4 session inventory 2014

8/10/2019 4 SESSION Inventory 2014

1/21

Lecture 1 480 1

Inventory Management in a Supply Chain

Supply Chain Management: 2014

Dr. RAVI SHANKARProfessor

Department of Management Studies

Indian Institute of Technology DelhiHauz Khas, New Delhi 110 016, India

Phone: +91-11-26596421 (O); 2659-1991(H); (0)-+91-9811033937 (m)Fax: (+66)-(2) 5246020

Email: [email protected], [email protected]://web.iitd.ac.in/~ravi1

What is an Inventory System

Inventory is defined as the stock of any item or

resource used in an organization.

An Inventory System is made up of a set of

policies and controls designed to monitor the

levels of inventory and designed to answer

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the following questions:

What levels should be maintained?

When stock should be replenished? and How large orders should be? i.e. what is the

optimal size of the order?

Purposes of Inventory

1. To maintain independence of operations

2. To meet variation in product demand

3. To allow flexibility in production scheduling

3

4. To provide a safeguard for variation in raw

material delivery time

5. To take advantage of economic purchase-order size


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Lecture 1 480 2

Inventory issues

Demand Constant vs. variable

deterministic vs. stochastic

Lead timeReview time

Continuous vs. periodic

Excess demand Backorders lost sales Inventor

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,

Inventory change Perish, obsolescence

Decisions:

When, What, and

how many to order

ABC Inventory Management

Based on Pareto concept (80/20 rule)

and total usage in Rs. of each item.

Classification of items as A, B, or C

based on usage.

5

Purpose is to set priorities on effort

used to manage different SKUs, i.e. to

allocate scarce managementresources.

SKU: Stock Keeping Unit

ABC Inventory Management

A items: 20% of SKUs, 80% of Rs. Value

B items: 30 % of SKUs, 15% of Rs. Value

C items: 50 % of SKUs, 5% of Rs. Value

6

.

Percents are approximate.

Danger: Rs. Value may not reflect importance of

any given SKU!


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Lecture 1 480 3

ItemAnnual Usage in

Units Unit Cost Rupees Usage

Percentage ofTotal Rupees

Usage

1 5,000 Rs. 1.50 Rs. 7,500 2.9%

2 1,500 8.00 12,000 4.7%

3 10,000 10.50 105,000 41.2%

Example of SKU list for 10 items

7

4 6,000 2.00 12,000 4.7%

5 7,500 0.50 3,750 1.5%

6 6,000 13.60 81,600 32.0%

7 5,000 0.75 3,750 1.5%8 4,500 1.25 5,625 2.2%

9 7,000 2.50 17,500 6.9%

10 3,000 2.00 6,000 2.4%

Total Rs. 254,725

100.0%

ABC Chart for SKU List

60.0%

80.0%

100.0%

120.0%

20 0%

25.0%

30.0%

35.0%

40.0%

45.0%

ive%

Usage

ntUsage A B C

8

0.0%

20.0%

40.0%

0.0%

5.0%

10.0%

15.0%

.

3 6 9 2 4 1 10 8 5 7

Cumula

Perce

Item No.

Cumulative Percentage

ABC Application: IMPLICATION IN A

SUPPLY CHAIN?Policies based on the ABC:

Develop links with A suppliers more;

Get tighter control of A items;

Forecast A more carefully.

9

Applications Jewelry Store

Dining Restaurant

Outdoor Retailer

Large Department Store


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Lecture 1 480 4

Basic inventory elements

Carrying cost,Carrying cost, Cc Include facility operating costs, record

keeping, interest, etc.

Ordering cost,Ordering cost, Co Include purchase orders, shipping, handling,

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inspection, etc.

Shortage (stock out) cost,Shortage (stock out) cost, Cs Sometimes penalties involved; if customer is

internal, work delays could result

Carrying Costs

Category

Cost (and Range) as aPercent of Inventory

Value

Housing costs (including rent or depreciation,operating costs, taxes, insurance)

6% (3 -10%)

Material handling costs (equipment lease orde r ecia ti on ower o er ati n cost

3% (1 - 3.5%), ,

Labor cost 3% (3 -5%)

Investment costs (borrowing costs, taxes, andinsurance on inventory)

11% (6 - 24%)

Pilferage, space, and o bsolescence 3% (2 -5%)

Overall carrying cost 26%

Inventory

- to study methods to deal with

how much stock of items should be kept

on hands that would meet customer

demand

2/7/201412 12

Objectives are to determine:

a) how much to order, and

b) when to order


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Lecture 1 480 5

Inventory models

Here, we study the following two different models:

1. Basic model

2. Model with re-order points

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Basic model

The basic model is known as:

Economic Order Quantity (EOQ) Models

Objective is to determine the optimal order size thatwill minimize total inventory costs

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How the objective is being achieved?

Quantity

on hand

Q Usagerate

Profile of Inventory Level Over Time

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Receiveorder

Placeorder

Receiveorder

Placeorder

Receiveorder

Lead time

Reorderpoint


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Lecture 1 480 6

Profile of Frequent OrdersIMPLICATION IN A SUPPLY CHAIN?

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Basic EOQ models

Three models to be discussed:

1 Basic EOQ model

2 EOQ model without instantaneous

recei t

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3. EOQ model with shortages.

The Basic EOQ Model

The optimal order size, Q, is to minimize the sum of carrying costs and ordering costs.

Assumptions and Restrictions:

- Demand is known with certainty and is relatively constant over time.

- No shortages are allowed.

- Lead time for the receipt of orders is constant. (will consider later)

- The order quantity is received all at once and instantaneously.

(c) Dr. Ravi Shankar, AIT (2008) 18

How to determine

the optimal valueQ*?


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Lecture 1 480 7

Determine of Q

We try to Find the total cost that need to spend for keeping

inventory on hands

= total ordering + stock on hands

Determine its optimal solution by finding its first

derivative with respect to Q

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How to get these values?

1. Find out the total carrying cost

2. Find out the total ordering cost

3. Total cost = (1) + (2)4. Equate (1) and (2) and Find Q*

The Basic EOQ Model

We assumed that, we will only keep half the inventory over a year then

The total carry cost/yr = Cc x (Q/2). Total order cost = Co x (D/Q)

Then , Total cost = 2Q

CQDCTC co += Finding optimal Q*

(c) Dr. Ravi Shankar, AIT (2008) 20

c

o

co

CDCQ

CQ

TC

2

2

*

min

=

+=

Cost Relationships for Basic EOQ(Constant Demand, No Shortages)

TotalCost

Carrying

2/7/201421 21

OrderingCost

EOQ balances carrying

costs and orderingcosts in this model.

Q* Order Quantity (how much)


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Lecture 1 480 8

The Basic EOQ Model

Total annual inventory cost is sum of ordering and carrying cost:

2Q

CQDCTC co +=

To order inventory

To keep inventory

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Figure The EOQ cost model

Try to get this value

Numerical Illustration

000,3.2

)000,2()50.1(

000,2000,10

)300(2*

*)(:costinventoryannualTotal

Kg000,2)50.1(

)000,10)(300(22*:sizeorderOptimal

kg10,000DRs.300,C,50.1.C:parametersModel

min

oc

=+=+=

===

===

RsQ

CQ

DCTC

CDC

Q

Rs

co

c

o

23

inventory-store-of-Days735365*/days365time-cycle-Order

5000,2000,10

*:year-per-orders-of-Number

===

==

QD

QD

Robustness of EOQ model

IMPLICATION IN A SUPPLY CHAIN?

TotalCost

TC

Very Flat Curve - Good!!

2/7/201424 24

Order QuantityQ*Q*-Q Q*+Q

Would have to mis-specify Q* by quite a bit

before total annual inventory costs wouldchange significantly.


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Lecture 1 480 9

Model with re-order points

Thereorder point is the inventory level at which a new order is placed.

Order must be made while there is enough stock in place to cover demand during lead time.

Formulation: R = dL, whe re d = demand rate per time period, L = lead time

Then R = dL = (10,000/311)(10) = 321.54

Working days/yr

2/7/201425 (c) Dr. Ravi Shankar, AIT (2008) 25

What happens to Reorder

level when

Inventory level depletes at slower or faster rate

during lead time.

s s ue to t e act t at eman s uncerta n

during the lead time

To cope up with uncertainty of

demand during lead time

Keep safety stock as a safeguard or hedge

against stock-out scenarios.


10/21

Lecture 1 480 10

How to decide Safety Stock?

)( LZLdR d+=

28

Safety stock

2/7/201429 (c) Dr. Ravi Shankar, AIT (2008) 29

Numerical Illustration

Find Reorder point and safety

stock for service level of 95%

dayperKg5days,10Lday,perKg30 d ===d

30

Kg.26.1:stockSafety

Kg1.3261.26300)10()5()65.1()10(30

1.65Zlevel,-service95%For

=+=+=+=

=

LZLdR d


11/21

Lecture 1 480 11

CASE STUDY IN A TUTORIAL MODE

A TUTORIAL ON RISK POOLING

Dr. RAVI SHANKAR

Professor

Department of Management Studies

Indian Institute of Technology DelhiHauz Khas, New Delhi 110 016, India

Phone: +91-11-26596421 (O); 2659-1991(H); (0)-+91-9811033937 (m)Fax: (+91)-(11) 26862620

Email: [email protected]

http://web.iitd.ac.in/~ravi1

RISK POOLING

Risk pooling is an important

concept in supply chain

management. The idea of risk

pooling is executed by a

centralized distribution system

which caters to the requirements

of all the markets in a givenregion instead of separate

warehouse allocated for different

markets.

Risk Pooling

Consider these two systems:

Warehouse One Market One

Market TwoWarehouse Two

Market Two

Supplier Warehouse

Market One


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Lecture 1 480 12

DISTRIBUTOR

Centralized Systems

Warehouse

Retailers

Decentralized System

DISTRIBUTOR

Warehouses

Retailers

Factory

Central

warehouse

Market two


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Lecture 1 480 13

Factory

Warehouse 1

Warehouse 2

Decentralized Warehouses

Factory

Market one

Market two

Centralised

warehouse at

Ayutthaya

Market OnePathumthani Warehouse

Factory: ABC

Central

warehouse

Market Two

Market Two

ABC Chiang

Rai

Market One

Prachin Buri Warehouse

Central

warehouse:

Ayutthaya

Market Pathumthani

Market Prachin Buri


14/21

Lecture 1 480 14

Market OnePathumthani Warehouse Market one

Market Two

Market Two

ABC company

Market One

Prachin Buri Warehouse

Central

warehouse

(Ayutthaya)

Market two

Market one

Market two

WEEK 1 2 3 4 5 6 7 8

Pathumthani 68(-17) 37(+14) 45(+6) 58(-7) 16(+35) 32(+19) 72(-21) 80(-29)

Prachin Buri 87(-27) 62(-3) 55(+4) 67(-8) 12(+47) 42(+17) 69(-10) 81(-22)

TOTAL 155(-45) 99(+11) 100(+10) 125(-15) 28(+82) 74(+36) 1 41 (-31 ) 1 61 (-51 )

PRODUCT A

100EMAND

HISTORICAL DEMAND DATA

51

59

110

Average

0

10

20

30

40

50

60

70

80

90

1 2 3 4 5 6 7 8

WEEK

AVERAGEWEEKLYD

DEMANDPathumthaniDEMAND Prachin Buri

TERMINOLOGY

D: Average daily demand faced by the distributor.

d: standard deviation of the daily demand faced bythe distributor.

L: Replenishment lead time from the supplier to thedistributor in days

Co: Fixed cost (set up cost) incurred every time thewarehouse places an order, it includestransportation cost.

Cc: Cost of holding one unit of the product in theinventory for one day at the warehouse.

: Service level -the probability of not stocking outduring lead time.


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Lecture 1 480 15

Average demand during lead time =LD.

This ensures that if a distributor places an order the system hasenough inventory to cover expected demand during lead time.

Safety stock = z d

This is the amount of inventory distributor needs to keepto meet deviations from average demand during lead time.

z: Safet factor which is chosen from statistical

L

table to ensure that probability of stock out isexactly (1-)

Reorder level (s) = average demand during leadtime + safety stock

s = LD + z d

Whenever the inventory level drops below reorder level thedistributor should place new order to raise its inventory.

L

Order quantity (Q): It is the number of items orderedeach time places an order that minimizes the averagetotal cost per unit of time distributor.

co QCQDCTC

2min +=

Order-up-to level (S): Since there is variability indemand the distributor places an order for Q itemswhenever inventory is below reorder level (s).

S= Q + s

c

o

CDCQ 2* =

Average inventory = Q/2 + z d

Coefficient of variation = (d ) / DL

L


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Lecture 1 480 16

CASE STUDY OF RISK POOLING

Let us illustrate this with an example of a Chiang Raibased company ABC that produces certain type ofproducts and distributes them in the SouthThailand region .

The current distribution system partitions S-Thailandregion into two markets each of which has aware ouse.

1. One warehouse is located in Prachin Buri

2. Another one located in Pathumthani.

Alternative strategy of centralized distribution systemreplaces two warehouses by a single warehouselocated between the two cities in Ayutthaya thatwill serve all customer orders in both markets

ASSUMPTIONS

Manufacturing facility has sufficient

capacity to satisfy any warehouse demand

Lead time for delivery to each warehouse is

about one week and is assumed to be

cons an .

Delivery time does not change significantly

if we adopt a centralized distribution

system. Service level of 95% that is the probability of

stocking out is 5% is maintained.

DATA ANALYSIS

Now with analysis of weekly demand

for two different products, product A

and product B produced by ABC

company for last 8 weeks in both

decide which distribution strategy

will be more efficient and cost

effective.


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Lecture 1 480 17

WEEK 1 2 3 4 5 6 7 8

Pathumthani 68 37 45 58 16 32 72 80

Prachine Buri 87 62 55 67 12 42 69 81

TOTAL 155 99 100 125 28 74 141 161

PRODUCT-A

100EMAND

HISTORICAL DEMAND DATA FOR PRODUCT-A

0

10

20

30

40

50

60

70

80

90

1 2 3 4 5 6 7 8

WEEK

AVERAGEWEEKLYD

DEMAND Pathumthani

DEMAND Prachine Buri

WEEK 1 2 3 4 5 6 7 8

Pathumthani 0 0 1 3 2 4 0 1

Prachine Buri 1 0 2 0 0 3 1 1

TOTAL 1 0 3 3 2 7 1 2

PRODUCT-B

D EM AN D P at hu mt ha ni D EM AN D P ra ch in e B ur i

HISTORICAL DEMAND DATA FOR PRODUCT-B

0

0.5

1

1.52

2.5

3

3.5

4

4.5

1 2 3 4 5 6 7 8

WEEK

AVERAGE

DEMAND

PRODUCT AVERAGE

DEMAND

STANDARD

DEVIATION

COEFFICIENT

OFVARIATION

Pathumthani A 51 20.70 0.41

Pathumthani B 1.38 1.41 1.02

ANALYSIS OF HISTORICAL DATA

Prachin Buri A 59.38 22.23 0.32

Prachin Buri B 1 1 1

CENTRALWarehouse

A 110.38 39.14 0.35

CENTRALWarehouse

B 2.38 1.99 0.84


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Lecture 1 480 18

SAMPLE CALCULATIONS

FOR PRODUCT-A IN PATHUMTHANI

WAREHOUSE

1. Average demand = (68+37+45+58+16+32+72+80)/8=51

2. Standard deviation of demand =

= 20.7

3. Coefficient of variation = 20.7/51 = 0.41

2 2 2(68 51) (51 37) .............. (80 51)

8

+ +

GENERALIZATIONS

Average demand for Product-A is much higher thanProduct-B, which is a slow moving product.

Both standard deviation (absolute) and coefficient ofvariation (relative to average demand) are measureof variability of demand, but we find that STD forProduct-A is higher but coefficient of variation ofProduct-B is higher.

For centralized distribution average demand issimply the sum of the demand faced by each of

existing warehouse

However the variability of demand as measured by or COV faced by central warehouse is lower thanthat faced by the two existing ones.

NUMERICAL VALUES

Safety factor (Z) =1.65

Fixed cost for both the products (Co)

= Rs 3500

Inventory holding cost (Cc)

= Rs 18.5 er unit er week.

Cost of transportation from warehouse toa customer Current distribution system = Rs 50 per

product Centralized distribution system = Rs 60 perproduct.


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Lecture 1 480 19

INVENTORY LEVELS

PRODUCT AVERAGEDEMANDDURINGLEAD TIME

SAFETYSTOCK(SS)

REORDERPOINT(s)

ORDERQUANTITY(Q)

ORDERUPTOLEVEL(S)

AVERAGEINVENTORY

PathumthaniA 51 34.16 85 139 224 104

PathumthaniB 1.38 2.33 4 23 27 14

PrachineBuriA 59.38 36.68 96 150 246 112

PrachineBuri B 1 1.65 3 19 22 11CENTRALIZED

W/H A 110.38 64.58 175 204 379 167CENTRALIZED

W/H B 2.38 3.28 6 30 36 18

4. Safety stock =1.65 20.7 = 34.16

5. Reorder point = 51 + 34.16 = 85.16

1

SAMPLE CALCULATIONSFOR PRODUCT-A IN PATHUMTHANI WAREHOUSE

6. Order quantity = = 139

7. Order up to level = 139 +85 = 224

8. Average inventory = 139/2 +34.16 = 103.66

18.5

PERCENT REDUCTION IN INVENTORY

REDUCTION IN AVERAGE INVENTORY

PRODUCT A = = 22.7%(104 112 167) 100(104 112)

+

+

PRODUCT B = = 28%(14 11 18)

100(14 11)

+

+


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Lecture 1 480 20

ANALYSIS AT DIFFERENT

SERVICE LEVELS

When average inventory for different level ofservice is calculated corresponding tovarying value of z it was found that thereexists a trade-off between service level and

.

SERV

ICELEVE

L (%)

90 91 92 93 94 95 96 97 98 99 99.9

Z 1.29 1.34 1.41 1.48 1.56 1.65 1.75 1.88 2.05 2.33 3.08

PERCENTAGE REDUCTION IN

SERVICELEVEL

(%)

90 91 92 93 94 95 96 97 98 99 99.9

PRODUCT-A 24 23.7 23.4 23.1 23 22.7 22.3 21.8 21.7 21.2 19.5

PRODUCT-B 27.12 27.07 27.0 26.94 26.89 26.82 26.72 26.59 26.44 26.2 25.65

PERCENT REDUCTION IN AVERAGE INVENTORY

0

5

10

15

20

25

30

90 93 96 99

SERVICE LEVEL

%R

EDUC

TIONINAVG

INVENTORY

PRODUCT-A

PRODUCT-B

If a supply chain goes for higher level of service ithas to compromise with the percent reduction in theinventory level and vice versa.

Comment on the Following Generalizations:

o prov e g servce eve servce eve as omaintain high inventory too.

Percent reduction in inventory decreases with

increase in service level.


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Lecture 1 480 21

IDEAL SITUATION

This works best for:

High coefficient of variation, which

reduces required safety stock.

Negatively correlated demand as in

such a case the high demand from

one customer will be offset by lowdemand from another

4 session inventory 2014

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