AGIFORS1995-EPIM-QUILLINAN
-
Upload
john-quillinan-crme -
Category
Documents
-
view
76 -
download
0
Transcript of AGIFORS1995-EPIM-QUILLINAN
1Expendable Parts IM
Expendable PartsInventory Management
atDelta Air Lines
by
John D. Quillinan
September 18, 1995
3Expendable Parts IM
Considerations
• The time when the order is released– a shortage before the material can arrive– average investment in inventories
• The quantity order at one time– number of replenishment orders required
annually, and cost of processing them– average investment in inventories
4Expendable Parts IM
Inventory Costs
• Cost of Ordering
• Cost of Carrying Working Stock
• Acquisition Cost of Safety Stock
• Cost of Carrying Safety Stock
• Cost of Not Having Parts On Hand
5Expendable Parts IM
Total Cost
Total cost=
annual cycle-inventory cost+
cost of carrying safety stock+
cost of a stockout
6Expendable Parts IM
The Goal
Minimize total quantifiable cost
• Minimize annual cycle-inventory cost and cost of carrying safety stock
• Meet or exceed a customer service level
7Expendable Parts IM
Typical Inventory History
Back orders
Stock on hand
Stock on hand
Order quantity
Stock on order
Total available stock
Orderpoint
Time
Piec
es
8Expendable Parts IM
Terminology
• Demand - historical consumption• EOQ - Economic Order (Reorder) Quantity• Buffer - safety stock• Forecast - estimate of consumption in a given
period t+n produced at time t• Reorder Point - inventory level at which an
order is placed (usage forecasted over lead time plus safety stock)
9Expendable Parts IM
Demand Defined
Historical Consumption (constrained demand) is defined by Delta Part Number and Station as
normal issue+ station issue- shop credit quantity- scrap quantity (removed 12/29/95)
10Expendable Parts IM
(r,Q) Model
• Reorder Point-Reorder Quantity Model
• Reorder Quantity, Q, is determined using the EOQ (economic order quantity) model.
• The reorder point, r, is chosen to protect us or provide a specified level of service during the lead time. If demand is known with certainty, then r is set equal to the demand during the lead time.
11Expendable Parts IM
Service Level
Service Level may be defined in terms of
• Time– a level provided by simply carrying x periods of
supply on-hand• Stockouts
– fraction of time that no stockout will occur, or the probability of no stockout
• Back Orders– fraction of demand expected to be filled from
stock, or the probability of no back order
12Expendable Parts IM
A Little History
On December 6, 1995, a prototype program was presented to Material Services.
The DT Prototype predicts future consumption and safety stock levels for a user-specified Delta part number, station and service level for the last twelve months plus one month into the future.
Over the next couple months, an inventory decision model capable of handling price breaks or quantity discounts, and packaging and lot sizes, was incorporated in the prototype.
13Expendable Parts IM
Cost Savings (75 parts)
TargetService
Level
AverageService
LevelCost
Savings
PercentCost
Savings92.00% 94.25% $52,985 28.08%
92.66% 94.54% $49,959 26.48%
95.00% 96.03% $31,769 16.84%
96.00% 96.59% $25,150 13.33%
97.00% 97.33% $15,468 8.20%
15Expendable Parts IM
Forecast Models
8 Forecast Models Coded in Natural 2.Simple (equally-weighted) 6-month moving averageUnequally-weighted 6-month moving averageSimple 12-month moving averageExponential-smoothing (utilizing Trigg-Leach method)Double-exponential smoothingHolt-Winter’s multiplicative (seasonal) model with trendHolt-Winter’s multiplicative (seasonal) model w/o trendTime series -- simple linear regression against time
16Expendable Parts IM
Basic IM Terms
A = ordering (or setup) costs, in dollars per order lot
S = expected annual usage, pieces per yearr = carrying costv = actual cost, dollars per pieceQ = order quantityk = safety factorr = reorder point
17Expendable Parts IM
Cycle-Inventory Costs
• Annual cost of ordering(S / Q) × A
• Annual cost of carrying inventory(Q / 2) × r × v
• Total annual cycle-inventory cost((Q / 2) × r × v) + ((S / Q) × A)
18Expendable Parts IM
A Live Example
DPN: 012202134Station: ATLDescription: BULB, 28V, 600W, QUARTZ SEAL
Variable Description ValueA ordering cost 50.00$ S expected annual usage 9,527r carrying cost 18.33%v actual cost per unit $0.70
package ratio 100supplier unit of issue EA
19Expendable Parts IM
Graphical Solution
Inventory Costs
$0.00
$10.00
$20.00
$30.00
$40.00
$50.00
$60.00
$70.00
$80.00
$90.00
$100.00
5000
1000
0
1500
0
2000
0
2500
0
3000
0
3500
0
4000
0
4500
0
5000
0
5500
0
Q, Order quantity (pieces)
Annualcosts
Total CostCost to CarryCost to OrderMinimum
20Expendable Parts IM
EOQ Model
• Annual cycle-inventory cost =((Q / 2) × r × v) + ((S / Q) × A)
• Take derivative of cost with respect to Q, set equal to 0, and solve for Q.
d{((Q / 2) × r × v) + ((S / Q) × A)}/dQ = 0((1 / 2) × r × v) + ((−S / Q2) × A) = 0
1/ Q2 = (r × v) / (2 × A × S)Q = √ (2 × A × S) / (r × v)
21Expendable Parts IM
Mathematical Solution
DPN: 012202134Station: ATLDescription: BULB, 28V, 600W, QUARTZ SEAL
Variable Description ValueA ordering cost 50.00$ S expected annual usage 9,527r carrying cost 18.33%v actual cost per unit $0.70
package ratio 100supplier unit of issue EA
Q economic order quantity 27,249optimal package quantity 272
Q | packaging optimal order quantity given package ratio 27,200
Legend: Yellow area contains f ield descriptionsGreen area for user entriesRed area is restricted and for displaying calculated values
22Expendable Parts IM
Lower Ordering Cost
DPN: 012202134Station: ATLDescription: BULB, 28V, 600W, QUARTZ SEAL
Variable Description ValueA ordering cost 25.00$ S expected annual usage 9,527r carrying cost 18.33%v actual cost per unit $0.70
package ratio 100supplier unit of issue EA
Q economic order quantity 19,268optimal package quantity 193
Q | packaging optimal order quantity given package ratio 19,300
Halfing our ordering cost reduces our order quantity from 272 to 193 packages.
23Expendable Parts IM
Some Observations
• As the cost of ordering increases, the order quantity also increases, while the number of replenishment orders decreases.
• As the cost of carrying inventory increases, the order quantity decreases, while the number of replenishment orders increases.
• Both cost drivers affect the average stock on hand.
24Expendable Parts IM
Inventory versus Order Quantity
Average
Average
Stockon
hand
Time
Larger order quantities result in reduced annual ordering costs, but at the cost of carrying larger inventories
25Expendable Parts IM
Additional IM Terms
σ = standard deviation of lead-time forecasterrors
E[k] = partial expectationF[k] = cumulative probability functionP = fraction of demand expected to be filled
from stockp0 = target service level
26Expendable Parts IM
Reorder Point Logic
R = µLT + k × σ,
whereµLT = lead-time forecast.
µLT = ΣLTµt, t ≠ LT
27Expendable Parts IM
Setting Safety Stocks
Probability of no back orders is denoted by:P = ( S − σ × E[k] × S / Q) / S
= 1 − E[k] × σ / Q
Expected quantity short (or partial expectation):E[k] = p{k} − k × F(k)
p{k} − k × F(k) = Q / σ × (1 − P)
28Expendable Parts IM
Normally Distributed Demand
A non-linear line search was used to find the value of k whose E[k] was closest to {Q / σ × (1 − p0)}
The method for setting safety stocks was used for expendable parts having an average lead-time forecast ≥ 10, and assumes the demand and forecast errors can be represented by a normal (Gaussian) distribution.
29Expendable Parts IM
Slow Moving Items
In the case of slow-moving items (µLT < 10, on average), Laplace-distributed (exponential) forecast errors are assumed.
( )kQ P
=−
12 2 2 1
lnσ
30Expendable Parts IM
Another Example
Bulb, 28V, 250 W, Screw Terminal
Forecasting methodology selected: simple exponential smoothing
Standard deviation of forecast errors: 184.93Annual forecast: 7,894Unit price: $5.61Price per piece: $5.61Ordering cost: $50.00Carrying cost: 18.33%
31Expendable Parts IM
An Example continued ...
Q = √ (2 × A × S) / (r × v)= 877
Target E[k] = Q / σ × (1 − p0) = 877 / 184.93 × (1− 0.97) = 0.14277
Tables in the literature* tell us that k must fall between 0.70 and 0.71, becauseE[k] = 0.142879 for k = 0.70 andE[k] = 0.140475 for k = 0.71
* first appeared in Decision Rules for Inventory Management by R.G. Brown, 1967.
32Expendable Parts IM
An Example continued ...
Golden Section Search gives usk = 0.7025
B = k × σ≈ 130
R = µLT + k × σ= 788
P = 1 − (0.311 − 0.7025 × 0.7588) × 184.93 / 877= 0.969999 ≈ 0.97
33Expendable Parts IM
EFSSeptember 1995 - TransQuest began documentation of old system.December 1995 - All of the prototype modules converted into structured-format subprograms and parameter and local data areas replaced the specification of parameters lists within calling programs.January 1996 - TransQuest worked on development of utility programs.February 1996 - EFS loaded in test; user acceptance testing begins.March 30, 1996 - EFS loaded in production.
34Expendable Parts IM
Tangible Benefits
• 113,000 expendable items stocked in ATL• $7,496,368 reduction of inventory held for
safety stock
35Expendable Parts IM
Intangible Benefits
• Economic Order Quantity model
• Multiple forecasting models
• Minimum sales and lot sizes quantities
• Price breaks or quantity discounts