Inventory Management, Supply Contracts and Risk Pooling
沈厚才 博士(Dr. Houcai SHEN)
南京大学
hcshen@
Outline of the Presentation
Introduction to Inventory Management
The Effect of Demand Uncertainty
(s,S) Policy
Supply Contracts
Risk Pooling
Centralized vs. Decentralized Systems
Practical Issues in Inventory Management
Supply
Sources:
plants
vendors
ports
Regional
Warehouses:
stocking
points
Field
Warehouses:
stocking
points
Customers,
demand
centers
sinks
Production/
purchase
costs
Inventory &
warehousing
costs
Transportation
costs
Inventory &
warehousing
costs
Transportation
costs
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
Goals:
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
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)
Understanding Inventory
The inventory policy is affected by:
Demand Characteristics
Lead Time
Number of Products
Objectives
Service level
Minimize costs
Cost Structure
Cost Structure
Order costs
Fixed
Variable
Holding Costs
Insurance
Maintenance and Handling
Taxes
Opportunity Costs
Obsolescence
经济批量的定货模型
基本假设
计划期很长
初始库存为0
订货提前期为0，可以在库存下降为0时，作补充订货。
单位库存保管成本为H
订货固定成本为K
供应商能无限供货，每次订货为Q单位
需求量保持不变，每天为D单位产品
7
6
5
4
3
2
1
总库存成本 = K + H*（Q/2）* T，T 为两次订货之间的时间。
订货量Q=TD，或者，T=Q/D
平均成本 =总库存成 本/T = KD/Q + HQ/2
最小平均成本应在：-KD/Q^2+H/2 = 0
所以，最佳经济批量为 Q = SQRT（2KD/H）
经济批量定货的特点
最佳定货策略是在库存保管成本与订货固定成本之间权衡
保管成本（HQ/2）= 固定成本（KD/Q）
总库存成本对订货批量的变动不敏感
在订货扁离经济批量定货的80%到120%, 误差<3%
%
%
%
%
0
%
%
%
成本的增加
1
订货扁离Q
The 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
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
The 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
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 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.
Supply Chain Time Lines
Jan 00
Jan 01
Jan 02
Feb 00
Sep 00
Sep 01
Design
Production
Retailing
Feb 01
Production
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 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.
SnowTime Demand Scenarios
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
SnowTime Best Solution
Find order quantity that maximizes weighted average profit.
Question: Will this quantity be less than, equal to, or greater than average demand?
What 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
SnowTime 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
SnowTime Expected Profit
SnowTime Expected Profit
SnowTime Expected Profit
SnowTime:
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?
Probability of Outcomes
Key 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
Supply Contracts
Manufacturer
Manufacturer DC
Retail DC
Stores
Fixed Production Cost =$100,000
Variable Production Cost=$35
Selling Price=$125
Salvage Value=$20
Wholesale Price =$80
Demand Scenarios
Distributor Expected Profit
Distributor Expected Profit
Supply 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?
Supply Contracts
Manufacturer
Manufacturer DC
Retail DC
Stores
Fixed Production Cost =$100,000
Variable Production Cost=$35
Selling Price=$125
Salvage Value=$20
Wholesale Price =$80
Retailer Profit
(Buy Back=$55)
Retailer Profit
(Buy Back=$55)
$513,800
Manufacturer Profit
(Buy Back=$55)
Manufacturer Profit
(Buy Back=$55)
$471,900
Supply Contracts
Manufacturer
Manufacturer DC
Retail DC
Stores
Fixed Production Cost =$100,000
Variable Production Cost=$35
Selling Price=$125
Salvage Value=$20
Wholesale Price =$80
Retailer Profit
(Wholesale Price $70, RS 15%)
Retailer Profit
(Wholesale Price $70, RS 15%)
$504,325
Manufacturer Profit
(Wholesale Price $70, RS 15%)
Manufacturer Profit
(Wholesale Price $70, RS 15%)
$481,375
Supply Contracts
Supply Contracts
Manufacturer
Manufacturer DC
Retail DC
Stores
Fixed Production Cost =$100,000
Variable Production Cost=$35
Selling Price=$125
Salvage Value=$20
Wholesale Price =$80
Supply Chain Profit
Supply Chain Profit
$1,014,500
Supply Contracts
Supply 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
Supply 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
Supply 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)
Other 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
SnowTime Costs: 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
SnowTime Expected Profit
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?
Initial Inventory and Profit
Initial Inventory and Profit
Initial Inventory and Profit
Initial Inventory and Profit
(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
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
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 .
Case Study: The Supply Chain
Inbound
Product Flow
Factory
Order Flow
DC
4) Production Planning
3) Order Processing
Outbound
Distributor
End User
DC
1) Order Processing
2) Forecasting Replenishment
Demand Variability: Example 1
Demand Variability: Example 1
Reminder:
The Normal Distribution
Average = 30
Standard Deviation = 5
Standard Deviation = 10
The DC holds inventory to:
Satisfy demand during lead time
Protect against demand uncertainty
Balance fixed costs and holding costs
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. This is expressed as the the likelihood that the distributor will not stock out during lead time.
Intuitively, how will this effect our policy?
A View of (s, S) Policy
Time
Inventory Level
S
s
0
Lead
Time
Lead
Time
Inventory Position
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:
The Lead Time
Average demand
Demand variability
Service level
Fixed Order Schedule
Suppose the distributor places orders every month
What policy should the distributor use?
What about the fixed cost?
Base-Stock Policy
,
L
L
L
r
1
r
2
r
3
Units
Time
Target Inventory
Expected UB
Expected LB
Risk Pooling
Consider these two systems:
Market Two
Supplier
Warehouse One
Warehouse Two
Market One
Market Two
Supplier
Warehouse
Market One
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?
Risk Pooling Example
Compare the two systems:
two products
maintain 97% service level
$60 order cost
$.27 weekly holding cost
$ transportation cost per unit in decentralized system, $ in centralized system
1 week lead time
Risk Pooling Example
Risk Pooling Example
Risk Pooling Example
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?
To Centralize or not to Centralize
What is the effect on:
Safety stock?
Service level?
Overhead?
Lead time?
Transportation Costs?
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%)
Changes In Inventory Turnover
Inventory turns increased by 30% from 1995 to 1998
Inventory turns increased by 27% from 1998 to 2000
Overall the increase is from turns per year to over 13 per year over a five year period ending in year 2000.
Inventory Turnover Ratio
Factors that Drive Reduction in Inventory
Top management emphasis on inventory reduction (19%)
Number of SKUs in the warehouse (10%)
Improved forecasting (7%)
Use of sophisticated inventory management software (6%)
Coordination among supply chain members (6%)
Others
Factors that will Drive Inventory Turns Change by 2000
Better software for inventory management (%)
Reduced lead time (15%)
Improved forecasting (%)
Application of SCM principals (%)
More attention to inventory management (%)
Reduction in SKU (%)
Others
