Inventory Management and Risk Pooling (2)

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Inventory Management and Risk Pooling (2)

• Designing Managing the Supply Chain
• Chapter 3
• Byung-Hyun Ha
• bhha_at_pusan.ac.kr

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Outline

• Introduction to Inventory Management
• The Effect of Demand Uncertainty
• (s,S) Policy
• Supply Contracts
• Periodic Review Policy
• Risk Pooling
• Centralized vs. Decentralized Systems
• Practical Issues in Inventory Management

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Supply Contracts

• Assumptions for Swimsuit production
• In-house manufacturing
• ? Usually, manufactures and retailers
• Supply contracts
• Pricing and volume discounts
• Minimum and maximum purchase quantities
• Delivery lead times
• Product or material quality
• Product return policies

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Supply Contracts

• Condition

Wholesale Price 80
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Demand Scenario and Retailer Profit
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Demand Scenario and Retailer Profit

• Sequential supply chain
• Retailer optimal order quantity is 12,000 units
• Retailer expected profit is 470,700
• Manufacturer profit is 440,000
• Supply Chain Profit is 910,700
• Is there anything that the distributor and
  manufacturer can do to increase the profit of
  both?
• Global optimization?

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Buy-Back Contracts

• Buy back55

retailer
manufacturer
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Buy-Back Contracts

• Sequential supply chain
• Retailer optimal order quantity is 12,000 units
• Retailer expected profit is 470,700
• Manufacturer profit is 440,000
• Supply Chain Profit is 910,700
• With buy-back contracts
• Retailer optimal order quantity is 14,000 units
• Retailer expected profit is 513,800
• Manufacturer expected profit is 471,900
• Supply Chain Profit is 985,700
• Manufacture sharing some of risk!

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Revenue-Sharing Contracts

• Wholesale Price from 80 to 60, RS 15

Supply Chain Profit is 985,700
retailer
manufacturer
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Other Types of Supply Contracts

• Quantity-flexibility contracts
• Supplier providing full refund for returned
  (unsold) items up to a certain quantity
• Sales rebate contracts
• Direct incentive to retailer by supplier for any
  item sold above a certain quantity
• Consult Cachon 2002

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Global Optimization

• What is the most profit both the supplier and the
  buyer can hope to achieve?
• Assume an unbiased decision maker
• Transfer of money between the parties is ignored
• Allowing the parties to share the risk!
• Marginal profit90, marginal loss15
• Optimal production quantity16,000
• Drawbacks
• Decision-making power
• Allocating profit

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Global Optimization

• Revised buy-back contracts
• Wholesale price75, buy-back price65
• Global optimum
• Equilibrium point!
• No partner can improve his profit by deciding to
  deviate from the optimal decision
• Consult Ch14 of Winston, Game theory
• 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

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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

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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)

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A Multi-Period Inventory Model

• Situation
• Often, there are multiple reorder opportunities
• A central distribution facility which orders from
  a manufacturer and delivers to retailers
• The distributor periodically places orders to
  replenish its inventory
• Reasons why DC holds inventory
• Satisfy demand during lead time
• Protect against demand uncertainty
• Balance fixed costs and holding costs

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Continuous Review Inventory Model

• Assumptions
• 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
• expressed as the likelihood that the distributor
  will not stock out during lead time.
• Intuitively, how will the above assumptions
  effect our policy?
• (s, S) Policy
• Whenever the inventory position drops below a
  certain level (s) we order to raise the inventory
  position to level S

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Reminder The Normal Distribution
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A View of (s, S) Policy
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(s, S) Policy

• Notations
• 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)
• The probability of stocking out is 100 - SL (for
  example, 5)
• Policy
• s reorder point, S order-up-to level
• Inventory Position
• Actual inventory (items already ordered, but
  not yet delivered)

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(s, S) Policy - 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 stock-outs during lead-time 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
  S Q s

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(s, S) Policy - Example

• The distributor has historically observed weekly
  demand of
• AVG 44.6 STD 32.1
• Replenishment 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
• Weekly inventory holding cost .87
• Therefore, Q679
• Order-up-to level thus equals
• Reorder Point Q 176679 855

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Periodic Review

• Periodic review model
• Suppose the distributor places orders every month
• What policy should the distributor use?
• What about the fixed cost?
• Base-Stock Policy

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Periodic Review

• Base-Stock 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

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Risk Pooling

• Consider these two systems
• 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
• .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

• Risk Pooling Performance

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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 increases
  required safety stock.
• Negatively correlated demand. Why?
• What other kinds of risk pooling will we see?

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Inventory in Supply Chain

• Centralized Distribution Systems
• 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 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

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Forecasting

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

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Judgment 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

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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.

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Time 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)

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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