Title: Chapter 3 Inventory Management, Supply Contracts and Risk Pooling
1Chapter 3 Inventory Management, Supply Contracts
and Risk Pooling
- Qi Xu
- Professor of Donghua University
- Tel 021-62378860
- E-mail xuqi_at_dhu.edu.cn
2Outline of the Presentation
- 3.1 Introduction to Inventory Management
- 3.2 Single Warehouse Inventory
- (1) EOQ
- (2) Demand Forecast
- (3) Supply Contracts
- (4) A multi-Period Inventory Model
- (5) Periodic Review Policy
- 3.3 Risk Pooling
- 3.4 Centralized vs. Decentralized Systems
- 3.5 Managing Inventory in the SC
- 3.6 Practical Issues in Inventory Management
3(No Transcript)
4Case JAM Electronics Service Level Crisis
- JAM Electronics is a Korean manufacturer of
products such as industrial relays.The company
has five manufacturing facilities in different
countries in the Far East with headquarters in
Seoul,South Korea. - JAM produces about 2,500 different products, all
of them manufactured in the Far East. Finished
products are stored in a central warehouse in
Korea and are shipped from there to different
countries. Items sold in the US are transported
by ship to the warehouse in Chicago.
5Case JAM Electronics
- Problems the service level is at an all-time
low. Only about 70 of all orders are delivered
on time. - Difficulty forecasting customer demand.
- Long lead time in the supply chain.
- The large number of SKUs handled by JAM USA.
6Case JAM Electronics
7- By the end of this chapter, you should be able to
understand the following issues - How a firm can cope with huge variability in
customer demand. - What the relationship is between service and
inventory levels. - What an effective inventory management policy is.
8 4.1 Inventory
- Where do we hold inventory?
- Suppliers and manufacturers
- warehouses and distribution centers
- retailers
- Types of Inventory
- WIP
- raw materials
- finished goods
- Why do we hold inventory?
- Economies of scale
- Uncertainty in supply and demand
- Lead Time, Capacity limitations
9Goals Reduce Cost, Improve Service
- By effectively managing inventory
- Xerox eliminated 700 million inventory from its
supply chain - Wal-Mart became the largest retail company
utilizing efficient inventory management - GM has reduced parts inventory and transportation
costs by 26 annually
10Goals 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)
11Understanding Inventory
- The inventory policy is affected by
- Demand Characteristics
- Lead Time
- Number of Products
- Objectives
- Service level
- Minimize costs
- Cost Structure
12Cost Structure
- Order costs
- Fixed
- Variable
- Holding Costs
- Insurance
- Maintenance and Handling
- Taxes
- Opportunity Costs
- Obsolescence
134.2.1 EOQ A Simple Model
EOQ illustrates the trade-offs between ordering
and storage costs.
- A Case Book Store Mug Sales
- Demand is constant, at 20 units a week (D for a
year) - Fixed order cost of 12.00, no lead time (k)
- Holding cost of 25 of inventory value annually
(H) - Mugs cost 1.00, sell for 5.00
- Question
- How many(Q), when to order?
14EOQ A View of Inventory
Note No Stockouts Order when no inventory
Order Size determines policy
Inventory
Order Size
Avg. Inven
Time
15EOQ 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
16EOQTotal Cost
Total Cost
Holding Cost
Order Cost
17EOQ Optimal Order Quantity
- Optimal Quantity (2DemandSetup
Cost)/holding cost - QSqrt((2DK)/H)Sqrt(2205212)/25)316
- So for our problem, the optimal quantity is 316
18EOQ
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19EOQ
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20EOQ Important Observations
- Tradeoff between set-up costs and holding costs
when determining order quantity. - Total Cost is not particularly sensitive to the
optimal order quantity
21The Effect of Demand Uncertainty
- 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 - Recent technological advances have increased the
level of demand uncertainty - Short product life cycles
- Increasing product variety
22Outline
- 4.1 Introduction to Inventory Management
- 4.2 Single Warehouse Inventory
- (1) EOQ
- (2) Demand Forecast
- (3) Supply Contracts
- (4) A multi-Period Inventory Model
- (5) Periodic Review Policy
- 4.3 Risk Pooling
- 4.4 Centralized vs. Decentralized Systems
- 4.5 Managing Inventory in the SC
- 4.6 Practical Issues in Inventory Management
234.2.2 Demand Forecast
- 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
24Case SnowTime Sporting Goods
Case 2
- 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 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.
25Supply Chain Time Lines
Jan 01
Jan 02
Jan 00
Design
Production
Retailing
Feb 00
Sep 00
Sep 01
Feb 01
Production
26SnowTime Demand Scenarios
27SnowTime Costs
- The variable Production cost per unit (C) 80
- Selling price per unit (S) 125
- Salvage value per unit (V) 20
- Fixed production cost (F) 100,000
- To start production ,the manufacturer has to
invest 100,000 independent of the amount
produced. - Q is production quantity, D demand
- Profit Revenue - Variable Cost - Fixed Cost
Salvage
28SnowTime Scenarios
Profit Revenue - Variable Cost - Fixed Cost
Salvage
- 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
29SnowTime Best Solution
- Find order quantity that maximizes weighted
average profit. - Question Will this quantity be less than, equal
to, or greater than average demand?
30What to Make?
- Question Will this quantity be less than, equal
to, or greater than average 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
31SnowTime Expected Profit
- The quantity that maximizes average profit, is
about 12,000.
32SnowTime Expected Profit
- It indicates that producing 9,000 units or
producing 16,000 units will lead to about the
same average profit of 294,000.
33SnowTime 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?
34SnowTime Expected Profit
35Probability of Outcomes
- When the production quantity is 16,000 units, the
distribution of profit is not symmetrical. Losses
of 220,000 happen about 11, while profits of at
least 410,000 happen 50. - When the production quantity is 9,000 units ,the
distribution has only two possible outcomes.
Profit is either 200,000 with probability of
about 11,or 305,000 with probability of about
89.
36Key Insights 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
37SnowTime Costs The Effect of Initial Inventory
- 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
38SnowTime Expected Profit
39Initial 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 5000 units remaining, what
should SnowTime do? What should they do if there
are 10,000 remaining?
40Initial Inventory and Profit
41Initial Inventory and Profit
42Initial Inventory and Profit
If the manufacturer does not produce any
additional suits, no more than 5,000 units can
be sold and no additional fixed cost will be
incurred. However, it the manufacturer decides
to produce, a fixed production cost is charged
independent of the amount produced.
43Initial Inventory and Profit
Average profit excluding fixed production cost
Average profit including fixed production cost
44Analysis
- (1) there are 5000 units remaining
- If nothing is produced, average profit is equal
to 625000. - Production should increase inventory from 5,000
units to 12,000 units. Thus, average profit is
equal to 771000 (from the figure). - (2) there are 10,000 units remaining
- It is easy to see that there is no need to
produce anything because the average profit
associated with an initial inventory of 10,000 is
larger than what we would achieve if we produce
to increase inventory to 12,000 units. - If we produce, the most we can make on average is
a profit of375,000. This is the same average
profit that we will have if our initial inventory
is about 8,500 units. - Hence, if our initial inventory is below 8,5000
units, we produce to raise the inventory level to
12,000 units. If initial inventory is at least
8,5000 units,we should not produce anything.
45(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
464.2.3 Supply Contracts
Wholesale Price 80
Who takes the risk? What would the manufacturer
like?
47Demand Scenarios
48Distributor Expected Profit
49Distributor Expected Profit
470,000
50Supply Contracts (cont.)
- Distributor optimal order quantity is 12,000
units - Distributor expected profit is 470,000
- Manufacturer profit is 440,000
- Supply Chain Profit is 910,000
- Is there anything that the distributor and
manufacturer can do to increase the profit of
both?
51Supply Contracts (between manufacturer and
retailer)
In the previous strategy, the retailer takes all
the risk and the manufacturer takes zero risk.
This is why the retailer has to be very
conservative with the amount he orders. If the
retailer can transfer some of the risk to the
manufacturer, the retailer may be willing to
increase his order quantity and thus increase
both his profit and the manufacturer profit.
Wholesale Price 80
52Retailer Profit (Buy Back55)
53Retailer Profit (Buy Back55)
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,???513800?????,????????????471900
54Manufacturer Profit (Buy Back55)
55Manufacturer Profit (Buy Back55)
471,900
56Supply Contracts (between manufacturers
wholesale price and retailer)
What does wholesale price drive? How can
manufacturer benefit from lower price?
Wholesale Price ??
57Retailer Profit (Wholesale Price 70, Retailers
back 15 to manufacturer )
58Retailer Profit (Wholesale Price 70, RS 15)
504,325
59Manufacturer Profit (Wholesale Price 70, RS 15)
60Manufacturer Profit (Wholesale Price 70, RS 15)
481,375
61Supply Contracts
Wholesale Price 70, RS 15
62Supply Contracts
What is the maximum profit that the supply chain
can achieve? To answer this question, one needs
to forget about the transfer of money from the
retailer to the manufacturer.
Wholesale Price 80
63Supply Chain Profit
64Supply Chain Profit (Global optimization)
65Supply Contracts
66Supply Contracts Key Insights
- Effective supply contracts allow supply chain
partners to replace sequential optimization by
global optimization - Buy Back and Revenue Sharing contracts achieve
this objective through risk sharing
67Supply Contracts Case Study
- Example Demand for a movie newly released video
cassette typically starts high and decreases
rapidly - Peak demand last about 10 weeks
- Blockbuster purchases a copy from a studio for
65 and rent for 3 - Hence, retailer must rent the tape at least 22
times before earning profit - Retailers cannot justify purchasing enough to
cover the peak demand - In 1998, 20 of surveyed customers reported that
they could not rent the movie they wanted
68Supply Contracts Case Study
- Starting in 1998 Blockbuster entered a revenue
sharing agreement with the major studios - Studio charges 8 per copy
- Blockbuster pays 30-45 of its rental income
- Even if Blockbuster keeps only half of the rental
income, the breakeven point is 6 rental per copy - The impact of revenue sharing on Blockbuster was
dramatic - Rentals increased by 75 in test markets
- Market share increased from 25 to 31 (The 2nd
largest retailer, Hollywood Entertainment Corp
has 5 market share)
69Other Contracts
- Quantity Flexibility Contracts
- Supplier provides full refund for returned items
as long as the number of returns is no larger
than a certain quantity - Sales Rebate Contracts
- Supplier provides direct incentive for the
retailer to increase sales by means of a rebate
paid by the supplier for any item sold above a
certain quantity
704.2.4 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
71The DC holds inventory to
- Satisfy demand during lead time
- Protect against demand uncertainty
- Balance fixed costs and holding costs
72Reminder The Normal Distribution
Standard Deviation 5
Standard Deviation 10
Average 30
73The Multi-Period Continuous Review 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.
This is expressed as the the likelihood that the
distributor will not stock out during lead time. - Intuitively, how will this effect our policy?
74A View of (s, S) Policy
S
Inventory Position
Lead Time
Lead Time
Inventory Level
s
0
Time
75The (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
- The Lead Time
- Average demand
- Demand variability
- Service level
76 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
- K fixed cost
- SL service level (for example, 95). This
implies that the probability of stocking out is
100-SL (for example, 5) - Also, the Inventory Position at any time is the
actual inventory plus items already ordered, but
not yet delivered.
77 Analysis
- The reorder point (s) has two components
- To account for average demand during lead
time LT?AVG - To account for deviations from average (we call
this safety stock) z ? STD ? ?LTwhere z is
chosen from statistical tables to ensure that the
probability of stockouts during leadtime is
100-SL. - Since there is a fixed cost, we order more than
up to the reorder point Q?(2 ?K ?AVG)/h - The total order-up-to level is
SQs
78 Example
What is Reorder point? what is the
order-up-to-level?
- The distributor has historically observed weekly
demand 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 of
supply at warehouse and in the pipeline
79Example, Cont.
- Weekly inventory holding cost .87
- Therefore, Q679
- Order-up-to level thus equals
- Reorder Point Q 176679 855
804.2.5 Periodic Review
- Suppose the distributor places orders every month
- What policy should the distributor use?
- What about the fixed cost?
81Base-Stock Policy
82Periodic Review Policy
- Each review echelon, inventory position is raised
to the base-stock level. - The base-stock level includes two components
- Average demand during rL days (the time until
the next order arrives) (rL)AVG - Safety stock during that time zSTD ?rL
834.3 Risk Pooling Example
- Consider these two systems
- Some problems faced by ACME, a company that
produces and distributes electronic equipment in
the Northeast of the United States. - (1)The current distribution system partitions the
Northeast into two markets, each of which has a
single warehouse. Retailers receive items
directly from the warehouses each retailer is
assigned to a single market and receives
deliveries from the corresponding warehouse.
84Risk Pooling Example (cont)
- (2)Replace the two warehouses with a single
warehouse. The same service level,97, be
maintained regardless of the logistics strategy
employed. - This system allows ACME to achieve either the
same service level of 97 with much lower
inventory or a higher service level with the same
amount of total inventory.
85Risk Pooling Example (cont)
- 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?
86Risk Pooling Example (cont)
- Compare the two systems
- two products(A,B)
- maintain 97 service level
- 60 order cost
- .27 weekly holding cost
- 1.05 transportation cost per unit in
decentralized system, 1.10 in centralized system - 1 week lead time
87Risk Pooling Example
Table 1 Historical Data for Product A and B
- The tables include weekly demand information for
each product for the last eight weeks in each
market area. Observe that Product B is a
slow-moving product the demand for Product B is
fairly small relative to the demand for Product A.
88Risk Pooling Example
Table 2 Summary of Historical Data
Product Average Demand Standard Deviation Demand Coefficient of Variation
Market1 A 39.3 13.2 0.34
Market1 B 1.125 1.36 1.21
Market2 A 38.6 12.0 0.31
Market2 B 1.25 1.58 1.26
Total A 77.9 20.71 0.27
Total B 2.375 1.9 0.81
89Risk Pooling Example
Table 3 Inventory Levels
Product AVG D Safety Stock Reorder point Q Order-up to level
Market1 A 39.3 25.8 65 132 197
Market1 B 1.125 2.58 4 25 29
Market2 A 38.6 22.8 62 131 193
Market2 B 1.25 3 5 24 29
Total A 77.9 39.35 118 186 304
Total B 2.375 3.61 6 33 39
90Risk PoolingImportant 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 increases
required safety stock. - Negatively correlated demand. Why?
- What other kinds of risk pooling will we see?
91Risk PoolingTypes of Risk Pooling
- Risk Pooling Across Markets
- Risk Pooling Across Products
- Risk Pooling Across Time
- Daily order up to quantity is
- LT?AVG z ? AVG ? ?LT
Orders
10
12
11
13
14
15
Demands
924.4 To Centralize or not to Centralize
- What are the trade-offs that we need to consider
in comparing centralized distribution systems
with decentralized distribution systems? - What is the effect on
- Safety stock?
- Service level?
- Overhead?
- Lead time?
- Transportation Costs?
93Centralized vs Decentralized system
- Safety stock. Clearly, safety stock decreases as
a firm moves from a decentralized to a
centralized system. - Service level. When the centralized and
decentralized systems have the same total safety
stock, the service level provided by the
centralized system is higher. - Lead time. Since the warehouses are much closer
to the customers in a decentralized
system,response time is much lower.
944.5 Managing Inventory in the SC (Centralized
Systems)
- The warehouse echelon inventory
The warehouse policy controls its echelon
inventory position, that is, whenever the echelon
inventory position for the W is below s, an order
is placed to raise its echelon inventory position
to S.
95Centralized 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.
964.6 Inventory Management Best Practice
- Periodic inventory reviews
- Tight management of usage rates, lead times and
safety stock - ABC approach
- Reduced safety stock levels
- Shift more inventory, or inventory ownership, to
suppliers - Quantitative approaches
97Changes In Inventory Turnover
- 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 a five year period
ending in year 2000.
98Inventory Turnover Ratio
99Factors that Drive Reduction in Inventory
- Top management emphasis on inventory reduction
(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)
- Others
100Factors that Drive Inventory Turns Increase
- 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
101Forecasting
- Recall the three rules
- Nevertheless, forecast is critical
- General Overview
- Judgment methods
- Market research methods
- Time Series methods
- Causal methods
102Judgment Methods
- Assemble the opinion of experts
- Sales-force composite combines salespeoples
estimates - Panels of experts internal, external, both
- Delphi method
- Each member surveyed
- Opinions are compiled
- Each member is given the opportunity to change
his opinion
103Market Research Methods
- Particularly valuable for developing forecasts of
newly introduced products - Market testing
- Focus groups assembled.
- Responses tested.
- Extrapolations to rest of market made.
- Market surveys
- Data gathered from potential customers
- Interviews, phone-surveys, written surveys, etc.
104Time Series Methods
- Past data is used to estimate future data
- Examples include
- Moving averages average of some previous demand
points. - Exponential Smoothing more recent points
receive more weight - Methods for data with trends
- Regression analysis fits line to data
- Holts method combines exponential smoothing
concepts with the ability to follow a trend - Methods for data with seasonality
- Seasonal decomposition methods (seasonal patterns
removed) - Winters method advanced approach based on
exponential smoothing - Complex methods (not clear that these work better)
105Causal Methods
- Forecasts are generated based on data other than
the data being predicted - Examples include
- Inflation rates
- GNP
- Unemployment rates
- Weather
- Sales of other products
106Selecting the Appropriate Approach
- What is the purpose of the forecast?
- Gross or detailed estimates?
- What are the dynamics of the system being
forecast? - Is it sensitive to economic data?
- Is it seasonal? Trending?
- How important is the past in estimating the
future? - Different approaches may be appropriate for
different stages of the product lifecycle - Testing and intro market research methods,
judgment methods - Rapid growth time series methods
- Mature time series, causal methods (particularly
for long-range planning) - It is typically effective to combine approaches.