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Inventory Management and Risk Pooling
Chap 03 王仁宏 助理教授
國立中正大學企業管理學系
©Copyright 2001 製商整合科技中心
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Outline of the Presentation
Introduction to Inventory Management
The Effect of Demand Uncertainty (s,S) Policy Risk Pooling
Centralized vs. Decentralized Systems
Practical Issues in Inventory Management
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Supply
Sources:plantsvendorsports
RegionalWarehouses:stocking points
Field Warehouses:stockingpoints
Customers,demandcenterssinks
Production/purchase costs
Inventory &warehousing costs
Transportation costs Inventory &
warehousing costs
Transportation costs
Logistics Network
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Case: JAM Electronics
• JAM produces about 2,500 different products in the Far East.
• Central warehouse in Korea• 70% service level for JAM USA
– difficulty forecasting customer demand– long lead time in supply chain to USA– large number of SKUs handled by JAM USA– low priority given the US subsidiary by
headquarter in Seoul
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Inventory (1/2)
• Where do we hold inventory?– Suppliers and manufacturers– warehouses and distribution centers– retailers
• Types of Inventory– WIP– raw materials– finished goods
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Inventory (2/2)
• Why do we hold inventory?– Uncertainty in customer demand
• short life cycle implies that historical data may not be available
• many competing products in the marketplace
– Uncertainty in quantity and quality of the supply, supplier costs, and delivery times
– Economies of scale offered by transportation companies
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Goals: Reduce Cost, Improve Service
• By effectively managing inventory:– Xerox eliminated $700 million inventory from its suppl
y chain– Wal-Mart became the largest retail company utilizing
efficient inventory management– GM has reduced parts inventory and transportation co
sts by 26% annually
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Goals: Reduce Cost, Improve Service
• By not managing inventory successfully– In 1994, “IBM continues to struggle with shortages in their
ThinkPad line” (WSJ, Oct 7, 1994)– In 1993, “Liz Claiborne said its unexpected earning decline is the
consequence of higher than anticipated excess inventory” (WSJ, July 15, 1993)
– In 1993, “Dell Computers predicts a loss; Stock plunges. Dell acknowledged that the company was sharply off in its forecast of demand, resulting in inventory write downs” (WSJ, August 1993)
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Understanding Inventory
• The inventory policy is affected by:– Demand Characteristics: known in advance or
random– Lead Time– Number of Different Products Stored in the
Warehouse– Length of Planning Horizon– Objectives
• Service level• Minimize costs
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Cost Structure
– Cost Structure • order costs:
– cost of product – transportation costs
• holding costs: – tax– insurance– obsolescence – opportunity cost
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EOQ: A Simple Model*
• 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 value
annually– Mugs cost $1.00, sell for $5.00
• Question– How many, when to order?
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EOQ: A View of Inventory*
Time
Inventory
OrderSize
Note:• No Stockouts• Order when no inventory• Order Size determines policy
Avg. Inven
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EOQ: Calculating Total Cost*
• Purchase Cost Constant• Holding Cost: (Avg. Inven) * (Holding Cost)
• Ordering (Setup Cost):Number of Orders * Order Cost
• Goal: Find the Order Quantity that Minimizes These Costs:
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EOQ:Total Cost*
0
20
40
60
80
100
120
140
160
0 500 1000 1500
Order Quantity
Co
st
Total Cost
Order Cost
Holding Cost
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EOQ: Optimal Order Quantity*
• Optimal Quantity =
(2*Demand*Setup Cost)/holding cost
• So for our problem, the optimal quantity is 316
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EOQ: Important Observations*
• Tradeoff between set-up costs and holding costs when determining order quantity. In fact, we order so that these costs are equal per unit time
• Total Cost is not particularly sensitive to the optimal order quantity
b for b*EOQ 50% 80% 90% 100% 110% 120% 150% 200%
Cost Increase 25% 2.5% 0.5% 0 0.4% 1.6% 8.0% 25%
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The Effect of Demand Uncertainty (1/2)
• Most companies treat the world as if it were predictable:– Production and inventory planning are
based on forecasts 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 process as if the forecast truly represents reality
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The Effect of Demand Uncertainty (1/2)
• Recent technological advances have increased the level of demand uncertainty:– Short product life cycles – Increasing product variety
• The three principles of all forecasting techniques:
– Forecasting is always wrong– The longer the forecast horizon the worst is the forecast – Aggregate forecasts are more accurate
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Case: Swimsuit Production
• Fashion items have short life cycles, high variety of competitors
• Swimsuit products – New designs are completed– One production opportunity– Based on past sales, knowledge of the industry,
and economic conditions, the marketing department has a probabilistic forecast
– The forecast averages about 13,000, but there is a chance that demand will be greater or less than this.
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Swimsuit Demand Scenarios
Demand Scenarios
0%5%
10%15%20%25%30%
Sales
P
robabili
ty
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Swimsuit 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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Swimsuit Scenarios
• Scenario One:– Suppose you make 12,000 jackets and demand 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 and demand ends
up being 11,000 jackets.– Profit = 125(11,000) - 80(12,000) - 100,000 + 20(1000) = $
335,000
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Swimsuit Best Solution
• Find order quantity that maximizes weighted average profit.
• Question: Will this quantity be less than, equal to, or greater than average demand?
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What to Make?
• 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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Swimsuit Expected Profit
Expected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Pro
fit
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Swimsuit Expected Profit
Expected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Pro
fit
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Swimsuit Expected Profit
Expected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Pro
fit
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Swimsuit : Important Observations
• Tradeoff between ordering enough to meet demand and ordering too much
• Several quantities have the same average profit• Average profit does not tell the whole story
• Question: 9000 and 16000 units lead to about the same average profit, so which do we prefer?
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Probability of Outcomes
0%
20%
40%
60%
80%
100%
Cost
Pro
ba
bilit
y
Q=9000
Q=16000
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Key Points from this Model
• The optimal order quantity is not necessarily equal to average forecast demand
• The optimal quantity depends on the relationship between marginal profit and marginal cost
• As order quantity increases, average profit first increases and then decreases
• As production quantity increases, risk increases. In other words, the probability of large gains and of large losses increases
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Initial Inventory
• Suppose that one of the jacket designs is a model produced last year.
• Some inventory is left from last year• Assume the same demand pattern as before• If only old inventory is sold, no setup cost
• Question: If there are 7000 units remaining, 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
Production Quantity
Pro
fit
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Initial Inventory and Profit
0
100000
200000
300000
400000
500000
Production Quantity
Pro
fit
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Initial Inventory and Profit
0
100000
200000
300000
400000
500000
Production Quantity
Pro
fit
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Initial Inventory and Profit
0
100000
200000
300000
400000
500000
5000
6000
7000
8000
9000
1000
0
1100
0
1200
0
1300
0
1400
0
1500
0
1600
0
Production Quantity
Pro
fit
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(s, S) Policies
• For some starting inventory levels, it is better to not start production
• If we start, we always produce to the same level• Thus, we use an (s,S) policy. If the inventory level
is below s, we produce up to S. • s is the reorder point, and S is the order-up-to level• The difference between the two levels is driven by
the fixed costs associated with ordering, transportation, or manufacturing
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A Multi-Period Inventory Model
• Often, there are multiple reorder opportunities
• Consider a central distribution facility which orders from a manufacturer and delivers to retailers. The distributor periodically places orders to replenish its inventory
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Case Study: Electronic Component Distributor
• Electronic Component Distributor
• Parent company HQ in Japan with world-wide manufacturing
• All products manufactured by parent company
• One central warehouse in U.S.
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Case Study:The Supply Chain
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Demand Variability: Example 1
Product Demand
150
75
225
100
150
50
125
61 48 53
104
45
0
50
100
150
200
250
Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar
Month
Demand(000's)
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Demand Variability: Example 1
Histogram for Value of Orders Placed in a Week
0
5
10
15
20
25
$25
,000
$50
,000
$75
,000
$10
0,00
0
$12
5,00
0
$15
0,00
0
$17
5,00
0
$20
0,00
0
Value of Orders Placed in a Week
Fre
qu
ency
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Reminder: The Normal Distribution
0 10 20 30 40 50 60
Average = 30
Standard Deviation = 5
Standard Deviation = 10
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The distributor holds inventory to:
• Satisfy demand during lead time
• Protect against demand uncertainty
• Balance fixed costs and holding costs
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The Multi-Period Inventory Model
• Normally distributed random demand• Fixed order cost plus a cost proportional to
amount ordered.• Inventory cost is charged per item per unit time• If an order arrives and there is no inventory, the
order is lost• The distributor has a required service level. • Intuitively, what will a good policy look like?
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A View of (s, S) Policy
Time
Inve
ntor
y L
evel
S
s
0
LeadTimeLeadTime
Inventory Position
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The (s,S) Policy
• (s, S) Policy: Whenever the inventory position drops below a certain level, s, we order to raise the inventory position to level S.
• The reorder point is a function of:– Lead Time– Average demand– Demand variability– Service level
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Notation
• AVG = average daily demand• STD = standard deviation of daily demand• LT = lead time in days• h = holding cost of one unit for one day• SL = service level (for example, 95%). • Also, the Inventory Position at any time is
the actual inventory plus items already ordered, but not 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 that the probability of stockouts during leadtime is 100%-SL.
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Example
• The distributor has historically observed weekly demand of:
AVG = 44.6 STD = 32.1lead time is 2 weeks, 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 of supply at warehouse and in the pipeline
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Model Two: Fixed Costs*
• In addition to previous costs, a fixed cost K is paid every time an order is placed.
• We have seen that this motivates an (s,S) policy, where reorder point and order quantity are different.
• The reorder point will be the same as the previous model, in order to meet meet the service 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 stock z 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 the following 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 quantityQ=(2 4500 44.6) / 0.87 = 679
• Order-up-to level:s + Q = 85 + 679 = 765
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Market Two
Risk Pooling
• Consider these two systems:
Supplier
Warehouse One
Warehouse Two
Market One
Market Two
Supplier Warehouse
Market OneLT = 1 week
1500 products, 10000 accounts
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Risk Pooling
• For the same service level, which system will require more inventory? Why?
• For the same total inventory level, which system will have better service? Why?
• What are the factors that affect these answers?
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Risk Pooling Example
• Compare the two systems:– two products– maintain 97% service level– $60 order cost– $0.27 weekly holding cost– $1.05 transportation cost per unit in decentralized
system, $1.10 in centralized system– 1 week lead time
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Risk Pooling Example
Week 1 2 3 4 5 6 7 8
Prod A, Market 1
33 45 37 38 55 30 18 58
Prod A, Market 2
46 35 41 40 26 48 18 55
Prod B, Market 1
0 2 3 0 0 1 3 0
Product B, Market 2
2 4 0 0 3 1 0 0
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Risk Pooling Example
Warehouse Product AVG STD CV s S Avg.Inven.
%Dec.
Market 1 A 39.3 13.2 .34 65 158 91
Market 2 A 38.6 12.0 .31 62 154 88
Market 1 B 1.125 1.36 1.21 4 26 15
Market 2 B 1.25 1.58 1.26 5 27 15
Centralized A
Centralized
77.9 20.7 .27 118 226 132 26%
B 2.375 1.9 .81 6 37 20 33%
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Risk Pooling:Important Observations
• Centralizing inventory control reduces both safety stock and average inventory level for the same service level.
• This works best for – High coefficient of variation, which reduces
required safety stock.– Negatively correlated demand. Why?
• What other kinds of risk pooling will we see?
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Risk Pooling:Types of Risk Pooling*
• Risk Pooling Across Markets• Risk Pooling Across Products• Risk Pooling Across Time
– Daily order up to quantity is:• LTAVG + z AVG LT
10 1211 13 14 15
Demands
Orders
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To Centralize or not to Centralize
• What is the effect on:– Safety stock?– Service level?– Overhead?– Lead time?– Transportation Costs?
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• Centralized Decision
Supplier
Warehouse
Retailers
Centralized Systems*
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Centralized Distribution Systems*
• Question: How much inventory should management keep at each location?
• A good strategy:
– The retailer raises inventory to level Sr each period
– The supplier raises the sum of inventory in the retailer and supplier warehouses and in transit to Ss
– If there is not enough inventory in the warehouse to meet all demands from retailers, it is allocated so that the service level at each of the retailers will be equal.
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Inventory Management: Best Practice
• 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 inventory
ownership, to suppliers (31%)• Quantitative approaches (33%)
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Inventory Turnover Ratio
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
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Memo