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Planning for Aircraft Spare Engine and Engine Parts with Simulation

Operations Research and Advanced Analytics

IIE, Montréal, Canada, June 3th, 2014.

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The OR group at AAWho we are and where we came from

• Started at AA in the 80’s• Provide analytical consulting and

decision support tools for multiple business units

• Spin-off with Sabre in 1996, “re-insourced” in 2000

• 36 OR practitioners from 12 countries, 6 continents, 20 languages

• 60+ advanced degrees in Operations Research or equivalent

• 11 patents and 75+ journal articles published

VP Airline Operations Technology

MD Operations Research and

Advanced AnalyticsCIO

Sr Mgr Technical Operations

Sr Mgr Revenue Management

Sr Mgr

Network

Planning

Director Operations

Contro

l

Mgr

Customer

Services

Mgr

Customer

Insights

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Outline

• Background

• Spare Engine Model• Process Modeling & Simulation• Case Studies

• Shop Pool Calculator• Process Modeling & Simulation• Case Studies

• Conclusion

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Background• Airlines own or lease spare engines to cover the operation while engines are

overhauled.

• Due to the high cost of engines and engine parts, accurate planning can yield significant savings in terms of engine ownership and part inventory cost, e.g., CFM56 engines used in 737 aircraft costs ~ $10M.

• Accurate part planning can reduce overhaul time which will also reduce engine ownership.

• Due to the complexity of maintenance programs and the uncertainty of engine removal and repair process, we chose to use simulation to determine the engine and the part inventory.

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Spare Engine Problem

• How many engines does the company need to own in order to support the completion of the promised flying schedule? “Single Echelon Part Inventory Problem for Repairable Components.”

Transp. Eng. to Base for Repair

Repair

Determine Eng. Repair

Prgm.

Select Spare Destination

Adjust Spare Level

Engine Installation

+-

Transport Spare to Station

Removed Engine Sent for Repair

Engine SpareRequest

Engine Removed

Aircraft to Receive Engine Replacement

Aircraft in Queue Waiting for Spare

Engine

Engine Received for Installation

Select NextAircraft

for Engine Replacement

Wait for Available Spare to Fulfill

Request

Aircraft Exits

Aircraft Arrives

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The Closed Form Solution• The textbook formula that models both demand and repair time variability would over plan the spare

level. The formula assumes one outstanding back order at a time which is clearly violated in the engine repair process.

Where L2 and D

2 represents the variance of the repair time of the engine and demand, respectively, D is the daily demand rate, L is the engine repair lead time, and k is a point determined from the standard normal distribution depending on the desired service level.

• We adjusted the variances to accommodate for the assumption violation for specific repair distributions such as the gamma, Weibull, normal and geometric distribution. A simulation was developed to evaluate these adjustments.

• The simulation also allowed us to model more complex but essential processes such as shop capacity and external repair. The simulation was eventually delivered as a software tool to the users.

h𝑂𝑤𝑛𝑒𝑟𝑠 𝑖𝑝=𝐷𝐿+𝑘√𝜎𝐷2 𝐿+𝜎 𝐿

2 𝐷2

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Simulating the process

Determine Repair Program Based on Expected Demand

Repair Capacity

Available?

No

Yes Send Next Engine to

Repair Process

Send to Destination

Engine Arrives to the Repair

Shop

Put Engine in Queue

Waiting for Repair

• Capacity constraints based on number of heavy repairs• Time in queue considered towards pre-intro work • After time in queue, any remaining pre-intro work is added to the repair time

Repair by Outside Vendor?

Send to Outside Vendor

External Vendor Repair Process(deterministic)

Yes

No

Engine Repair Process

(Repair time – Gamma Dist.)

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Ownership Calculation

The simulation model’s output corresponds to the variation of the level of spares in time. Through the run of many replications, the ownership is calculated at given service level, or percentile of spare level.

0 16 32 48 64 80 96 1121281441601761922082242402562722883043203363520

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Days

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Warm-up Steady-state

Initial Ownership

Estimating Ownership by Simulation:e.g., the required ownership is obtained from the avg. 10th percentile across multiple simulation replications of the spare level output in steady state, and by subtracting from the initial value.

Determining required ownership to satisfy a 90% service level

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Single or Multi-Location Engine Spare Model

• Single location model: when an engine needs a replacement, the aircraft can be routed to a station where a spare engine is available.

• Multiple location model: when an engine needs a replacement, a spare engine is needed on the spot.

• Most engine types have both “routed” and “on the spot” demand. However, the information is collected. We sometimes run both models to give upper and lower bounds of the spare level.

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Multi-Location Model: Dispatch by Highest Stockout Probability Rule

• Each request from the distribution centers for a new spare is assigned a stockout probability based on the current number of available spares and daily removal rate. The request with the highest probability is chosen to be fulfilled:

That is, the probability that in a single day the number of removals is greater than the current number of available spares.

• Assuming a Poisson daily removal rate , and let k be the ASC, then the probability of having equal or more available spares than the number of removals X in a single day is given by

• Thus, the probability of having more removals X than available spares, i.e., stockout probability, is given by

𝑆𝑡𝑜𝑐𝑘𝑜𝑢𝑡 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦=𝑃 ( 𝑋>𝑘 )=1−𝑃 (𝑋≤𝑘)

0%

20%

40%

60%

80%

100%

0 1 2 3 4 5 6 7 8 9 10

Stoc

kout

Pro

babi

lity

ASC

Stockout Probability vs. ASC

𝟏−𝒆−

𝟎

Sto

ck

Pro

bab

ilit

y

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Measuring Service Level

• Service level is traditionally defined as the ratio of successfully satisfied demand at the station (or system-wide) to total number of spare requests received, i.e., “hit or miss.”

• Another way to evaluate the performance in the management of the spares is by measuring different metrics related aircraft Out of Service (OTS).

• OTS related metrics provide a different perspective of the performance in the field it may be more important to know the expected number of OTS and days under such condition in a given period of time (e.g., in a day, week, year), and/or the duration of such events.

• Thus, three type of OTS metrics were defined and tested: (1) OTS-days/year(2) OTS events/year (3) OTS duration statistics

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• The figure below provides a simple example of OTS metrics measured over a period of 6 days.

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Spare Levelat

Dist. Center

2

-1

-2

1

0t1 2 3 5 6

OTS Events: 2OTS-Days: 1 + 2 + 1 = 4OTS Duration: 3

1

0t1 2 3 4 5 6

2

1

Engine Removal*

New Spare Arrival

*Whenever an engine removal occurs, then a spare is taken from shelf. If no spare is available, then a request is sent to move an available spare from either the shops or TUL (if possible).

Spares sent from the shops

OTS Metrics For The Engine Spare Model (Cont.)

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Case Study: Spare Ownership & OTS Metrics

• The tables summarize the results obtained for the single-location and multi-location* cases (threshold: No borrowing to 4 spares)

Note: The numbers shown are for illustration purpose only

NO BORROWINGDIST. CENTER SL (%) ASC OTS-DAYS/YR OTS/YR MEAN STD DEV

TUL 97.0 5.7 5.0 1.8 4.0 4.3DFW 77.3 0.8 21.3 5.0 5.1 5.2LAX 0.0 0.0 11.6 0.9 12.2 11.4STL 82.0 0.8 10.1 2.0 7.1 7.4

ORD 83.7 0.8 12.8 1.2 9.2 9.2SYSTEM 89.1 8.1 60.8 10.9 --- ---

OTS METRICS/YEAR OTS DURATION (DAYS)

THRESHOLD: 5 SPARESDIST. CENTER SL (%) ASC OTS-DAYS/YR OTS/YR MEAN STD DEV

TUL 96.9 5.6 5.0 1.8 3.9 4.0DFW 79.5 0.8 8.5 4.5 3.7 4.7LAX 0.0 0.0 6.4 1.0 6.4 9.5STL 84.5 0.8 4.5 1.7 4.1 6.2

ORD 86.3 0.9 5.9 1.0 4.7 6.7SYSTEM 89.9 8.1 30.3 10.1 --- ---

OTS METRICS/YEAR OTS DURATION (DAYS)

THRESHOLD: 4 SPARESDIST. CENTER SL (%) ASC OTS-DAYS/YR OTS/YR MEAN STD DEV

TUL 96.7 5.5 5.5 2.0 3.8 4.1DFW 80.1 0.8 7.6 4.4 3.9 5.6LAX 0.0 0.0 5.9 1.0 5.9 9.0STL 84.2 0.8 4.3 1.8 3.3 5.4

ORD 86.7 0.9 4.8 1.0 4.6 7.5SYSTEM 90.0 8.0 28.1 10.1 --- ---

OTS METRICS/YEAR OTS DURATION (DAYS)

SL: Service level.*Ownership for the multi-location cases was set to: STA 1 -15, STA 2 -1, STA 3 -0, STA 4 -1, STA 5 -1.

SINGLE-LOCATIONSL (%) OWNERSHIP ASC OTS-DAYS/YR OTS/YR MEAN STD DEV

90 14 4.5 50.0 10.4 7.4 10.695 16 6.4 14.3 3.5 6.1 7.9

99.9 21 11.4 0.4 0.1 4.8 3.7

OTS DURATION (DAYS)OTS METRICS/YEAR

Multi-location cases

STA 1STA 2STA 3STA 4STA 5

STA 1STA 2STA 3STA 4STA 5

STA 1STA 2STA 3STA 4STA 5

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Engine Repair Process

General Engine Repair Process

A typical process map for engine overhaul

Engine Arrival(Intro)

DisassemblyPiece Part

Repair (PPR) Process

AssemblyEngine

TestEngine

Shipping

TAT Target (collecting parts for assembly)

• Engines are repaired under different repair programs: Light & Heavy

• Heavy repairs usually require longer turn-times and are more expensive than the light repairs.

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Background: Engine Spare Parts – Shop Pool

• For parts with repair time longer than the allowed piece part repair time, spares are needed so the engine will not wait for the parts.

• Such spare part inventory is usually known in the industry as the “shop pool” needed to support the engine repair process (heavy & light repairs).

• The shop pool calculation depends on different parameters including: expected demand of engines, part turn-times (repair process), number of parts per engine, repair probabilities.

• OR designed both analytical formulas and simulation models that are used to estimate the required ownership of engine parts for the shop pool.

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Case Study: Spare Engine Ownership & Shop Pool Investment

• As the TAT decreases, the need for spare engines also decrease, however the investment for shop pool parts increases

• The holistic view of the engine repair cost structure helped business to make better decisions about their investments

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Engine Completion TAT (days)

CF6-B6: Spare Onwers. & Addl. Shop Pool Investment (LB) 98% SL Under Different Engine TAT : 2014 Forecast

S.P. Addl. Investment Spare Ownership @ 90% SL

Current Ownership (13) Spare Ownership @ 95% SL

Spare Ownership @ 99% SL

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1.696

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Engine Completion TAT (days)

CF6-B6: Spare Onwers. & Addl. Shop Pool Investment (UB) 98% SL Under Different Engine TAT: 2014

S.P. Addl. Investment Spare Ownership @ 90% SL

Current Ownership (13) Spare Ownership @ 95% SL

Spare Ownership @ 99% SL

Spare Ownership vs. Shop Pool Investment

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Conclusion

• Inventory planning for expensive asset requires special modeling.

• Simulation is a good tool to solve inventory problems for items with complex replenishment processes. Compared to closed form solutions, it can model the processes more accurately with less restrictions.

• Savings are significant• As AA upgrades the fleets, the retiring fleets and growing fleets are benefiting from

the more accurate planning methodology compared to learning from experience.• For 2012, the Shop Pool inventory of CFM56 engine parts (used in 737 aircraft)

calculated with our model would have saved 15% in inventory compared to the manually planned inventory.