SCM Inventory Part -II.pdf

8/19/2019 SCM Inventory Part -II.pdf

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Inventory Management

Part-II


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EOQ Problem 1: Let monthly demand at a retailer is 1000 units. Fixed

ordering costs are Rs 4000 per order. Item cost is 500 peritem. Inventory holding costs are 20%.

Determine:

1. Nos. of units in each replenishment lot.

2. Cycle inventory

3. Nos. of orders per year

4. Annual Inventory related costs (ordering and inventory holding costs)

5. Average material flow time

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Annual demand, D = 1,000 x 12 = 12,000 units

Order cost per lot, Co = Rs 4,000

Unit cost of item, C = Rs500Inventory holding cost per unit per year (as a fraction of unitcost) Cc = 0.2 x 500 = Rs 100

Qopt = 2 Co D / Cc = 2 x 4000 x 12000 / 100= 980 units

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Cycle Inventory = Qopt / 2 = 980/2 = 490

Nos. of orders per year = D / Qopt = 12000 / 980 =

12.24 Annual ordering and inventory holding costs

= (D / Qopt )x Co + (Qopt / 2 ) x Cc

= 12.24 x 4000 + 490 x 100 = Rs 97960

Average material flow time = Qopt / 2 D

= 980 / 2 x 12000 = .041 year = .49 months =14.96 days

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Now if in the previous example, manager wants toreduce the lot size to 200, then what are the annualinventory related costs. With Q=200

(D / Q )x Co + (Q / 2 ) x Cc = Rs 250,000. This lot size is

undesirable as total costs have increased. What need to be done make the lot size reduction

optimal ?

Qopt = 200, D = 1000x12=12000, Cc = .2 x 500 = 100

Qopt = 2 Co D / Cc can be written as :Co = Cc (Qopt)^2 / 2 x D = 166.7

Manager has to reduce the ordering cost from Rs 4000 to Rs166.7 for the lot size of 200 to be optimal.

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EOQ Problem 2:

The epaint store stocks paint in its warehouse and sells itonline on its internet website. The store stocks severalbrands of paint. However its biggest seller is Sharman-

Wilson Ironcoat paint. The company wants to determinethe optimal order size and total inventory cost for Ironcoatpaint given an estimated annual demand of 10,000 gallons

of paint, an annual carrying cost of $ 0.75 per gallon and anordering cost of $150 per order. Also determine the nos. of orders per annum and time between orders (i.e. order cycletime) with 311 working days per year.

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EOQ Problem 2

13-7

C c = $0.75 per gallon C o = $150 D = 10,000 gallons

Qopt =2C o D

C c

Qopt =2(150)(10,000)

(0.75)

Qopt = 2,000 gallons

TC min = +C o D

Q

C cQ

2

TC min = +(150)(10,000)

2,000

(0.75)(2,000)

2

TC min = $750 + $750 = $1,500

Orders per year = D/Qopt

= 10,000/2,000

= 5 orders/year

Order cycle time = 311 days/( D/Qopt)

= 311/5

= 62.2 store days


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Problem:

Assume that epaint store has its own manufacturing facility in which it produces ironcoat paint. The ordering cost Co isthe cost of setting up the production process. Co = $150.

Cc= $0.75 per gallon and D=10,000 gallons per year. Themanufacturing facility operates for 311 days in a year, sameas store. Manufacturing facility produces 150 gallons perday. Determine the optimal order size, total inventory cost,

length of time to receive an order, number of orders per year and maximum inventory level with 311 working daysper year.

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Production Quantity Model


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ro uct on uant ty o e –

ro em(related to Problem 2)

13-9

C c = $0.75 per gallon C o = $150 D = 10,000 gallonsd = 10,000/311 = 32.2 gallons per day p = 150 gallons per day

Qopt = = = 2,256.8 gallons

2C o D

C c 1 - d

p

2(150)(10,000)

0.75 1 - 32.2150

TC = + 1 - = $1,329d

p

C o D

Q

C cQ

2

Production run = = = 15.05 days per order= Length

of time to receive an order

Q

p

2,256.8

150


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Production Quantity Model

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Number of production runs = = = 4.43 runs/year

= Nos. of orders per year

D

Q

10,0002,256.8

Maximum inventory level = Q 1 - = 2,256.8 1 -

= 1,772 gallons

d

p

32.2

150


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Safety Inventory :• Cycle Safety Inventory model assumed that there is no

uncertainty in demand and supply.

Actual Demand may differ from the forecasted demandfor a given period due to demand fluctuations or forecasterrors – Demand Uncertainty

• Also, supplier lead time may be uncertain – Supply

Uncertainty

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• The uncertainty in demand or supply may lead to a

“stockout situation”.

• To take care of stockout situations, firms carry safety

inventory

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Safety Inventory Model:

R= reorder point

• Safety Inventory is the average inventory in hand

when the replenishment lot arrives.


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Cycle Stock + Safety Stock

Inventory

Time

Average

Inventory

Cycle Inventory

Safety Inventory

Average inventory carried by the firm is the average

cycle inventory plus safety inventory.



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Tradeoff – Increase in safety inventory improves

product availability i.e. decrease stock out costs but it

also increases inventory carrying costs of the firm.

In today’s business environment, a firm faces:

a. Pressure to improve product availability

b. Increased product variety

c. Shorter product life cycle

• a and b pushes a firm to increase safety inventory whereas

c pushes it to decrease safety inventory.

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Level of Safety inventory is decided by capturing :

1. Uncertainty in demand

2. Uncertainty in supply

for a given Target service level

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Capturing Uncertainty:

Uncertainty in demand is captured using demand distribution.

In real life situations, demand can be assumed to follow a normaldistribution.

Uncertainty is measured using: Standard deviation ,Coefficient of variation, Range.

Standard deviation is most widely used measure.

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Coefficient of Variation = Standard deviation / Mean

Slow moving items typically have higher uncertainty and

higher CV while fast moving items have lower uncertainty andlower CV.

For a new item or new supplier where past data is not available,

a subjective assessment of standard deviation can be made as :Standard Deviation =

Range (i.e optimistic estimate – pessimistic estimate)/ 6

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Demand distribution is characterized by mean demandand standard deviation of demand.

Let d1, d2, d3, d4………….. dn be the demand observed for n

days. Mean or average demand = d=(d1 + d2+ d3+ d4 …. dn )/ n

Standard deviation of daily demand = d

= ((d1 - d)^2 + (d2 - d)^2 + ………….(dn - d)^2) / n

Similarly for supply uncertainty, mean lead timebe L and standard deviation of lead time is L

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Safety Inventory Model:

Referring to the model, there is no possibility of stockout between the point

the replenishment arrives and reorder point.

Firm is exposed to stockout only after placement of order and arrival of

replenishment i.e. during the lead time.


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Let LTD denotes the mean value of the total lead timedemand and Lead Time Demand is the standard deviation of lead time demand.

Uncertainty during the lead time is because of uncertainty in actual demand and/or uncertainty is

supply.

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Value of LTD and Lead Time Demand can be calculated from leadtime demand distribution, if it is available from historicaldata.

Or by using the formulas as:

(L= Average Lead time, d = Average Daily Demand)

LTD = L x d

Lead Time Demand = L d2 + d2 L2

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Safety Stock = K x Lead Time Demand

Here K is the Safety Factor= Nos. of standarddeviation corresponding to service level probability.

K indicates product availability.

Safety Stock = K d L if L is zero

Reorder Point (when to place the order)=

LTD + Safety Stock = LTD + K Lead Time Demand 4-23



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Safety Stock

Distribution of Demand During Lead Time


LTD = d L

Probability of Stockout


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Reorder Point For a Service Level

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Probability ofmeeting demand duringlead time = service level

Probability ofa stockout

R

Safety stock

d L

Demand

K d L


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Demand Data

d1 d2 d3 d4 d5 d6 d7 d 8 d 9 d10

Demand 115 95 150 125 28 90 93 115 93 96

Lead-time data

L1 L2 L3 L4 L5 L6 L7 L 8 L 9 L10

Lead-time

12 15 4 21 18 11 12 18 19 20

Determine safety stock, R eorder point with a 95% servicelevel and a 5% stockout probability. Basic demand and lead-time data is given.

Safety Stock For Variable Demand with supplyuncertaintyIllustration - 1


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Daily Demand d, Mean d = 100 , d = 30

Supplier Performance

Mean lead time = L= 15 Days , L = 5

LTD = 100 x 15=1500

Lead Time Demand = 513

Now,

Safety Stock = K x Lead Time Demand

For a 95% service level, K = 1.65

Safety Stock = 846

Reorder Point = 1500 +846 = 2346



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There exists a relationship between service level and K (which isnon-linear). Given the desired service level, value of K can bedetermined or vice versa

( Using excel function :Service level = NORM.DIST(K,0,1,1) or K

= NORM.INV (s/100, 0,1); or K = NORMSINV(s); Alternatively ztable can be used.

In the present problem, if K=1 then Service Level = 84.1%,then Safety stock = 513 units.

It means with this safety stock chances of stockout in areplenishment cycle are 15.9 percent only (100-84.1).

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Impact of Service Level On Safety StockInventory Management


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Measuring Product Availability

• Cycle service level (CSL)

Fraction of replenishment cycles that end with all customer

demand being met.

It is the probability of not having stockout in a replenishment

cycle

• Product fill rate ( fr ) : Fraction of product demand satisfied

from product in inventory

• Order fill rate: Fraction of orders filled from available inventory


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Safety Stock For Variable Demand but no supplyuncertaintyIllustration - 2

Copyright 2011 John Wiley & Sons, Inc. 13-31

Daily demand of a product at a paint store is 30 gallons and standard deviation of 5

gallons per day. Demand is normally distributed. Lead time for receiving a new order

is 10 days with no uncertainty. The paint store wants a reorder point with a 95% CSL

and a 5% stockout probability

d = 30 gallons per day L = 10 days

d = 5 gallons per day

LTD= Lead Time Demand= d L

For a 95% service level, K = 1.65

R = dL + K d L

= 30(10) + (1.65)(5)( 10)

= 326.1 gallons

Safety stock = K d L

= (1.65)(5)( 10)

= 26.1 gallons


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Inventory Control Systems

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Continuous system (fixed-order-quantity) Constant amount ordered when inventory declines to

predetermined level Inventory is tracked continuously

Time between orders is not fixed Order quantity is fixed

Periodic system (fixed-time-period) Order placed for variable amount after fixed passage of time

Order is placed to raise the inventory to prespecified threshold. Inventory is not tracked continuously Time between orders is fixed Order quantity is not fixed


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Impact of Supply Chain Redesign on Inventory: Impact of Aggregation : Centralisation vs Decentralisation

Any supply chain redesign has a significant impact on costs

especially inventory and transportation costs.

With centralization, firm will be able to reduce inventory relatedcosts but will increase its transportation cost to maintain sameservice level.

Supply chain managers need to justify the same with rigorous cost– benefit analysis by taking into account inventory related costsand transportation costs.

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Impact of Aggregation on

Safety Inventory

Aggregation and safety inventories in Centralisation

Di: Mean weekly demand in region i, i = 1,…, k

i: Standard deviation of weekly demand in region i, i = 1,…, k

r

ij

: Correlation of weekly demand for regions i, j,

1 ≤ i ≠ j ≤ k

: Demand faced by Central location

: Standard Deviation of weekly demand for central location

DC = Dii=1

k

; var DC ( ) = i

2+2

ij i j

i> j

i=1

k

;

D

C = var D

C ( )

C D

C

D


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Centralization vs Decentralization

Illustration:

Let us consider the case of a company that currently has 16 regionalstock points/warehouses and serves its dealers from the closest

stock point.

The supply chain manager is exploring the option of centralising itsinventory.

Let each region have similar demand distribution with meandaily demand=d= 100 and standard deviation = 30.

Demand of different regions in independent

Each stock point/ warehouse in both centralisation and

decentralization gets served by plant with lead time of exactly 15days. 4-35



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Average transportation cost in decentralization case is Rs 1 / unitand in centralization case increases by 10% i.e. Rs 1.1 / unit.

Ordering Cost = Co (or S) = Rs 256 / order

Inventory holding cost per unit per year = Cc = Rs 6

Required service level = 97.7% (K=2)

Working days per year = 300

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Cycle Inventory:

Centralized case

D = 16 x 100 x 300; Qopt = 6400,

Hence Cycle Inventory = 6400/2 = 3200

Decentralized case D for each Stock point in decentralized case = 100 x 300;

Qopt = 1600, Hence Cycle Inventory = 1600/2 = 800

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Safety Inventory:

Demand faced by centralized stock point:

d = d1 +d2 + d3…………dn

D = d12 + d22 + d32 ………. dn2 The phenomenon is called “Risk Pooling” which

suggests that demand uncertainty is reduced whendemand across demand locations is pooled.

It happens because higher demand in one loactionoffsets lower demand in another location.

Lower demand uncertainty leads to lower safety stockin the centralized case.

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Safety Stock:

In case of centralisation

D = 302 x 16 = 120

Safety stock = K D L = 2 x 120 x 15 = 928

In case of Decentralisation

For each regional stock point,d= 30, K=2, Safety stock = K d L = 2 x 30 x 15 = 232

For all 16 locations, Safety Inventory = 16 x 232

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Decentralised system – 16

stock points

Centralised system – 1

stock point

Cycle stock/stock point =

Qopt / 2

800 3200

Safety Stock per stock point 232 928

Total Inv. in units for the

system

(232+800) 16

= 16512

928+3200

= 4128

Total Inv. carrying cost 16512 6

= 99072

4128 6

= 24768

Incremental Transportation

cost

300100160.1

=48,000


Option of centralising the inventory should be chosen


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Note:

Safety stock decreases due to risk pooling and lowerdemand uncertainty faced by centralised location.

Cycle stock in centralized case reduces because of aggregation.

If in this case, transportation costs say increases by say 25%

, then centralisation will not be beneficial.

Benefit of centralization / aggregation decreases asdemand of different decentralized locations becomepositively correlated.

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Impact of Aggregation on

Safety Inventory

The Square-Root Law

If nos. of independent stocking locations decreases by m, the

average safety inventory decreases by a factor of

m


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Centralisation vs Decentralisation:i. Higher the demand uncertainty of the product, higher will be

the savings in safety stock when moving from decentralisationto centralisation.

ii. For fast moving products like salt, wheat with low demand uncertainty and high transportation cost, centralisation is notbeneficial.

iii. For slow moving products with high demand uncertainty, it isbetter to centralise.

iv. Higher the nos. regional stock points, higher will be the savingsin cycle inventory in case of centralization because of

economies of scale (square root law). 4-43



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• Two possible disadvantages to aggregation

Increase in response time to customer order

Increase in transportation cost to customer



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Managerial Levers to Reduce safety Stock:

1. Reduction in Demand Uncertainty:

This can be achieved with better forecasting or entering intocontracts with some customers with assured stable demand.

2. Reduction in Supplier Lead Time: This can be achieved by working with supplier and by using faster mode of transport.

3. Reduction in supply uncertainty: This can be achieved usingmore reliable modes of transport and working with supplier.

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Managing Seasonal Inventory:

A firm that faces seasonal variation in demand can followeither of the two basic approaches:

Chase Option: Produce as per demand in each season andcarry no seasonal inventory. During peak season demandcan be met by either hiring more labour, running overtime,outsourcing etc.

Level Option: Produce at the same level through out the year and build inventory during lean season and use thisinventory to take care of excess demand during the peakseason.

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Illustration: A toy manufacturer faces demand for toys as given.

Inventory carrying cost per unit per quarter is Rs3. Each worker can produce 500 units of toys per quarter.

Each temporary worker hired during the peak demandquarter (Q4) will result in additional cost of Rs 6000.

Manufacturer needs to decide whether to pursue chase orlevel option to meet demand.

Relevant costs to be considered are the incremental costs of hiring in chase option and inventory carrying costs in caseof level option.

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Short lifecycle products:

1. Selling season is small.

2. Either physical deterioration (perishable goods) or

perceived value (style goods) decreases after sellingseason.

3. One does not have opportunity of replenishmentduring selling season.

4. Sales should be anticipated before selling season andrequisite stock carried.

5. E.g. fashion products, bread, newspaper

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Optimum Order size for short life cycle products Cu = Cost of understocking

Co = Cost of Overstocking

Optimal service level = (Cu x 100) / (Cu + Co) Optimal order size = Mean Demand + K x

standard deviation of demand

K = Service factor

Cost of understocking is an opportunity loss by thefirm for each unit of lost sales.

The cost of overstocking is the loss incurred by a firmfor each unit at the end of the selling season.

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Illustration: Optimum Order for a New Music CD

CD purchase price = Rs. 200

CD sales price = Rs. 300

CD sales price after first weeks = Rs. 62.

Demand: Average 100 and Standard Deviation 30

Find optimum order quantity.

If manufacturer offers buyback scheme with cost of

administering return- Rs. 53, what would be thedecision?



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With Cu = 100, Co = 138

Optimum service level = .42 = 42 %

Corresponding K = -0.2Optimum order size = 100 – 0.2 x 30 = 94

In case of buyback:

Cu = 100, Co = 53

Optimum service level = .655 = 65.5 %

Corresponding K = 0.4

Optimum order size = 100 + 0.4 x 30 = 112

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Multiple – item, Multiple location InventoryManagement:

1. Managing inventory in actual supply chain involvesdealing a large number of items often stocked at multiplestock points at various stages in the supply chain.

2. Inventory management need to be carried out at each of these stock points and integrated with the rest of thesupply chain.



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Inventory Management For multiple items, theoretically inventory

management and supply chain analysis is to be carriedout for each and every items.

Since nos. of items are in general large and have varying importance, managers divide items intomultiple categories and handle different

categories in different ways. There are several classification schemes for

categorizing items or SKU

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Inventory Management1. ABC Classification:

Items are classified on the basis of sales on value terms.

A = very Important

B = Moderate Important

C = Little Important

ABC analysis is used for a) allocation of management time b)Improvement Efforts c) Setting up service levels d)Stocking decisions – e.g. A category items at regionaldistribution points, C category items at central warehouse,B category at few regional locations

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ABC Classification

Class A

5 – 15 % of units

70 – 80 % of value Class B

30 % of units

15 % of value

Class C 50 – 60 % of units

5 – 10 % of value

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Illustration:

The maintenance department for a small manufacturingfirm has responsibility for maintaining an inventory of spare parts for the machinery it services. The partsinventory, unit cost, annual usage are given in followingtable.

The department manager wants to classify the inventory parts according to the ABC system to determine whichstocks of parts should be closely monitored.

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ABC Classification

ABC Classification Illustration


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ABC Classification- Illustration

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1 $ 60 90

2 350 40

3 30 130

4 80 60

5 30 100

6 20 180

7 10 170

8 320 50

9 510 6010 20 120

PART UNIT COST ANNUAL USAGE/Demand

ABC Cl ifi ti


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ABC Classification

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9 $30,600 35.9 6.0 6.0

8 16,000 18.7 5.0 11.0

2 14,000 16.4 4.0 15.0

1 5,400 6.3 9.0 24.0

4 4,800 5.6 6.0 30.03 3,900 4.6 10.0 40.0

6 3,600 4.2 18.0 58.0

5 3,000 3.5 13.0 71.0

10 2,400 2.8 12.0 83.0

7 1,700 2.0 17.0 100.0

TOTAL % OF TOTAL % OF TOTAL

PART VALUE VALUE QUANTITY % CUMMULATIVE

A

B

C

$85,400

ABC Classification


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ABC Classification

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Example 10.1

% OF TOTAL % OF TOTALCLASS ITEMS VALUE QUANTITY

A 9, 8, 2 71.0 15.0

B 1, 4, 3 16.5 25.0

C 6, 5, 10, 7 12.5 60.0


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2. FSN classification

Items are classified as Fast moving , slow moving andnon-moving.

Slow moving items are stored centrally and fastmoving items are stocked de-centrally.

Non-moving items are candidates for disposal.

This type of classification is popular in retail industry.

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3. VED Classification:

Items are classified on criticality:

Vital = V, Essential = E , Desirable = D

This type of classification is popular in maintenancemanagement.

One can fix different service levels for different items.

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Two Forms of Demand

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Dependent

Demand for items used to produce final products

Tires for autos are a dependent demand item Independent

Demand for items used by external customers

Cars, appliances, computers, and houses are

examples of independent demand inventory


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Decoupling Inventory:

• Entire supply chain is usually divided into multiple stages with

multiple decision makers.

• Decision making units can be both at both organisational and

departmental level.• At organisational and departmental boundaries large

inventories can be held.

• The decoupling inventory provides the flexibility needed

by each decision making unit to manage its operations

independently and to optimise its performance.

• Improved coordination among stages can reduce decoupling

inventory significantly. 4-64


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Illustration :

LT -Shipment by air = 7 days

LT- Shipment by sea = 45 days

Average demand = 100/day

Pipeline Inventory ( Shipment by air) = 700 units

Pipeline Inventory ( Shipment by Sea = 4500 units



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Dead Inventory or Stock:

Dead Stock refers to that part of non-movinginventory that is unlikely to be of any further use insupply chain operations or markets.

Dead Stock, essentially includes items that have become

obsolete because of changes in customer preferences,design, production processes.

Unfortunately, in many firms dead stock is allowed toaccumulate as disposal of dead stock show up in balance

sheets as financial loss. Rather it is wrongly shown asassets.

Firms should carefully monitor dead stock and find meansto reduce it.

SCM Inventory Part -II.pdf

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