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Chapter 3 Inventory Management, Supply Contracts and Risk Pooling


Chapter 3 Inventory Management, Supply Contracts and Risk Pooling Qi Xu Professor of Donghua University Tel: 021-62378860 E-mail: – PowerPoint PPT presentation

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Title: Chapter 3 Inventory Management, Supply Contracts and Risk Pooling

Chapter 3 Inventory Management, Supply Contracts
and Risk Pooling
  • Qi Xu
  • Professor of Donghua University
  • Tel 021-62378860
  • E-mail

Outline 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

(No Transcript)
Case 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.

Case 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.

Case JAM Electronics
  • 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.

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

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,
  • In 1993, Liz Claiborne said its unexpected
    earning decline is the consequence of higher than
    anticipated excess inventory (WSJ, July 15,
  • 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

4.2.1 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
  • Fixed order cost of 12.00, no lead time (k)
  • Holding cost of 25 of inventory value annually
  • Mugs cost 1.00, sell for 5.00
  • Question
  • How many(Q), when to order?

EOQ A View of Inventory
Note No Stockouts Order when no inventory
Order Size determines policy
Order Size
Avg. Inven
EOQ Calculating Total Cost
  • Purchase Cost Constant
  • Holding Cost (Avg. Inven) (Holding Cost)
  • Ordering (Setup Cost)Number of Orders Order
  • Goal Find the Order Quantity that Minimizes
    These Costs

EOQTotal Cost
Total Cost
Holding Cost
Order Cost
EOQ 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

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  • ?????????????????????????????????????????,R/Q?????
  • ????????????????Q,???TC???Q???????,?TC???Q??

  • ? ?0,??????Q?

EOQ 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

The Effect of Demand Uncertainty
  • Most companies treat the world as if it were
  • 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

  • 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

4.2.2 Demand Forecast
  • The three principles of all forecasting
  • Forecasting is always wrong
  • The longer the forecast horizon the worst is the
  • Aggregate forecasts are more accurate

Case 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

Supply Chain Time Lines
Jan 01
Jan 02
Jan 00
Feb 00
Sep 00
Sep 01
Feb 01
SnowTime Demand Scenarios
SnowTime 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
  • Q is production quantity, D demand
  • Profit Revenue - Variable Cost - Fixed Cost

SnowTime Scenarios
Profit Revenue - Variable Cost - Fixed Cost
  • 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
  • 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 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 Expected Profit
  • The quantity that maximizes average profit, is
    about 12,000.

SnowTime 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.

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?

SnowTime Expected Profit
Probability 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

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

SnowTime 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

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 5000 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
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.
Initial Inventory and Profit
Average profit excluding fixed production cost
Average profit including fixed production cost
  • (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.

(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
  • The difference between the two levels is driven
    by the fixed costs associated with ordering,
    transportation, or manufacturing

4.2.3 Supply Contracts
Wholesale Price 80
Who takes the risk? What would the manufacturer
Demand Scenarios
Distributor Expected Profit
Distributor Expected Profit
Supply Contracts (cont.)
  • Distributor optimal order quantity is 12,000
  • 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

Supply Contracts (between manufacturer and
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
Retailer Profit (Buy Back55)
Retailer Profit (Buy Back55)
Manufacturer Profit (Buy Back55)
Manufacturer Profit (Buy Back55)
Supply Contracts (between manufacturers
wholesale price and retailer)
What does wholesale price drive? How can
manufacturer benefit from lower price?
Wholesale Price ??
Retailer Profit (Wholesale Price 70, Retailers
back 15 to manufacturer )
Retailer Profit (Wholesale Price 70, RS 15)
Manufacturer Profit (Wholesale Price 70, RS 15)
Manufacturer Profit (Wholesale Price 70, RS 15)
Supply Contracts
Wholesale Price 70, RS 15
Supply 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
Supply Chain Profit
Supply Chain Profit (Global optimization)
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
  • 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
  • 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

4.2.4 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

The DC holds inventory to
  • Satisfy demand during lead time
  • Protect against demand uncertainty
  • Balance fixed costs and holding costs

Reminder The Normal Distribution
Standard Deviation 5
Standard Deviation 10
Average 30
The 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?

A View of (s, S) Policy
Inventory Position
Lead Time
Lead Time
Inventory Level
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

  • 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.

  • 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
  • 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

What is Reorder point? what is the
  • 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
  • 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

Example, Cont.
  • Weekly inventory holding cost .87
  • Therefore, Q679
  • Order-up-to level thus equals
  • Reorder Point Q 176679 855

4.2.5 Periodic Review
  • Suppose the distributor places orders every month
  • What policy should the distributor use?
  • What about the fixed cost?

Base-Stock Policy
Periodic 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

4.3 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.

Risk Pooling Example (cont)
  • (2)Replace the two warehouses with a single
    warehouse. The same service level,97, be
    maintained regardless of the logistics strategy
  • 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.

Risk 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?

Risk 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

Risk 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.

Risk 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
Risk 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
Risk 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?

Risk 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

4.4 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?

Centralized 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.

4.5 Managing Inventory in the SC (Centralized
  • 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.
Centralized Distribution Systems
  • Question How much inventory should management
    keep at each location?
  • A good strategy
  • The retailer raises inventory to level Sr each
  • 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.

4.6 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
  • Quantitative approaches

Changes In Inventory Turnover
  • Inventory turnover ratio annual
    sales/avg. inventory level
  • Inventory turns increased by 30 from 1995 to
  • Inventory turns increased by 27 from 1998 to
  • Overall the increase is from 8.0 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
  • 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

Factors 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

  • Recall the three rules
  • Nevertheless, forecast is critical
  • General Overview
  • Judgment methods
  • Market research methods
  • Time Series methods
  • Causal methods

Judgment Methods
  • Assemble the opinion of experts
  • Sales-force composite combines salespeoples
  • Panels of experts internal, external, both
  • Delphi method
  • Each member surveyed
  • Opinions are compiled
  • Each member is given the opportunity to change
    his opinion

Market 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.

Time Series Methods
  • Past data is used to estimate future data
  • Examples include
  • Moving averages average of some previous demand
  • 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
  • Winters method advanced approach based on
    exponential smoothing
  • Complex methods (not clear that these work better)

Causal 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

Selecting the Appropriate Approach
  • What is the purpose of the forecast?
  • Gross or detailed estimates?
  • What are the dynamics of the system being
  • Is it sensitive to economic data?
  • Is it seasonal? Trending?
  • How important is the past in estimating the
  • 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.
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