11 inventory control

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INVENTORY CONTROL

(INDEPENDENT DEMAND)



Inventory is the store of goods and stock

Inventory control is the activity that

maintains stocks at desired level



OBJECTIVES OF INVENTORY

•To maintain overall investment at the

lowest

•To supply items to users at right time andright place

•To keep waste and surplus at minimum

•To minimize shortage and handling cost

•To maximize efficiency of production



FUNCTIONS OF INVENTORY

•Return on investment

•Buffer stock

•Decoupling

•Production smoothing

•Reduce material handling

•Bulk purchasing



TYPES OF MANUFACTURING INVENTORIES

•Raw material

•Work in process

•Finished goods

•Spares and consumables

•Miscellaneous



PRESSURES FOR LOW INVENTORY

•Interest

•Opportunity cost

•Storage and handling cost

•Taxes / insurance

•shrinkage



PRESSURES FOR HIGH INVENTORY

•Customer service

•Ordering cost

•Setup cost

•Transportation cost

•Quantity discounts



MULTISTAGE INVENTORY

Items stocked at more than one point in sequential

production process

MULTIECHELON INVENTORY

Inventory of finished products at various levels in

distribution system



FACTORS AFFECTING INVENTORY

•Economic parameters•Price

•Procurement cost

•Carrying cost

•Shortage cost•Demand

•Ordering cycle

•Lead time

•Number of supply echelons•Number of stages of inventory

•Availability of items

•Government policy



INVENTORY COST

•Cost of items

•Procurement cost

•Carrying cost

•Stock out cost•System cost



Order quantity

An

nua

lcost

Q*

TC* Holding cost

Ordering cost

Total cost



OPERATING DOCTRINE

HOW MUCH TO ORDER Q

WHEN TO ORDER R



INVENTORY CONTROL SYSTEMS

FIXED ORDER QUANTITY SYSTEM (QR SYSTEM)

•Order quantity remains fixed

•Demand may be constant or variable

FIXED ORDER TIME SYSTEM (PERIODIC SYSTEM)

•Time of order is fixed

•Demand is variable



FIXED ORDER QUANTITY SYSTEM

(CONSTANT DEMAND)

.

time

I n v e n t o r y

l e v e l

Q

R T1 T2

T1 = T2

Q = Q max



FIXED ORDER QUANTITY SYSTEM

(VARIABLE DEMAND)

time

I n v e n t o r y

l e v e l

R

L1 L2



FIXED ORDER TIME SYSTEM

(VARIABLE DEMAND)

.

time

I n v e n t o r y l e v e l

T1 T2

T1 = T2 = T3

Q max is fixed

T3



NOATATIONS

D total annual demand

Q order quantityQ* optimal order quantity

R reorder point

R* optimal reorder point

L lead timeS setup / procurement cost per order

C cost per unit

I carrying cost per unit per year

P production rated demand per unit time during lead time

D total demand during lead time

TC total annual cost

TC* minimum total annual cost

L

L



ECONOMIC ORDER QUANTITYD is constant

L is constant

C is constant

No stock out is allowed

No. of orders = D / Q Average inventory = Q / 2

Order cost = SD / Q Holding cost = ICQ / 2

Total inventory cost = CD + SD /Q + ICQ / 2

dTC / dQ = -SD / Q + IC / 22

Total cost is minimum when dTC / dQ = 0

Q* = 2SD / ICR = 0 if L = 0

R = Ld if L = 0L



SENSITIVITY ANALYSIS FOR EOQ MODEL

TC 1 q Q

TC* 2 Q q +=

Total ordering and holding costs are relatively stable

around the EOQ. A firm is better served by ordering a

convenient lot size close to EOQ rather than theprecise EOQ



GRADUAL REPLACEMENT MODEL

ECONOMIC BATCH SIZE

p - d

-d

Tp

Qmax

Tp = Q / p

Qmax = (p-d) Q / p

= p – d Q

p

Inven

torylevel



GRADUAL REPLACEMENT MODEL

ECONOMIC BATCH SIZE

Average inventory = Q p-d

2 p

TC = CQ + SD / Q + ICQ/2 p-d

p

Total cost is minimum when dTC / dQ = 0

dTC / dQ = -SD / Q + IC / 2 ( p-d / p )

Q* = 2DS p

IC p-d

2DS P

IC P-D



QUANTITY DISCOUNT

EOQ at lowest price

range

Price range

feasible Not feasible

Compute total cost

Total cost at lowestQ for each price

Choose minimum

total cost

EOQ at next

lowest price



INVENTORY DECISIONS OF PERISHABLE PRODUCTS

Cu = cost of shortage

Co = cost of overstock

Critical fractile = Cu

Cu + Co

Inventory order = minimum demand +

CF ( maximum demand – minimum demand )



INVENTORY CONTROL UNDER UNCERTAIN DEMAND

Safety stock is required to face uncertainty in demand

if daily demand standard deviation is s,

The standard deviation б during lead time of n days

= s1 + s2 + s3 + sn2 2 2 2

R = Ld + zб

Z = number of standard deviations equivalent

to confidence level

L



Reorder Point

ROP

Risk of a stock out

Service level

Probability of

no stock out

Expected

demand Safety

stock

0 z

Quantity

z-scale



INVENTORY CLASSIFICATION

By cost ABC analysis

By importance VED analysis

By frequency of use FSN analysis



VED analysis

V ( vital ) items which are absolutely essential to the

operations

E ( essential ) items, absence of which adversely affectsproductivity or quality or both

D ( desirable ) items required for smooth operations

although not essential



FSN analysis

F fast moving items

S slow moving items

N non moving items



ABC analysis

Based on Pareto law

•10% of items account for 70% of cost

•20% items account for 20% of cost

•70% of items account for 10% of cost



ABC analysis

.

. . .. . . . .

items

f r e

q u e

n c y

%

70

90100

A class items

B class items

C class items

11 inventory control

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