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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
2/7/20142 2
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
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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
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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!!
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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.
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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
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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
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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