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Role of Inventory in theSupply Chain
Overstocking: Amount available
exceeds demand
Liquidation, Obsolescence, Holding
Understocking: Demand exceeds
amount available
Lost margin and future sales
Goal: Matching supply and demand
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Understanding Inventory
The inventory policy is affected by:
Demand Characteristics
Lead Time
Number of Products Objectives
Service level
Minimize costs
Cost Structure
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Cost Structure
Order costs
Fixed
Variable
Holding Costs
Insurance
Maintenance and Handling
Taxes
Opportunity Costs
Obsolescence
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EOQ: A View of Inventory*
Time
Inventory
Order
Size
Note:
No Stockouts
Order when no inventory
Order Size determines policy
Avg. Inventory
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EOQ:Total Cost*
0
20
40
60
80
100
120
140
160
0 500 1000 1500
Order Quantity
Cost
Total Cost
Order Cost
Holding Cost
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EOQ: Calculating TotalCost*
Purchase Cost Constant
Holding Cost: (Avg. Inven) * (HoldingCost)
Ordering (Setup Cost):Number of Orders * Order Cost
Goal: Find the Order Quantity thatMinimizes These Costs:
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Fixed costs: Optimal Lot Size and
Reorder Interval (EOQ)
R: Annual demandS: Setup or Order
Cost
C: Cost per unit
h: Holding cost peryear as afraction ofproduct cost
H: Holding cost perunit per year
Q: Lot Size
T: Reorder intervalRHST
HRSQ
hCH
2
2
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Example
Demand, R = 12,000 computersper year
Unit cost, C = $500
Holding cost, h = 0.2Fixed cost, S = $4,000/order
Q = 980 computersCycle inventory = Q/2 = 490
Flow time = Q/2R = 0.49 month
Reorder interval, T = 0.98 month
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EOQ: Another Example
Book Store Mug Sales
Demand is constant, at 20 units a week
Fixed order cost of $12.00, no lead time
Holding cost of 25% of inventory valueannually
Mugs cost $1.00, sell for $5.00
QuestionHow many, when to order?
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EOQ: ImportantObservations*
Tradeoffbetween set-up costs andholding costs when determining orderquantity. In fact, we order so that these
costs are equal per unit time Total Cost is not particularly sensitive
to the optimal order quantity
Order Quantity 50% 80% 90% 100% 110% 120% 150% 200%
Cost Increase 125% 103% 101% 100% 101% 102% 108% 125%
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The Effect ofDemand Uncertainty
Most companies treat the world as if it werepredictable:
Production and inventory planning are based onforecasts of demand made far in advance of the selling
season Companies are aware of demand uncertainty when they
create a forecast, but they design their planning processas if the forecast truly represents reality
Recent technological advances have increasedthe level of demand uncertainty:
Short product life cycles
Increasing product variety
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Example: SnowTime Sporting Goods
Fashion items have short life cycles,high variety of competitors
SnowTime Sporting Goods
New designs are completed One production opportunity
Based on past sales, knowledge of theindustry, and economic conditions, the
marketing department has a probabilisticforecast
The forecast averages about 13,000, butthere is a chance that demand will be
greater or less than this.
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SnowTime DemandScenarios
Demand Scenarios
0%
5%
10%
15%
20%
25%30%
8000
1000
0
1200
0
1400
0
1600
0
1800
0
Sales
Probability
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SnowTime Costs
Production cost per unit (C): $80
Selling price per unit (S): $125
Salvage value per unit (V): $20
Fixed production cost (F): $100,000 Q is production quantity, D demand
Profit =Revenue - Variable Cost - Fixed Cost+ Salvage
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SnowTime Scenarios
Scenario One:
Suppose you make 12,000 jackets anddemand ends up being 13,000 jackets.
Profit = 125(12,000) - 80(12,000) - 100,000= $440,000
Scenario Two:
Suppose you make 12,000 jackets anddemand ends up being 11,000 jackets.
Profit = 125(11,000) - 80(12,000) - 100,000
+ 20(1000) = $ 335,000
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SnowTime Best Solution
Find order quantity that maximizesweighted average profit.
Question: Will this quantity be lessthan, equal to, or greater thanaverage demand?
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(s, S) Policies
For some starting inventory levels, it is better tonot start production
If we start, we always produce to the same level
Thus, we use an (s,S) policy. If the inventorylevel is below s, we produce up to S.
s is the reorder point, and S is the order-up-tolevel
The difference between the two levels is drivenby the fixed costs associated with ordering,transportation, or manufacturing
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Notation
AVG = average daily demand
STD = standard deviation of daily demand
LT = replenishment lead time in days
h = holding cost of one unit for one day SL = service level (for example, 95%). This
implies that the probability of stocking out is100%-SL (for example, 5%)
Also, the Inventory Position at any time is theactual inventory plus items already ordered, butnot yet delivered.
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Analysis
The reorder point has two components:
To account for average demand during lead time:LTAVG
To account for deviations from average (we call this
safety stock)z STD LT
where z is chosen from statistical tables to ensure thatthe probability of stockouts during leadtime is100%-SL.
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Example
The distributor has historically observed weeklydemand of:
AVG = 44.6 ; STD = 32.1Replenishment lead time is 2 weeks, and desired
service level SL = 97% Average demand during lead time is:
44.6 2 = 89.2
Safety Stock is:
1.88 32.1 2 = 85.3
Reorder point is thus 175, or about 3.9 weeks ofsupply at warehouse and in the pipeline
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Model Two:Fixed Costs*
In addition to previous costs, a fixed cost K ispaid every time an order is placed.
We have seen that this motivates an (s,S) policy,where reorder point and order quantity aredifferent.
The reorder point will be the same as theprevious model, in order to meet meet theservice requirement:
s = LTAVG + z AVG L What about the order up to level?
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Model Two:The Order-Up-To Level*
We have used the EOQ model to balance fixed,variable costs:
Q=(2 K AVG)/h If there was no variability in demand, we would
order Q when inventory level was at LT AVG.Why?
There is variability, so we need safety stockz AVG * LT
The total order-up-to level is:S=max{Q, [LT AVG+ z AVG * LT]}
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Model Two: Example*
Consider the previous example, but with thefollowing additional info:
fixed cost of $4500 when an order is placed
$250 product cost
holding cost 18% of product
Weekly holding cost:h = (.18 250) / 52 = 0.87
Order quantity
Q=(2 4500 44.6 / 0.87 = 679 Order-up-to level:
s + Q = 85 + 679 = 765
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What to Make?
Question: Will this quantity beless than, equal to, or greater thanaverage demand?
Average demand is 13,100 Look at marginal cost Vs. marginal
profit
if extra jacket sold, profit is 125-80 =45
if not sold, cost is 80-20 = 60
So we will make less than average
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SnowTime Expected Profit
Expected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Profit
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SnowTime Expected Profit
Expected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Profit
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SnowTime:Important Observations
Tradeoff between ordering enough tomeet demand and ordering too much
Several quantities have the same average
profit Average profit does not tell the whole
story
Question: 9000 and 16000 unitslead to about the same averageprofit, so which do we prefer?
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Key Points from this Model The optimal order quantity is not
necessarily equal to average forecastdemand
The optimal quantity depends on the
relationship between marginal profitand marginal cost
As order quantity increases, averageprofit first increases and then decreases
As production quantity increases, riskincreases. In other words, theprobability of large gains andof large
losses increases
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Initial Inventory
Suppose that one of the jacket designs isa model produced last year.
Some inventory is left from last year
Assume the same demand pattern asbefore
If only old inventory is sold, no setup cost
Question: If there are 7000 unitsremaining, what should SnowTime do?What should they do if there are 10,000
remaining?
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Initial Inventory and Profit
0
100000
200000
300000
400000
500000
5000
6500
8000
9500
1100
0
1250
0
1400
0
1550
0
Production Quantity
Profit
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Periodic Review Policy
Each review echelon, inventoryposition is raised to the base-stocklevel.
The base-stock level includes twocomponents:
Average demand during r+L days (the
time until the next order arrives):(r+L)*AVG
Safety stock during that time:
z*STD*r+L
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Inventory Management: BestPractice
Periodic inventory review policy(59%)
Tight management of usage rates,lead times and safety stock (46%)
ABC approach (37%)
Reduced safety stock levels (34%)
Shift more inventory, or inventoryownership, to suppliers (31%)
Quantitative approaches (33%)
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Inventory Management: BestPractice
Periodic inventory reviews
Tight management of usage rates,lead times and safety stock
ABC approach
Reduced safety stock levels
Shift more inventory, or inventoryownership, to suppliers
Quantitative approaches
Ch I I t
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Changes In InventoryTurnover
Inventory turnover ratio =annual sales/avg. inventory
level
Inventory turns increased by 30%from 1995 to 1998
Inventory turns increased by 27%
from 1998 to 2000 Overall the increase is from 8.0 turns
per year to over 13 per year over afive year period ending in year 2000.
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Industry UpperQuartile
Median LowerQuartile
Dairy Products 34.4 19.3 9.2
Electronic Component 9.8 5.7 3.7
Electronic Computers 9.4 5.3 3.5
Books: publishing 9.8 2.4 1.3
Household audio &video equipment
6.2 3.4 2.3
Household electricalappliances
8.0 5.0 3.8
Industrial chemical 10.3 6.6 4.4
Inventory Turnover Ratio
F t th t D i R d ti
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Factors that Drive Reductionin Inventory
Top management emphasis on inventoryreduction (19%)
Reduce the Number of SKUs in the
warehouse (10%) Improved forecasting (7%)
Use of sophisticated inventory
management software (6%) Coordination among supply chain
members (6%)
Other
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Factors that Drive Inventory TurnsIncrease
Better software for inventory management(16.2%)
Reduced lead time (15%)
Improved forecasting (10.7%) Application of SCM principals (9.6%)
More attention to inventory management
(6.6%) Reduction in SKU (5.1%)
Others