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INV
بالله إال توفيقي وما
Dr. Attia Hussien GomaaMaintenance Engineering Consultant
2008
Engineering service - American University in Cairo (AUC)
Maintenance Spare Parts Management
“Every management mistake ends up in inventory.”
INV 2Inventory Control - Dr. Attia Gomaa - 2008
Maintenance Spare Parts Management:
Course Outline:
Inventory Management Overview
Spare Parts Classification
Annual Requirements Planning
Forecasting
Inventory Control
Case Studies
INV 3Inventory Control - Dr. Attia Gomaa - 2008
Total Inventory Management:
TIM is a systematic approach to maximize the
material productivity, through achieving 5 Rs:
Right quality,
Right quantity,
Right time,
Right cost,
Right supplier.
INV 4Inventory Control - Dr. Attia Gomaa - 2008
Inventory Management =
PL
AN
NIN
G
OR
GA
NIZ
ING
CO
NT
RO
LL
ING
Transport Strategy
• Transport fundamentals
• Transport decisionsCustomer
service goals
• The product
• Logistics service
• Ord . proc. & info. sys.
Inventory Strategy
• Forecasting
• Inventory decisions
• Purchasing and supply
scheduling decisions
• Storage fundamentals
• Storage decisions
Location Strategy
• Location decisions
• The network planning process
PL
AN
NIN
G
OR
GA
NIZ
ING
CO
NT
RO
LL
ING
Transport Strategy• Transport fundamentals
• Transport decisionsCustomer
service goals
• The product
• Logistics service
• Ord . proc. & info. sys.
Inventory Strategy• Forecasting
• Inventory decisions
• Purchasing and supply
scheduling decisions
• Storage fundamentals
• Storage decisions
Location Strategy• Location decisions
• The network planning process
Planning + Organizing + Controlling
INV 5Inventory Control - Dr. Attia Gomaa - 2008
Inventory management answers five questions
What is the item criticality?
What is the annual demand?
What is the annual budget?
How much to order?
When to order?
INV 6Inventory Control - Dr. Attia Gomaa - 2008
• Item criticality: item classification (A, B, C)
• Lead time: time interval between ordering and receiving the order
• Holding (carrying) costs: cost to carry an item in inventory for a length
of time, usually a year
• Ordering costs: costs of ordering and receiving inventory
• Shortage costs: costs when demand exceeds supply
• Order quantity: Order size (unit)
• Reorder Point - When the quantity on hand of an item drops to this amount, the item is reordered
• Safety Stock - Stock that is held in excess of expected demand due to variable demand rate and/or lead time.
Key Inventory Terms
INV 7Inventory Control - Dr. Attia Gomaa - 2008
Inventory Costs:
CarryingCosts
ExpectedStockout
Costs
Order/SetupCosts
INV 8Inventory Control - Dr. Attia Gomaa - 2008
Inventory Costs:
• Carrying Cost– cost of holding an item in inventory
• Ordering Cost– cost of replenishing inventory
• Shortage Cost– temporary or permanent loss of sales when demand
cannot be met
INV 9Inventory Control - Dr. Attia Gomaa - 2008
Inventory Control Decisions:
• What decisions are involved in inventory control?– How should I track inventory?
• Continuously versus periodically– When do I place an order?
• Safety stock• Reorder point
– How much should I order?• Order quantity
INV 10Inventory Control - Dr. Attia Gomaa - 2008
Inventory Control Systems:
• Fixed-order-quantity system (Continuous)– Constant amount ordered when inventory
declines to predetermined level
• Fixed-time-period system (Periodic)– Order placed for variable amount after fixed
passage of time
INV 11Inventory Control - Dr. Attia Gomaa - 2008
Independent Demand
A
B(4) C(2)
D(2) E(1) D(3) F(2)
Dependent Demand
Independent demand is uncertain. Dependent demand is certain.
Independent vs. Dependent Demand
• Dependent– items used to produce final products
• Independent– items demanded by external customers
INV 12Inventory Control - Dr. Attia Gomaa - 2008
How much to order?
We want to balance the
carrying cost
against the
ordering cost
cost of keeping
goods in inventorycost of placing
an order
INV 13Inventory Control - Dr. Attia Gomaa - 2008
Order / Setup Cost
Size of order (units)
Note: Order / setup cost reflects:
• Fixed costs (e.g., information and communications technology)
• Variable costs (e.g., reviewing stock levels, order processing/ preparation expense, etc.)
An
nu
al c
ost
INV 14Inventory Control - Dr. Attia Gomaa - 2008
Order Size (units)
Cost($)
Ordering S Costs OQ
= ( )OC
Ordering Costs
INV 15Inventory Control - Dr. Attia Gomaa - 2008
Order Size (units)
Cost($)
Ordering S Costs OQ
= ( )OC
Carrying Costs = ( ) CC OQ 2
Carrying Costs
INV 16Inventory Control - Dr. Attia Gomaa - 2008
Order Size (units)
Cost($)
Ordering S Costs OQ
= ( )OC
Carrying Costs = ( ) CC OQ 2
Total Costs = Carrying Costs + Order Costs
INV 17Inventory Control - Dr. Attia Gomaa - 2008
Inventory Management
• Determining Optimal Inventory– Economic Order Quantity (EOQ)
TotalInventory
Costs
TotalCarrying
Costs
TotalOrdering
Costs= +
INV 18Inventory Control - Dr. Attia Gomaa - 2008
Economic Order Quantity
Total cost=Procurement cost+Carrying cost
2
ICQS
Q
DTC
Optimal Order Quantity:
IC
DSQ
2*
Optimal Time Between Orders:
D
QT
**
Number of Times pre Year to Order:
**
Q
DN
TC = total annual relevant inventory cost, dollars
Q = size of each order to replenish inventory, units
D = annual demand for the item in inventory, units
S = procurement cost, dollars/order
C = value of the item carried in inventory, dollars/unit
I = carrying cost as a percent of item value, %/year
INV 19Inventory Control - Dr. Attia Gomaa - 2008
Time
OrderQuantity
Q
InventoryLevel
(units)
The EOQ Model assumes the firm orders a fixed amount Q at equal intervals.
INV 20Inventory Control - Dr. Attia Gomaa - 2008
Time
OrderQuantity
Q
InventoryLevel
(units)
The EOQ Model
Average Inventory =
Order Quantity2
Q2
INV 21Inventory Control - Dr. Attia Gomaa - 2008
Inventory Management with Safety Stock- Order before inventory is at zero.
Time
EOQ
InventoryLevel
(units)
Depleted StockDuring Delivery
InventoryOrder Point
ActualDelivery Time
SafetyStock
INV 22Inventory Control - Dr. Attia Gomaa - 2008
Basic Tradeoffs:
• As order quantity
(EOQ) increases:
– Annual inventory
carrying cost also
increases
– Annual ordering
cost decreases
– Annual shortage
cost decreases
An
nu
al c
ost
Size of order quantity
CarryingCost
Order/Set-upCost
Total Costs
ShortageCost
Minimum costreorder quantity
INV 23Inventory Control - Dr. Attia Gomaa - 2008
EOQ Sensitivity:
INV 24Inventory Control - Dr. Attia Gomaa - 20089-22
The reorder point = ROP = d(LT)
0 TimeLead time
Lead time
Order Placed
Order Placed
Order Received
Order Received
Inventory Level
Reorder point, R
Q
Quantity on-hand plus on-order
Safety Stock
INV 25Inventory Control - Dr. Attia Gomaa - 2008
Fixed-order-interval Model:
INV 26Inventory Control - Dr. Attia Gomaa - 2008
A Min-Max System of Inventory Control
INV 27Inventory Control - Dr. Attia Gomaa - 2008
M = maximum level Qi = order quantityLT = lead time
CR (2004) Prentice Hall, Inc.9-60
Q1
Stock order
LT
Order received
LT
Q2
M
0
Qua
ntity
on
hand
Time
~
Q3
A Min-Max System of Inventory Control
Safety Stock
INV 28Inventory Control - Dr. Attia Gomaa - 2008
INV 29Inventory Control - Dr. Attia Gomaa - 2008
Main Parameters:
• Reorder Point - When the quantity on hand of an
item drops to this amount, the item is reordered
• Safety Stock - Stock that is held in excess of
expected demand due to variable demand rate and/or
lead time.
• Service Level - Probability that demand will not
exceed supply during lead time.
INV 30Inventory Control - Dr. Attia Gomaa - 2008
Re-Order Level & Safety Stock
4 Cases: Constant
demand & Constant lead time
Variable demand & constant lead time
Constant demand & variable lead time
Variable demand & variable lead time
INV 31Inventory Control - Dr. Attia Gomaa - 2008
Reorder Point:
INV 32Inventory Control - Dr. Attia Gomaa - 2008
Reorder PointThe ROP based on a Normaldistribution of lead time demand
INV 33Inventory Control - Dr. Attia Gomaa - 2008
Data:
1) 10.3 2) 4.9 3) 8.9 4) 11.7 5) 6.3 6) 7.7
• Mean = the calculated average of the values
= 8.3
Variance ==XX XX
nnii
22
11 = 6.368= 6.368SS22
==
Standard Deviation = SS = 2.523= 2.523
Mean & Standard Deviation:
INV
A density curve is a smooth curve used to approximate a histogram.
Normal Distribution
INV 35Inventory Control - Dr. Attia Gomaa - 2008
Data MeasurementData Measurement
Lower Specification Limit
Upper Specification Limit
Histogram Plot
0$ 500$
No.
of M
inor
Mai
nt. W
Os
INV 36Inventory Control - Dr. Attia Gomaa - 2008
Process A B C
Mean 10 10 10
Range 6-14 8-12 9-11
Variance 4 1 0.25
Sigma 2 1 0.50
INV 37Inventory Control - Dr. Attia Gomaa - 2008
Mean & Standard Deviation
From:http://www.gifted.uconn.edu/siegle/research/Normal/instructornotes.html
INV 38Inventory Control - Dr. Attia Gomaa - 2008
N(10,2)N(12,2)
N(10,4)
INV 39Inventory Control - Dr. Attia Gomaa - 2008
68.26 percent
95.46 percent
99.73 percent
MM74
Normal Dist. CurveNormal Dist. Curve
INV 40Inventory Control - Dr. Attia Gomaa - 2008
Sigma Levels:
Sigma Level(Process Capability)
Defects Per Million Opportunities
2 308,537
3 66807
4 6210
5 233
6 3.4
99.99966% Good (6 Sigma)99% Good (3.8 Sigma)
INV 41Inventory Control - Dr. Attia Gomaa - 2008
Description Application Service level %
Z
A Major effect on HSE Rupture Disk, 99.99966 6
B Major effect on Process= High down time cost
99.73 3
C Normal effect on HSE Normal effect on process
Without standby
95.46 2
D Normal effect on HSE Normal effect on process
With standby
68.26 1
Item Criticality AnalysisItem Criticality Analysis
INV 42Inventory Control - Dr. Attia Gomaa - 2008
Determining the Reorder Point forConstant demand rate & Constant Lead Time
Reorder Point (ROP)= [Lead time length (in days)] X [Demand per day (in units per day)]
• Annual Demand = 600 unit • Operation condition = 300 days per year• Lead time length = 12 days• Safety Stock = 20 unit by default (1.5%)
Then Demand per day = 600 / 300
= 2 units/day
ROP = ( 12 days) ( 2 units/day) + Safety Stock (20 unit)
ROP = 44 units
INV 43Inventory Control - Dr. Attia Gomaa - 2008
Variable demand and variable lead time
R= d x LT + Z·√(LT· σd2 + d 2 · σ2
LT )
Constant demand rate
σd = 0
Constant lead time
σLT = 0
Reorder Point Model:
Where d= average daily or weekly demand,
σd = standard deviation of demand per day or week,
σLT = standard deviation of lead time per day or week
INV 44Inventory Control - Dr. Attia Gomaa - 2008
Reorder Point with Variable Demand
(Leadtime is Constant)
stocksafetyz
z
L
d
zLdR
d
level service desired for deviations standard of number=
time lead during demand ofdeviation standard
demand daily ofdeviation standard
time lead=
demand daily average=
where,
INV 45Inventory Control - Dr. Attia Gomaa - 2008
Fixed-order-interval order quantity
Given information:Annual Demand= D=520 units,
Order Quantity = EOQ=62 units,
Item Criticality is Medium:
Service level = 99%, (Z=3)
Demand Standard Deviation = d = 8 units/wk,
Lead time = LT=3 wk
Required:Number of Orders = n = D / EOQ = 520/62 = 8.4 order / year
Reorder Interval = 52 Week / n = 6.2 or 6 wk
Safety stock= Z·√(LT· σd2 ) = 3 . √(3*64) =
Demand rate = D / No. of periods = 520/52 = 10 unit/week
ROP = d x LT + Safety Stock = 10 * 3 +
INV 46Inventory Control - Dr. Attia Gomaa - 2008
Reorder Point (ROP)= [Lead time length (in days)] X [Demand per day (in units per day)]
+ Safety Stock
• Annual Demand = 600 unit • Operation condition = 300 days per year• Average Lead time = 12 days• Standard deviation of lead time = 2• Z = 3
• Safety Stock ?• ROP?
Determining the Reorder Point forConstant demand rate & Variable Lead Time
INV 47Inventory Control - Dr. Attia Gomaa - 2008
EOQ Cost Curves:
EOQ Example
0
250
500
750
1000
0 100 200 300 400 500 600 700 800 900 1000
Order Quantity
To
tal A
nn
ua
l Co
st
OrderingHoldingTotal
INV 48Inventory Control - Dr. Attia Gomaa - 2008
EOQ Example
D = 1,000 per year,
S = $62.50 per order, and
H = $0.50 per unit per year,
What is the economic order quantity?
Q* HDS2
5.0
5.62*1000*2
500
INV 49Inventory Control - Dr. Attia Gomaa - 2008
History for 2007: Month # Demand rate Stock-Outs
1 180 02 75 03 235 454 140 05 180 06 200 107 150 08 90 09 160 010 40 011 190 2512 130 0
Item Criticality is High Lead time = LT = 2 month
Variable demand rate & Constant Lead Time
Required:Number of Orders = n = D / EOQ = Reorder Interval = 52 Week / n = Safety stock= Z·√(LT· σd2 ) = Demand rate = D / No. of periods = ROP = d x LT + Safety Stock =
XX XX
nnii
22
11SS 22
==