and the repair order tab shows what happens when slots are short.
Present value of net cost by horizon
The vertical axis does not start at zero, so the gaps between the lines are visible.
| Years | Repair our own engine | Lease one | Buy one | Cheapest |
|---|---|---|---|---|
| 1 | $2,084,545 | $955,636 | $3,384,545 | Lease one |
| 2 | $2,506,860 | $1,824,397 | $3,806,860 | Lease one |
| 3 | $2,890,781 | $2,614,179 | $4,190,781 | Lease one |
| 4 | $3,239,801 | $3,332,163 | $4,539,801 | Repair our own engine |
| 5 | $3,557,092 | $3,984,875 | $4,857,092 | Repair our own engine |
| 6 | $3,845,538 | $4,578,250 | $5,145,538 | Repair our own engine |
| 7 | $4,107,762 | $5,117,682 | $5,407,762 | Repair our own engine |
| 8 | $4,346,147 | $5,608,074 | $5,646,147 | Repair our own engine |
| 9 | $4,562,861 | $6,053,886 | $5,862,861 | Repair our own engine |
| 10 | $4,759,874 | $6,459,169 | $6,059,874 | Repair our own engine |
All three are costed at the cost of capital of 10.0% set above, for an engine worth $7,300,000.
Six engines wait for a shop slot and every one will be repaired in the end. The question is the order. If an engine waits, its aircraft stays on the ground. The value of going first is the grounded days avoided times what a grounded day costs. Ranking by value for each repair dollar puts the best use of the budget first.
Value for each repair dollar
| Rank | Engine | Repair cost | Grounded days avoided | Cost of a grounded day | Value of going first | Value per dollar | Rank by value | Slot |
|---|---|---|---|---|---|---|---|---|
| 1 | $1,000,000 | 50 | $28,000 | $1,400,000 | $1.40 | 3 | Gets a slot | |
| 2 | $800,000 | 30 | $35,000 | $1,050,000 | $1.31 | 5 | Gets a slot | |
| 3 | $3,200,000 | 60 | $50,000 | $3,000,000 | $0.94 | 1 | Skipped: over budget | |
| 4 | $2,000,000 | 45 | $40,000 | $1,800,000 | $0.90 | 2 | Gets a slot | |
| 5 | $1,500,000 | 40 | $30,000 | $1,200,000 | $0.80 | 4 | No slot left | |
| 6 | $600,000 | 14 | $30,000 | $420,000 | $0.70 | 6 | No slot left |
Working for Engine F
- Grounded days avoided by going first
- 50
- Cost of one grounded day
- $28,000
- Value of going first
- $1,400,000
- Repair cost
- $1,000,000
- Value per repair dollar
- $1.40
- Outcome
- Gets a slot
Ranked 1 of 6 on value per dollar and 3 of 6 on total value.
3 of 3 slots used. Repair spend $3,800,000 of $4,000,000. Grounding cost avoided $4,250,000, which is $1.12 for each dollar spent.
Walking down the ranking, an engine gets a slot if a slot is free and its repair cost fits in the budget left. An engine that does not fit is skipped and the next one is tried. The rank by total value column shows how the order would change if money were no limit and only slots were scarce.
Checks on these numbers
19 of 19 pass. Each check rebuilds a figure a second way and compares the two.
Spares and capital
- PassEngines in the shop on average equal removals times shop days over 365
- PassThe chances of each shop count add to 100 percent
- PassThe spares meet the service level
- PassOne spare fewer would miss the service level
- PassSpares needed never falls as the service level rises
- PassIdle spare-days equal spares less the shop average, times 365, never below zero
- PassCapital tied up equals spares times the value of one engine
- PassThe cost of idle days equals the idle spares times value times cost of capital
Repair, lease or buy
- PassEach present value matches a closed-form calculation
- PassBuying less repairing equals the price less the repair cost and the sale value given up
- PassThe yearly figure times the annuity factor gives the present value
- PassA longer lease never costs less in present value
- PassThe option named cheapest has the lowest present value
Repair order
- PassEngines are listed by value per dollar, best first
- PassRanks run 1 to N once each
- PassEngines given a slot do not exceed the slots free
- PassRepair spend stays inside the budget
- PassThe value of the funded engines adds up to the total
- PassEvery row: value per dollar times repair cost gives its value
At 95.0% service, Quillhaven Air needs 8 spare engines, with 4.0 engines in the shop on an average day. That ties up $58.4M and leaves 1,460 idle spare-days a year, which cost $2,920,000 a year to carry. Over 5 years the cheapest way to get the next spare is to repair our own engine, at $3,557,092 in present value.