Modern Spares Analysis
For Non-Specialists
Robert Butler
Presented at LOA University, 19 October 2015, Washington D.C.
Analysis of Spare Stocks
•
•
•
•
Fundamental ideas
An example problem
Stock optimization
Time
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The Purpose of Spare Stocks
• Only an equipment or system can provide utility
• The quantity of a system’s utility actually delivered is
a joint function of
– The intrinsic benefits derived from having the use of the
system – performance
– The amount of performance delivered or deliverable –
operational availability or Ao
• Stocks of spares increase Ao and hence, the rate at
which utility is supplied
• Although any increase in stock will increase Ao the
greatest increase depends on economic optimization
• So we care about
– Enough stock to achieve a performance goal
– But at the lowest cost (er, maybe – more on this later)
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Fundamental Concepts
Stocks Versus Flows
The stock is the amount of water in the
bathtub, the flow is the rate at which it leaves
Flow1
Ao
Flow2
Notice that the stock remains the same only if Flow1= Flow2
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Alternative Stock Calculation
Methods
• Single item methods
– Rules of thumb
• Arbitrary percentage that seemed about right in the past
• Expert opinion: someone who knows a lot about the system guesses how many
spares
– Saw tooth deterministic inventory models
– Simple relationships with uncertainty – Poisson assumption
• Constant k models (
• USN’s FILSIP
S  t   t
)
– Item fill rate (probability of no stock out)
• System methods
– More satisfactory because they focus on delivery of utility
– Require knowledge of the fleet being spared
– Not necessarily optimized
• Steady state system optimization
– USAF/USN/US Army models all use VARI-METRIC approach based on work
originally done by Craig Sherbrooke at RAND and later, LMI
•
New issues: dealing with time
– Overcoming the limitations of steady state assumptions
– Application of optimizing techniques to day-to-day spares management
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The Theory versus What the Item
Manager Sees
•
Data for each item
include
– Q (order quantity)
– R (re-order point)
– demand rate
– foreseen events
s
Q
• Dues-in from repair or
replenishment
• Tests
R
• Shelf life expirations
•
•
The simulation starts
from the current position
and projects it forward
Each subsequent
simulation repeats this
with increased R
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t
Stock Optimization
• Mix of parts
– Buy more of the less expensive parts in substitution
for the more expensive parts, other things equal
– Buying lower-indenture items will reduce the number
of higher (more expensive) items required
• Geographic location of stocks
– The closer a part is located to the operating
equipment
•
•
The greater its impact on equipment at that location
The less its impact on all other equipment
– The higher the echelon at which a stock is kept
•
•
The smaller its impact on any specific equipment
The greater its contribution to all equipments
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General Optimization Process
Step 1: Choose item with
highest ratio
Step 2: Re-compute ratio
for that item
Step 3: Repeat steps 1
and 2 until target
reached
System
LRU1
LRU2
LRU3
LRU4
LRU5
LRU6
Ao
IP1
Ao
IP2
Ao
IP3
Ao
IP4
Ao
IP5
Ao
IP6
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The Effect of Multiple Indentures
and Locations/Echelons
• Complex hardware breakdown structures require
testing the effect of buying lesser parts to replace
their parent assemblies
• Problems arise such as
– A part is an LRU in one application and not in another
– An LRU is physically part of an SRU assembly (spark plug)
• The part search must be done for every location
• Other complications
• Each location may have different operating
programs, delay times, stock constraints and MOE
requirement
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Other Complicating Factors
• Weight and volume constraints and costs
– NASA requirement to account for up-mass
– Sparing helicopters on board small ships
– Solution is the use of shadow pricing – setting a
price per unit of weight or volume
• Redundancy calculations
– K of n redundancy is common in some
technologies
• Multiple prices
– Buying versus selling
– Repair from unserviceable inventory
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Operation of a Spares Model
Marginal Optimization
•
•
Each point is another calculation of
max “bang/buck” at the margin
The yellow line is the locus of
optimal solutions – nothing above
is feasible, all below is inferior
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Three Case Studies
• The first case: George AFB, 1965-66
• Canadian airlines
• Several commercial airlines
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George AFB Study, 1965-6
The Original METRIC Model
• Operations monitored for 6 months
– Flying hour program
– Not operationally ready rates (NORS rates)
compiled
• Re-stocked in middle of period
– Removed all existing base stock
– Re-stocked with METRIC recommendations
based on equal fill rate
• Results
– Slight drop in NORS rates
– Half the cost of stock
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Canadian Airlines
• Pilot project on A320 fleet using VMetric
• Starting inventory of $31 million
– Starting service level (fill rate) of 70%
– Final inventory of $19.4 million
• $18.6 million excess sold
• $7 million shortages acquired
– Final service level of 85%
• Study required 60 days
• Used simulation model to prove solution
correctness
• Adopted technique for all fleets – savings of $80
million out of $200 million starting inventory
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Optimization Works
The Case of Commercial Airline Fleets
•
Orange: increase in service level
•
Blue:
inventory reduction value
In all cases, maximum inventory
reduction at equal service level would
have been 50% or greater.
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What About Time?
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Accounting for Time in
Spares Optimization
• Steady state means:
– All inputs assumed to remain true indefinitely
– MOEs are true for average of all time, not each period
• Several problems are defined by time
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–
–
–
–
–
–
–
Long lead time versus short lead time parts
Phase-in and phase-out of fleets
Handling obsolescence and DMSMS
End of system life and life extension
Runs of luck – good and bad
Changing system configuration
MRO and parts supply delay changes
Part attribute changes from expected values
To name just a few…
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Two Ways to Deal With Time
• Spare parts planning
– Parts planners need optimizing models that
recognize and deal with time
• Spare parts management
– Parts managers need optimized advice for day-today actions
– This depends on what is where compared to what
should be where
– Which, in turn, depends on a complete model of
the system’s operation and maintenance over time
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Spares Optimization Over
Multiple Periods
Multi-period spares analysis can overcome
some of the problems of steady state models
• By dealing with time, trade-offs influenced by
time can be incorporated in the algorithm
• Specifically, this can resolve issues such as:
–
–
–
–
•
Fleet build up and run down
Long lead time vs. short lead time optimal choice
Obsolescence and technology insertion issues
Mid-life upgrade calculations
An optimization algorithm that translates
EBO into a monetary metric can optimize
spares for complex mixtures of metrics like
Ao and fill rate – often found in contractual
incentive clauses
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Predictable vs. Foreseeable
Changes
• Future events that are neither predictable nor foreseeable must
be ignored by models, though not by decision-makers
• Predictable changes can be ascribed to parts or part groups
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–
–
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Lead time to procure or repair parts
Proportion of parts subject to obsolescence
Average useful life (mean technological life, MTL) and expired life
Reliability improvement, configuration changes
• Foreseeable changes are usually attributes of the operating and
support scenarios
– Fleet build-up, run-down
– Basing changes
– Temporary deployments
– Operating pace changes
– Lead time improvements
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The Difference Between Steady
State and Time-Sensitive Models
• The bang-for-buck ratio at the heart of the
optimization process must now be changed to
recognize time
Steady State
EBO
IP1
Time-Sensitive
PV0 (EBOt1 ...t2 )
IP1,t0
• The “timeless” version of EBO is replaced by the
discounted present monetary value of the stream of
EBO reductions available from this part
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Life Cycle Inventory Cost (LCIC)
• The first period solution in a multi-period spares
optimization will be more costly than a steadystate solution
• Because, among the cheaper (myopic) steadystate choices, some will lose their utility in “less
than forever”
– End of system life
– Technological or market-driven obsolescence
– Major configuration changes (intended obsolescence)
• To understand full benefit, it is necessary to view
inventory from a life cycle perspective
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The Essence of LCIC
TimeSensitive
Solution
Steady
State
Solution
Right shift of curve is cost of
new part number stock
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Optimized Spares Management
• Spares optimization is good
– Easy to do
– Saves money up front
• Optimal solutions are vulnerable to change
– Balancing on a knife-edge of assumptions and predictions
– Reality is bound to disappoint
– Result is decay of effectiveness of the once-optimal solution
• Periodic re-optimization helps, but is costly
– Opportunity cost of not achieving higher effectiveness
– Periodic cost of the re-optimization exercise
– Cost of buying adjustment stock
• Optimal tactical management preserves the
value of optimization without the costs of periodic
re-optimization
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Continuous Optimization Requires
Optimal Day-to-Day Decisions
1.
2.
Optimize, either initial stock or stock adjustments (the orange area
)
This recovers the difference between extremely inefficient solutions and an
optimal solution – but the benefit decays over time as conditions change
Introduce optimization into the supply support chain itself (the blue area )
A supply optimization system attempts to recover the remaining lost profit
and operating margin, providing continuously optimal solutions
Support
Effectiveness
Ultimately, the third step will be to eliminate periodic
re-optimization in favor of “episodic” re-optimization
Time
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Optimal Reorder Point
• Standard practice is to fix
reorder point for 6-12
months
• By using asset visibility
and some math, it can be
reset automatically every
day, saving money as in
the example
Cost of Lost Incentive Fee
Cost of Inventory
Total Cost
*
LOA University October 2015
Optimal
reorder point
for this part for
today
* The step from r = 17 to r = 18 is
caused by the fact that stock is
expected to drop to 18 within the
simulation time horizon (before
the end of the incentive period).
This causes an order to occur
that wouldn’t be made at r = 17.
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System Optimized
Dynamic Stock Parameters
• Consolidation of single item
results across the system
– Optimal reorder point and
quantity (R, Q)
– Ratio of incentive fee
improvement to inventory cost
Incentive
Fee
Benefit
45º (cost = benefit)
Costless
adjustments
• List of stock control parameter
changes by descending order of
benefit to cost
– All zero cost adjustments made
automatically (dashed line)
• Optimal stopping point where
marginal cost = marginal benefit
• Central control of item
management budget
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Cost of
Inventory
adjustment
Optimal
stopping
point
Thank you for your attention
If you have questions or suggestions,
please contact me:
Bob Butler
+1 831 649 3800
[email protected]
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