021 maint spare parts management 31 01 08

بالله إال توفيقي وما

Dr. Attia Hussien GomaaMaintenance Engineering Consultant

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

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.

Inventory Management =

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

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

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?

• 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

Inventory Costs:

CarryingCosts

ExpectedStockout

Order/SetupCosts

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

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

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

Independent Demand

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

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

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.)

Order Size (units)

Cost($)

Ordering S Costs OQ

= ( )OC

Ordering Costs

Order Size (units)

Cost($)

Ordering S Costs OQ

= ( )OC

Carrying Costs = ( ) CC OQ 2

Carrying Costs

Order Size (units)

Cost($)

Ordering S Costs OQ

= ( )OC

Carrying Costs = ( ) CC OQ 2

Total Costs = Carrying Costs + Order Costs

Inventory Management

• Determining Optimal Inventory– Economic Order Quantity (EOQ)

TotalInventory

TotalCarrying

TotalOrdering

Costs= +

Economic Order Quantity

Total cost=Procurement cost+Carrying cost

Optimal Order Quantity:

Optimal Time Between Orders:

Number of Times pre Year to Order:

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

OrderQuantity

InventoryLevel

(units)

The EOQ Model assumes the firm orders a fixed amount Q at equal intervals.

OrderQuantity

InventoryLevel

(units)

The EOQ Model

Average Inventory =

Order Quantity2

Inventory Management with Safety Stock- Order before inventory is at zero.

InventoryLevel

(units)

Depleted StockDuring Delivery

InventoryOrder Point

ActualDelivery Time

SafetyStock

Basic Tradeoffs:

• As order quantity

(EOQ) increases:

– Annual inventory

carrying cost also

increases

– Annual ordering

cost decreases

– Annual shortage

cost decreases

Size of order quantity

CarryingCost

Order/Set-upCost

Total Costs

ShortageCost

Minimum costreorder quantity

EOQ Sensitivity:

INV 24Inventory Control - Dr. Attia Gomaa - 20089-22

The reorder point = ROP = d(LT)

0 TimeLead time

Lead time

Order Placed

Order Received

Inventory Level

Reorder point, R

Quantity on-hand plus on-order

Safety Stock

Fixed-order-interval Model:

A Min-Max System of Inventory Control

M = maximum level Qi = order quantityLT = lead time

CR (2004) Prentice Hall, Inc.9-60

Stock order

Order received

A Min-Max System of Inventory Control

Safety Stock

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.

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

Reorder Point:

Reorder PointThe ROP based on a Normaldistribution of lead time demand

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

Variance ==XX XX

11 = 6.368= 6.368SS22

Standard Deviation = SS = 2.523= 2.523

Mean & Standard Deviation:

A density curve is a smooth curve used to approximate a histogram.

Normal Distribution

Data MeasurementData Measurement

Lower Specification Limit

Upper Specification Limit

Histogram Plot

0$ 500$

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

Mean & Standard Deviation

From:http://www.gifted.uconn.edu/siegle/research/Normal/instructornotes.html

N(10,2)N(12,2)

N(10,4)

68.26 percent

95.46 percent

99.73 percent

Normal Dist. CurveNormal Dist. Curve

Sigma Levels:

Sigma Level(Process Capability)

Defects Per Million Opportunities

2 308,537

3 66807

4 6210

99.99966% Good (6 Sigma)99% Good (3.8 Sigma)

Description Application Service level %

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

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

Variable demand and variable lead time

R= d x LT + Z·√(LT· σd2 + d 2 · σ2

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

Reorder Point with Variable Demand

(Leadtime is Constant)

stocksafetyz

level service desired for deviations standard of number=

time lead during demand ofdeviation standard

demand daily ofdeviation standard

time lead=

demand daily average=

where,

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 +

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

EOQ Cost Curves:

EOQ Example

0 100 200 300 400 500 600 700 800 900 1000

Order Quantity

OrderingHoldingTotal

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

5.62*1000*2

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 =

11SS 22

021 maint spare parts management 31 01 08

expected demand

hse normal

variable demand

lead time

lt d2

variable demand

major effect

standard deviation

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