The document discusses inventory control and various inventory management systems. It describes the objectives of holding inventory such as protecting against uncertainties in demand and supply. It also discusses inventory cost structures including ordering, carrying, and stockout costs. The economic order quantity (EOQ) model is introduced as a method to determine the optimal order quantity to minimize total inventory costs. Other inventory review systems described include continuous review, periodic review, and selective inventory classification methods like ABC analysis.

1. Inventory Control

2. Inv.Control - ObjectivesInv.Control - Objectives
IntroductionIntroduction
Purpose of InventoriesPurpose of Inventories
Inventory Cost StructuresInventory Cost Structures
Independent versus Dependent DemandIndependent versus Dependent Demand
Economic Order QuantityEconomic Order Quantity
Continuous Review SystemContinuous Review System
Periodic Review SystemPeriodic Review System
Using P and Q System in PracticeUsing P and Q System in Practice
Selective Inventory Control SystemsSelective Inventory Control Systems

3. IntroductionIntroduction
Inventory: a stock of materials used toInventory: a stock of materials used to
facilitate production or to satisfy customerfacilitate production or to satisfy customer
demand.demand.
Types of inventoryTypes of inventory
– Raw materials (RM)Raw materials (RM)
– Work in process (WIP)Work in process (WIP)
– Finished goods (FG)Finished goods (FG)
– Maintenance, repair & operating supplies (MRO)Maintenance, repair & operating supplies (MRO)

4. A Material-Flow ProcessA Material-Flow Process
Work in
process
Work in
process
Work in
process
Finished
goods
Raw
Materials
Vendors Customer
Productive Process

5. A Water Tank Analogy for InventoryA Water Tank Analogy for Inventory
Supply Rate
Inventory Level
Demand Rate
Inventory Level

6. Purpose of InventoriesPurpose of Inventories
To protect againstTo protect against uncertaintiesuncertainties
– in demand (finished goods, MRO)in demand (finished goods, MRO)
– supply (RM, MRO)supply (RM, MRO)
– lead times (RM/PP or WIP)lead times (RM/PP or WIP)
– schedule changes (WIP)schedule changes (WIP)
To allow economic production andTo allow economic production and
purchase (as in discounts for buying RM/PPpurchase (as in discounts for buying RM/PP
in bulk)in bulk)

7. Purpose of Inventories (Contd.)Purpose of Inventories (Contd.)
To cover anticipated changes in demand (asTo cover anticipated changes in demand (as
in a level strategy) or supplyin a level strategy) or supply
– finished goodsfinished goods
– RM/PPRM/PP
To provide for transit (pipeline inventories)To provide for transit (pipeline inventories)
– RM/PPRM/PP
– finished goodsfinished goods
– WIP (independence of operations)WIP (independence of operations)

8. Inventory Cost StructuresInventory Cost Structures
Ordering (or setup) costOrdering (or setup) cost
– Paperwork, worker time (ordering)Paperwork, worker time (ordering)
– worker time, downtime (setup)worker time, downtime (setup)
– Typically expressed as a fixed cost per order orTypically expressed as a fixed cost per order or
setup.setup.

9. Inventory Cost Structures(contd.)Inventory Cost Structures(contd.)
Carrying (or holding) cost:Carrying (or holding) cost:
– Cost of capital (market rate or internal rate of return)Cost of capital (market rate or internal rate of return)
– Cost of storage (building, utilities, insurance, handling)Cost of storage (building, utilities, insurance, handling)
– Cost of obsolescence, deterioration, and lossCost of obsolescence, deterioration, and loss
(shrinkage)(shrinkage)
– Management cost (record keeping, counting)Management cost (record keeping, counting)
Typically expressed as a percentage of SKU cost.Typically expressed as a percentage of SKU cost.
Average in INDIA is estimated to beAverage in INDIA is estimated to be 25 percent25 percent
per year.per year.
Businesses often use only cost of capitalBusinesses often use only cost of capital
(understatement).(understatement).

10. Inventory Cost Structures(contd.)Inventory Cost Structures(contd.)
How the 25 percent carrying cost is distributedHow the 25 percent carrying cost is distributed
Cost of Capital—15 percentCost of Capital—15 percent
Obsolescence—2 percentObsolescence—2 percent
Storage—5 percentStorage—5 percent
Materials Handling—2 percentMaterials Handling—2 percent
Shrinkage/pilferage—1 percentShrinkage/pilferage—1 percent
Insurance—1 percentInsurance—1 percent

11. Inventory Cost Structures(contd.)Inventory Cost Structures(contd.)
Stock out Cost (Back order or Lost sales orStock out Cost (Back order or Lost sales or
Understocking Cost)Understocking Cost)
– record maintenancerecord maintenance
– lost incomelost income
– customer dissatisfactioncustomer dissatisfaction
– Typically expressed as a fixed cost per backorderTypically expressed as a fixed cost per backorder
or as a function of aging of backorders.or as a function of aging of backorders.

12. Inventory Cost Structures(contd.)Inventory Cost Structures(contd.)
Overstocking Cost ( Opportunity Loss Cost)Overstocking Cost ( Opportunity Loss Cost)
- Cost incurred due to carrying Inventories- Cost incurred due to carrying Inventories
excess to set normsexcess to set norms

13. Forms of DemandForms of Demand
Independent demandIndependent demand
– finished goods, spare parts, MROfinished goods, spare parts, MRO
– based on market demandbased on market demand
– requires forecastingrequires forecasting
– managed using ‘replenishment philosophy’, i.e.managed using ‘replenishment philosophy’, i.e.
reorder when you reach a pre-specified level.reorder when you reach a pre-specified level.

14. Forms of Demand(contd.)Forms of Demand(contd.)
Dependent demandDependent demand
– parts that go into the finished products, RM/PPparts that go into the finished products, RM/PP
oror WIPWIP
– dependent demand is a known function ofdependent demand is a known function of
independent demandindependent demand
– calculate instead of forecastcalculate instead of forecast
– Managed using a ‘requirements philosophy’,Managed using a ‘requirements philosophy’,
i.e. only ordered as needed for higher leveli.e. only ordered as needed for higher level
components or products.components or products.

15. Economic Order Quantity (EOQ)
Developed in 1915 by F.W. HarrisDeveloped in 1915 by F.W. Harris
Answers the question ‘How much do I order?’Answers the question ‘How much do I order?’
Used forUsed for independent demandindependent demand items.items.
Objective is to find order quantity (Q) that minimizesObjective is to find order quantity (Q) that minimizes
the total cost (TC) of managing inventory.the total cost (TC) of managing inventory.
Must be calculated separately for each SKU.Must be calculated separately for each SKU.
Widely used and very robust (i.e. works well in a lotWidely used and very robust (i.e. works well in a lot
of situations, even when its assumptions don’t holdof situations, even when its assumptions don’t hold
exactly).exactly).

16. Economic Order Quantity (EOQ)Economic Order Quantity (EOQ)
Basic Model AssumptionsBasic Model Assumptions
Demand rate is constant, recurring, and known.Demand rate is constant, recurring, and known.
Lead time is constant and known.Lead time is constant and known.
No stockouts allowed.No stockouts allowed.
Material is ordered or produced in a lot or batchMaterial is ordered or produced in a lot or batch
and the lot is received all at onceand the lot is received all at once
Costs are constantCosts are constant
– Unit cost is constant (no quantity discounts)Unit cost is constant (no quantity discounts)
– Carrying cost is a constant per unit (SKU)Carrying cost is a constant per unit (SKU)
– Ordering (setup) cost per order is fixedOrdering (setup) cost per order is fixed
The item is a single product or SKU.The item is a single product or SKU.

17. EOQ Lot Size ChoiceEOQ Lot Size Choice
There is a trade-off between frequency ofThere is a trade-off between frequency of
ordering (or the size of the order) and theordering (or the size of the order) and the
inventory level.inventory level.
– Frequent orders (small lot size) lead to a lowerFrequent orders (small lot size) lead to a lower
average inventory size,average inventory size, i.e.i.e. higher ordering costhigher ordering cost
and lower holding cost.and lower holding cost.
– Fewer orders (large lot size) lead to a largerFewer orders (large lot size) lead to a larger
average inventory size,average inventory size, i.e.i.e. lower ordering cost andlower ordering cost and
higher holding cost.higher holding cost.

18. Notations and measurementNotations and measurement
units in EOQunits in EOQ
DD == Demand rate, units per yearDemand rate, units per year
SS == Cost per order placed, or setup cost,Cost per order placed, or setup cost,
Rupees per orderRupees per order
CC == Unit cost, Rupees per unitUnit cost, Rupees per unit
ii == Carrying rate, percent of value per yearCarrying rate, percent of value per year
QQ == Lot size, unitsLot size, units
TCTC== total of ordering cost plus carrying costtotal of ordering cost plus carrying cost

19. Cost Equations in EOQCost Equations in EOQ
Ordering cost = (cost per order) x orders per
year) = SD/Q
Carrying cost per year = (annual carrying rate) x
(unit cost) x average inventory = iCQ/2
Total annual cost (TC) = ordering cost per year
+ carrying cost per year = SD/Q + iCQ/2

20. Total Cost of InventoryTotal Cost of Inventory

21. TC and EOQTC and EOQ
TC = ordering cost + holding costTC = ordering cost + holding cost
= S*(D/Q) + iC*(Q/2)= S*(D/Q) + iC*(Q/2)
EOQ =EOQ =
note: Although we have usednote: Although we have used annualannual costs, any time period is allcosts, any time period is all
right. Just be consistent! The same is true for currencyright. Just be consistent! The same is true for currency
designations.designations.
iC
SD
Q
2
=

22. Continuous Review SystemContinuous Review System
Relax assumption of constant demand.Relax assumption of constant demand.
Demand is assumed to be random.Demand is assumed to be random.
Check inventory position each time there is aCheck inventory position each time there is a
demand (i.e continuously).demand (i.e continuously).
If inventory position drops below the reorderIf inventory position drops below the reorder
point, place an order for the EOQ.point, place an order for the EOQ.
Also called fixed-order-quantity or Q systemAlso called fixed-order-quantity or Q system
(the fixed order size is EOQ).(the fixed order size is EOQ).

23. A Continuous Review (Q) SystemA Continuous Review (Q) System
R = Reorder Point
Q = Order Quantity
L = Lead time

24. A Continuous Review (Q) SystemA Continuous Review (Q) System
Amount to order = EOQ
Order when inventory position = reorder point.
Reorder point = lead time * demand/period
= R = lead time demand (when demand is
constant)
Reorder point is independent of EOQ!
EOQ tells how much to order.
Reorder point tells when to order.

25. Periodic Review SystemPeriodic Review System
Instead of reviewing continuously, we reviewInstead of reviewing continuously, we review
the inventory position atthe inventory position at fixed intervalsfixed intervals. For. For
example, the bread truck visits the groceryexample, the bread truck visits the grocery
store on the same days every week.store on the same days every week.
Also known as “P system”, “Fixed-order-Also known as “P system”, “Fixed-order-
interval system” or “Fixed-order-periodinterval system” or “Fixed-order-period
system”system”

26. Periodic Review SystemPeriodic Review System
(contd.)(contd.)
Each time we review the inventory, we eitherEach time we review the inventory, we either
order or don’t. The decision depends upon ourorder or don’t. The decision depends upon our
reorder point.reorder point.
The amount we order is the amount needed toThe amount we order is the amount needed to
bring us up to a target (T).bring us up to a target (T).

27. A Periodic Review (P) SystemA Periodic Review (P) System

28. Using P and Q System in PracticeUsing P and Q System in Practice
Use P system when orders must be placed atUse P system when orders must be placed at
specified intervals.specified intervals.
Use P systems when multiple items areUse P systems when multiple items are
ordered from the same supplier (joint-ordered from the same supplier (joint-
replenishment).replenishment).
Use P system for inexpensive items.Use P system for inexpensive items.

29. Using P and Q Systems inUsing P and Q Systems in
PracticePractice
P may be easier to use since levels areP may be easier to use since levels are
reviewed less often.reviewed less often.
P requires more safety stock since may onlyP requires more safety stock since may only
order at fixed points.order at fixed points.
P is more likely to run out since cannotP is more likely to run out since cannot
respond to increases in demandrespond to increases in demand
immediatelyimmediately
Either may be more costly: P in safetyEither may be more costly: P in safety
stock, Q in monitoring cost.stock, Q in monitoring cost.

30. FORMULAE –FORMULAE –
INVENTORY MANAGEMENTINVENTORY MANAGEMENT
E.O.Q. =E.O.Q. = 2 X Annual Demand X Ordering cost2 X Annual Demand X Ordering cost
Unit Price X Inv. Carr. Cost (%)Unit Price X Inv. Carr. Cost (%)
Fixed order Qty model ( “Q” System)Fixed order Qty model ( “Q” System)
o Order Qty = E.O.Q.Order Qty = E.O.Q.
o Reorder Point = Average Daily Demand X Lead-time in daysReorder Point = Average Daily Demand X Lead-time in days
Total Annual Cost = Annual + Annual + AnnualTotal Annual Cost = Annual + Annual + Annual
Purchase Ordering InventoryPurchase Ordering Inventory
Cost Cost Carr. CostCost Cost Carr. Cost
(i.e. Annual(i.e. Annual
Demand XDemand X
Unit Cost)Unit Cost)

31. o Safety Stock = Constant based X Std. deviationSafety Stock = Constant based X Std. deviation
on Service level in demandon Service level in demand
Fixed order Qty model with safety stockFixed order Qty model with safety stock
o Reorder Point = (Average daily demand + SafetyReorder Point = (Average daily demand + Safety
X StockX Stock
lead-time in days)lead-time in days)
Fixed – Time Period Model with Safety Stock (“P” System)Fixed – Time Period Model with Safety Stock (“P” System)
o Safety stock = Constant based X Std. deviationSafety stock = Constant based X Std. deviation
on Service level (during Reviewon Service level (during Review
period + leadtime )period + leadtime )
Where = (R.P. + L.T.) X (Std. Dev.)Where = (R.P. + L.T.) X (Std. Dev.) 22
*
*

32. o Optimal Order Qty (Q) =Optimal Order Qty (Q) =
Average Daily Demand X (Review Period +Leadtime) +Average Daily Demand X (Review Period +Leadtime) +
(Plus)(Plus)
Safety StocksSafety Stocks
–– (minus)(minus)
Current Inventory StatusCurrent Inventory Status
(Physical Stocks + Quantity on order)(Physical Stocks + Quantity on order)

33. Selective Inventory Control SystemSelective Inventory Control System
Methods of classification:-Methods of classification:-
Title Basis Main Use
A-B-C Value of Consumption To control- raw material/ w.i.p/
components
H-M-L (High-Med-
Low)
Unit price of the material Mainly to control purchase
X-Y-Z Value of items in storage To review the inventories & their
uses at scheduled intervals
V-E-D (vital/essen/
desirable
Criticality of the component To determine stock levels of spare
parts
F-S-N (fast/slow/non-
moving)
Consumption pattern of the
component
To control obsolescence
S-D-E
(scarce/diff/easy)
Problems faced in procurement Lead-time analysis & purchasing
strategy
G-O-L-F
(govt/open/local/fore
ign)
Source of materials Procurement strategies
S-0-S (seasonal/ off
seasonal)
Nature of supplies Procurement stocking strategies for
seasonal items like agricultural
V-E-I-N (vital/ essen/
imp/normal)
Plant &machinery Production Machinery
& Services

34. A-B-C AnalysisA-B-C Analysis
Class
‘A’
Class
‘B’
Class ‘C’
0
65
90
100
15 40 100
Cumulative % of Total number of items
Cumulative%ofAnnualconsumptionvalue

35. ABC Inventory ManagementABC Inventory Management
Based on “Pareto” concept (80/20 rule) andBased on “Pareto” concept (80/20 rule) and
total usage in dollars of each item.total usage in dollars of each item.
Classification of items as A, B, or C based onClassification of items as A, B, or C based on
usage.usage.
Purpose is to set priorities on effort used toPurpose is to set priorities on effort used to
manage different SKUs, i.e. to allocate scarcemanage different SKUs, i.e. to allocate scarce
management resources.management resources.

36. ABC Inventory ManagementABC Inventory Management
(contd.)(contd.)
‘‘A’ items: 20% of SKUs, 80% ofA’ items: 20% of SKUs, 80% of
Ann.Con.ValueAnn.Con.Value
‘‘B’ items: 30 % of SKUs, 15% ofB’ items: 30 % of SKUs, 15% of
Ann.Con.ValueAnn.Con.Value
‘‘C’ items: 50 % of SKUs, 5% of A.C.ValueC’ items: 50 % of SKUs, 5% of A.C.Value
Three classes is arbitrary; could be any number.Three classes is arbitrary; could be any number.
Percents are approximate.Percents are approximate.
Danger: Consumption Value may not reflectDanger: Consumption Value may not reflect
importance of any given SKU!importance of any given SKU!

37. Miscellaneous Systems:
Bin Systems
Two-Bin System
Full Empty
Order One Bin of
Inventory
One-Bin System
Periodic Check
Order Enough to
Refill Bin

38. The Two-Bin System
Second Bin
First Bin Re-order Level
Re-order point shifts with usage
Normal
Lead-time
Usage
Time
Safety stock
Lead-time
Q
O

39. Inventory Accuracy and Cycle
Counting
 Inventory accuracy refers to how
well the inventory records agree
with physical count
 Cycle Counting is a physical
inventory-taking technique in which
inventory is counted on a frequent
basis rather than once or twice a
year

40. 40
Question Bowl
The average cost of inventory in India
is which of the following?
a. 10 to 15 percent of its cost
b. 15 to 20 percent of its cost
c. 20 to 25 percent of its cost
d. 25 to 30 percent of its cost
e. 30 to 35 percent of its cost
Answer: d. 25 to 30 percent of its cost

41. 41
Question Bowl
Which of the following is a reason why firms
keep a supply of inventory?
a. To maintain independence of operations
b. To meet variation in product demand
c. To allow flexibility in production scheduling
d. To take advantage of economic purchase
order size
e. All of the above
Answer: e. All of the above (Also can include to provide a
safeguard for variation in raw material delivery time.)

42. 42
Question Bowl
An Inventory System should include policies
that are related to which of the following?
a. How large inventory purchase orders should
be
b. Monitoring levels of inventory
c. Stating when stock should be replenished
d. All of the above
e. None of the above
Answer: d. All of the above

43. 43
Question Bowl
Which of the following is an Inventory Cost item
that is related to the managerial and clerical
costs to prepare a purchase or production order?
a. Holding costs
b. Setup costs
c. Carrying costs
d. Shortage costs
e. None of the above
Answer: e. None of
the above (Correct
answer is Ordering
Costs.)

44. 44
Question Bowl
Which of the following is considered a
Independent Demand inventory item?
a. Bolts to a automobile manufacturer
b. Timber to a home builder
c. Windows to a home builder
d. Containers of milk to a grocery store
e. None of the above
Answer: d. Containers of milk to a grocery store

45. 45
Question Bowl
If you are marketing a more expensive
independent demand inventory item, which
inventory model should you use?
a. Fixed-time period model
b. Fixed-order quantity model
c. Periodic system
d. Periodic review system
e. P-model
Answer: b. Fixed-order quantity model

46. 46
Question Bowl
If the annual demand for an inventory item is
5,000 units, the ordering costs are Rs100 per
order, and the cost of holding a unit is stock for a
year is Rs10, which of the following is
approximately the Qopt?
a. 5,000 units
b. Rs5,000
c. 500 units
d. 316 units
e. None of the above
Answer: d. 316
units
(Sqrt[(2x5000x1
00)/10=316.227
7)

47. 47
Question Bowl
The basic logic behind the ABC Classification
system for inventory management is which of the
following?
a. Two-bin logic
b. One-bin logic
c. Pareto principle
d. All of the above
e. None of the above
Answer: c. Pareto principle

48. 48
Question Bowl
A physical inventory-taking technique in
which inventory is counted frequently rather
than once or twice a year is which of the
following?
a. Cycle counting
b. Mathematical programming
c. Pareto principle
d. ABC classification
e. Stockkeeping unit (SKU)
Answer: a. Cycle counting

49. 49
Solved Problems – OPERATIONS MANAGEMENT
(Class of 2010)
Q1. A supplier is offering stainless steel bars at Rs 95 per kg for order of upto 100kg each,
and at Rs 80 per kg for orders of 101kg and above. Your annual requirement is 1200kg.
If your ordering cost is Rs 300 per order, and holding cost is 20%, what would be the
most economical quantity to order?
(10 Marks)
Answer.
E.O.Q(1) = √2 × Annual Demand × Ordering Cost
√Unit Cost × Holding Cost
E.O.Q = √2 × 1200 × 300
√95 × 0.20
E.O.Q = 195 units
E.O.Q(2) = √2 × 1200 × 300
√80 × 0.20
= 212 units

50. 50
 Now, E.O.Q (1), i.e. 195 units does not fall in the category of upto 100kg
Therefore here consider it’s optimum E.O.Q as 100 units so that it falls under the
category of Rs 95 per kg
Now, find the Total Cost
 For 100 units
• Ordering Cost = 1200 × 300 = Rs 3600/-
100
• Purchase Cost = 1200 × 95 = Rs 1,14,000/-
• Holding Cost = 100 × 0.2 × 95 = Rs 950/-
Therefore Total Cost = Rs 1,18,550/-
 For 212 units
• Ordering Cost = 1200 × 300 = Rs 1698/-
212
• Purchase Cost = 1200 × 80 = Rs 96,000/-

51. 51
• Holding Cost = 212 × 0.2 × 80 = Rs 1696/-
2
Therefore Total Cost = Rs 99,394/-
Therefore most Economic Order Quantity to order is 212 kgs