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Inventory Planning, Control
& Valuation
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What is an Inventory ?
Inventory
the stock of any item or resource used in an organization: raw materials, finished products, component parts, supplies and work-in-process.
An inventory system
policies and controls for monitoring levels of inventory Information system that records transactions and enables
analysis of stock requirements and levels/quantities, costs etc
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Why hold inventory / stock?
Provide flexibility minimum delay in supplying customers
a good range
Protect against uncertainties
Enable economic purchasing
Anticipate changes in demand or supply Buffers to feed processes and enable efficient
scheduling
Strategic stock holdings
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Inventory Types
Raw-materials.
Work-in-progress or in-transit
Finished-goods In the warehouse, awaiting shipment, in delivery vehicles,
in tanks, on shelves, in the stores
Strategic inventory
Scrap & re-work
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The Nature of Inventory Planning
Inventory do not give revenues without operations.
Organizations resources are limited there for investments in inventory should be optimized ( Economic ).
Why to manage inventory ?
To ensure a continues operation activities (non-stop).
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Costs of Inventory
Ordering costs Offering prices, purchase order & office, shipping and/or set up
Holding / Carrying Costs tied up capital (item value), staff & equipment, obsolescence,
perish ability, shrinkage, insurance & security, (rent/lease), audit, taxes.
Cost of being out of stock, cancelling an order
Scrap and re-working
Shortage Costs .
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Inventory Costs
Item cost
Carrying costs Capital costs
Storage costs
Risk costs Obsolescence Damage Pilferage Deterioration
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Inventory Costs (cont)
Ordering costs Production control costs
Setup and teardown costs
Lost capacity costs
Purchase order costs
Stockout costs
Capacity-associated costs
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Material-Flows ProcessF
rom
Su
pp
lier
sT
o C
usto
mer
Production Processes
Inventory in transit
Stores warehouse
Finishedgoods
WIP
WIP
Work inprocess
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Stock : Input (Flow in), Storage (Holding) and Flow out (Usage)
Supply Rate
Inventory Level
Rate of Demand (Usage)
Stock Level
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Economic Order Quantity (EOQ)
In trying to minimize inventory costs a company must find the order quantity which spreads the ordering or set-up costs over as many units as possible without incurring excess holding costs.
The EOQ model attempts to determine the amount of units to purchase which will minimize the total costs associated with ordering and holding inventory
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Economic Order Quantity (EOQ)
How to calculate EOQ ?
Tabular Approach /Trial and Error. (waste time) Graphic Approach /By using charts. Formula Approach /Mathematically .
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EOQ Aim = Cost Minimization
Cost
Ordering Costs
HoldingCosts
Qeoq Order Quantity (Q)
Total Cost
Holding + Ordering costs = total cost curve.
Find Qeoq inventory order point to minimize total costs.
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Economic Order Quantity (EOQ)
EOQ Assumptions Demand is known and constant. Lead time is known and constant. Order and holding costs are averaged across all
transactions. Single product line No quantity discounts - stable unit cost No stock-outs allowed Items ordered/produced in a lot or batch Batch received all at once Holding cost is linear based on average stock level Fixed order + set up cost
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Calculate EOQ
Qeoq = 2DS
H =
2(Annual/Period Demand) (Order cost) Holding Cost
Exercise EOQ and reorder point?•Annual demand = 12,000 units•Days/year in average daily demand = 365•Cost to place an order = £500•Holding cost /unit p.a. = £12 ( 20% Cost per unit)•Lead time = 7 days•Cost per unit = £60
Exercise EOQ and reorder point?•Annual demand = 12,000 units•Days/year in average daily demand = 365•Cost to place an order = £500•Holding cost /unit p.a. = £12 ( 20% Cost per unit)•Lead time = 7 days•Cost per unit = £60
(total unit cost * %storage)=
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EOQ Solution
Q = 2DS
H =
2(12,000 )(500)
0.2 * 60 = 1000 units eoq
Number of orders = Annual Demand / EOQ
= 12000 / 1000 = 12 orders per year.
Orders Cost = 12 * 500 = 6000 £
Total Holding Cost = 0.2*60*1000
2
= 6000. £
There for Total Inventory Cost = 6000 + 6000 = 12000 £
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EOQ Table – minimum TVc
Item £ 3 Holding cost % = 25%
No. of Quantity Order Average Holding Total
orders Ordered cost stock cost cost1 1200 10 600 450 4602 600 20 300 225 2453 400 30 200 150 1804 300 40 150 113 1536 200 60 100 75 1358 150 80 75 56 136
10 120 100 60 45 14512 100 120 50 38 158
Avg.stock x item £ x hc % Oc + Hc
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Cost Estimation & Model Sensitivity
In practical way it’s difficult to estimate the variables in the EOQ model such as the holding cost.
Example:
In practical way it’s difficult to estimate the variables in the EOQ model such as the holding cost.
Example:
Daily demandDemand
during period
(240 days)EOQ
Total cost of inventory
40 Min 9600 units 894.4 units 10,733 £
60 Max 1440 units 1095.4 units 10,800 £
Not that much in sensitivity
Not that much in sensitivity
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Extensions of the EOQ model Extensions of the EOQ model
1. EOQ with Order Size Restrictions .
2. EOQ with Storage limitations .
3. EOQ with quantity discount .
1. EOQ with Order Size Restrictions .
2. EOQ with Storage limitations .
3. EOQ with quantity discount .
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Extensions of the EOQ model Extensions of the EOQ model
1. EOQ with Order Size Restrictions .1. EOQ with Order Size Restrictions .
Example:
AICO ltd Demand Expected next year : 5000 units.
Supplier packages only contains 400 unit for each.
EOQ = 1000 unit when ordering cost 10$ & holding cost per unit 0.1$
Example:
AICO ltd Demand Expected next year : 5000 units.
Supplier packages only contains 400 unit for each.
EOQ = 1000 unit when ordering cost 10$ & holding cost per unit 0.1$
We have two options : 800 unit or 1200 unit . We have two options : 800 unit or 1200 unit .
Option Ordering Cost Holding Cost Total Cost
800 unit 62.5 $ 40 $ 102.50 $
1200 unit 41.7 $ 60 $ 101.70 $
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Extensions of the EOQ model Extensions of the EOQ model
2. EOQ with Storage limitations .2. EOQ with Storage limitations .
Example:
AICO ltd Demand Expected next year : 5000 units.
Supplier packages only contains 400 unit for each.
EOQ = 1000 unit when ordering cost 10$ & holding cost per unit 0.1$
Example:
AICO ltd Demand Expected next year : 5000 units.
Supplier packages only contains 400 unit for each.
EOQ = 1000 unit when ordering cost 10$ & holding cost per unit 0.1$
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Extensions of the EOQ model Extensions of the EOQ model
3. EOQ with quantity discount .3. EOQ with quantity discount .
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The Reorder Point (ROP)
Reorder point ROP = D * L D = Avg daily demand (constant) L = Lead time (constant)
when to place an order in units?
Annual Demand = 10,000 unitsDays per year considered in average daily demand = 365Cost to place an order = £10Holding cost per unit per year = 10% of cost per unitLead time = 10 daysCost per unit = £15
Annual Demand = 10,000 unitsDays per year considered in average daily demand = 365Cost to place an order = £10Holding cost per unit per year = 10% of cost per unitLead time = 10 daysCost per unit = £15
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EOQ and ROP example
365.148 (366 units)=1.50
2(10,000)(10)=H
2DS=Q
eoq
D =10,000 units/year
365 days
= 27.397 units/day
If lead time = 10 days, Reorder point = 27.39 * 10 days
= 273.97 = 274 units
Place order for 366 units. When 274 left, place next order for 366.
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Order Quantities & Reorder Points
R = Reorder pointL = Lead time
LL
q
R
Time
No. of unitson hand
safety orbuffer level
Average stock q/2Average stock q/2
q
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Order Quantities & Reorder Points
200
400
0
Days 10 20 30 40 50 60
Inventory
Orderplaced
Orderarrival
Orderplaced Average
cycleinventory
A. Order quantity of 400 units
Orderarrival
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Safety Stock and Re-order Levels
Reserve - buffer - cushion against uncertain demand (usage) & lead time.
A basis for a "2-bin" system
Application to JIT?
EOQ assumes certain demand & lead time. If uncertain, then:
ROL =
Average usage in lead time + safety stock
(Avg. lead time x Avg. daily usage)
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How Much Safety Stock? Cost vs. safety level
Depends on:Uncertainty: demand & lead time
cost of
being out of stock
carrying inventory
increasingly better service
Service level policy
% confidence of not hitting a stock-out situation
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Order Point with Safety StockU
nit
s
Days
Safety Stock
Actual leadtime is 3 days!
(at day 21)
2200
2000
OrderPoint
400
200
0 18 21
Dip into safety stock
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End of Part OneEnd of Part One