Chapter 3 Inventory Management and Risk Pooling - PowerPoint PPT Presentation

About This Presentation
Title:

Chapter 3 Inventory Management and Risk Pooling

Description:

Suppose you make 12,000 swimsuits and demand ends up being 11,000 swimsuits. ... For the swimsuit example, if the manufacturer is willing to give discounts, the ... – PowerPoint PPT presentation

Number of Views:4313
Avg rating:3.0/5.0
Slides: 80
Provided by: pwsSt
Category:

less

Transcript and Presenter's Notes

Title: Chapter 3 Inventory Management and Risk Pooling


1
Chapter 3 Inventory Management and Risk Pooling
2
Outline of the contents
  • Introduction to Inventory Management
  • The Effect of Demand Uncertainty
  • (s,S) Policy
  • Periodic Review Policy
  • Supply Contracts
  • Risk Pooling
  • Centralized vs. Decentralized Systems
  • Practical Issues in Inventory Management

3
Inventory
  • Where do we hold inventory?
  • Suppliers and manufacturers
  • Warehouses and distribution centers
  • Retailers
  • Types of Inventory
  • Raw materials
  • WIP
  • Finished goods
  • Why do we hold inventory?
  • Economies of scale
  • Uncertainty in supply and demand
  • Lead Time, Capacity limitations

4
Inventory
  • Managing inventory in complex supply chains is
    typically difficult, and may have a significant
    impact on the customer service level and supply
    chain system-wide cost.
  • Inventory in three types
  • Raw material inventory (where?)
  • Work-in-process inventory (where?)
  • Finished product inventory (where?)

5
Why hold Inventory?
  • Unexpected changes in customer demand.
  • The short life cycle of an increasing number of
    products. Thus, historical data may not be
    available or may be quite limited.
  • The presence of many competing products in the
    marketplace. (Discussed in Chapters 5 and 9)
  • The presence in many situations of a significant
    uncertainty in the quantity and quality of the
    supply, supplier costs, and delivery times.
  • A need to hold inventory due to delivery lead
    times even if there is no uncertainty in supply
    or demand.
  • Economies of scale offered by transportation
    companies that encourage firms to transport large
    quantities of items, and therefore hold large
    inventories.

6
Managing inventory examples
  • 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 .

7
Managing inventory examples
  • By not managing inventory successfully
  • In 1993, Dells stock plunged after the company
    predicted a loss. (sharply off in its forecast of
    demand)
  • 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 2001, Cisco took a 2.25B excess inventory
    charge due to declining scales.

8
Two important issues in inventory management
  • Demand forecasting
  • Forecast demand is a critical element in
    determining order quantity.
  • What is the relationship between forecast demand
    and the optimal order quantity?
  • Should the order quantity or gt or lt the
    forecast demand?
  • ..
  • Order quantity calculation

9
A single warehouse inventory example
10
Key factors affecting inventory policy?
  • Customer demand
  • Known in advance or may be random (forecasting
    tools can be used).
  • Replenishment lead time
  • May be known at the time we place the order or
    may be uncertain.
  • The number of different products
  • High-mix and low volume?
  • The length of the planning horizon

11
Key factors affecting inventory policy?
  • Costs (order cost and inventory holding cost)
  • Order cost the cost of the product and the
    transportation cost
  • Inventory holding cost
  • State taxes, property taxes, and insurance on
    inventories
  • Maintenance costs
  • Obsolescence cost (an item will lose some of its
    value because of changes in the market.)
  • Opportunities costs (the return on investment
    that one would receive had money been invested in
    something else (e.g. stock market) instead of
    inventory.

12
Key factors affecting inventory policy?
  • Service level requirements
  • It is not possible to meat customer orders 100
    percent of the time. Managements need to specify
    an acceptable level of service

13
3.2.1 The Economic Lot Size model
  • Economic lot size model is used to trade-off the
    costs between ordering and storage.
  • Assumptions (for a single item and has a
    unlimited quantity of the product)
  • Demand is constant at a rate of D items per day.
  • Order quantities are fixed at Q items per order.
  • A fixed cost (setup cost) K, incurred every time
    the warehouse places an order.
  • An inventory carrying cost, h, also referred to
    as a holding cost, is accrued per unit held in
    inventory per day that the unit is held.
  • The lead time, the time that elapses between the
    placement of an order and its receipt, is zero
  • Initial inventory is zero.
  • The planning horizon is long (infinite).

14
3.2.1 The Economic Lot Size model
  • Goal
  • Find the optimal order policy that minimizes
    annual purchasing and carrying costs while
    meeting all demand.
  • Realistic system?
  • A known fixed demand over a long horizon is clear
    unrealistic.
  • This model will help us to develop inventory
    policies that are effective for more complex
    realistic systems.

15
3.2.1 The Economic Lot Size model
Notes No Stockouts Order when no inventory
Order Size determines policy
Inventory
Order Size
Avg. Inven
Time
Saw-toothed inventory pattern
16
3.2.1 The Economic Lot Size model
  • Total costs
  • Purchase Cost is Constant
  • Holding Cost (Avg. Inven) (Holding Cost)
  • Ordering (Setup Cost)
  • Number of Orders Order Cost
  • Goal Find the order Quantity that minimizes
    these costs.

17
3.2.1 The Economic Lot Size model
  • Total inventory cost in a cycle of length T
  • Average total cost per unit of time
  • EOQ model

An inventory holding cost
Q/2 average inventory Level.
A fixed cost (setup cost)
QTD -gt TQ/D
Setup cost/unit
Holding/unit
18
3.2.1 The Economic Lot Size model
Total Cost
Holding Cost
Order Cost
19
Economic Lot Size model 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

Q bQ
See page. 48.
20
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

21
Demand Forecasts
  • 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

22
Swimsuit production
  • (Read the case on page 49)
  • Fashion items have short life cycles, high
    variety of competitors
  • Swimsuit
  • 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.

23
Probabilistic forecast
24
Data
  • 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

25
Example scenarios
  • Scenario One
  • Suppose you make 12,000 swimsuits and demand ends
    up being 13,000 swimsuits.
  • Profit 125(12,000) - 80(12,000) - 100,000
    440,000
  • Scenario Two
  • Suppose you make 12,000 swimsuits and demand ends
    up being 11,000 swimsuits.
  • Profit 125(11,000) - 80(12,000) - 100,000
    20(1000) 335,000

26
What to make?
  • Find order quantity that maximizes weighted
    average profit.
  • Question Will this quantity be less than, equal
    to, or greater than average demand?

See Excel Spreadsheet for Chapter 3
27
What to Make?
  • Average demand is 13,100
  • Look at marginal cost vs. marginal profit
  • if extra swimsuit sold, profit is 125-80 45
  • if not sold, cost is 80-20 60
  • So we will make less than average demand

28
Expected Profit
29
Expected Profit
30
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?

31
Probability of Outcomes
32
Key Points from this case study
  • 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

33
The effect of Initial Inventory
  • Suppose that one of the swimsuit 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
  • From Figure 3-6, the profit can be obtained
  • 225000500080625,000

34
Initial Inventory and Profit
Fix production costs
225000
35
Questions
  • If there are 7000 units remaining, what should
    the company do?
  • What should they do if there are 10,000 remaining?

36
Initial Inventory and Profit
37
(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
  • Swimsuit case s 8,500 and S 12,000

38
Supply contracts
  • In as supply contract, the buyer and supplier may
    agree on
  • Pricing and volume discounts
  • Maximum and minimum purchase quantities
  • Delivery lead times
  • Product or material quality
  • Product return policies
  • Refer to the Excel spreadsheet (supply contract).

39
Swimsuit example again
  • (Read the case of example 3-2 on page 53)
  • Sequential supply chain
  • each party determines its own course of action
    independent of the other parties.
  • For the earlier example, the retailer assumes all
    of the risk, of having more inventory than sales,
    while the manufacturer takes no risk.
  • Larger the order is, better it is for the
    manufacturer but it has a reverse impact to the
    retailer.

40
Buy-back contracts
  • In a buy-back contract, the seller agrees to buy
    back unsold goods from the buyer for some
    agreed-upon price.
  • Study example 3-3 on page 54 and explain how does
    it work?

41
Revenue-sharing contracts
  • For the swimsuit example, if the manufacturer is
    willing to give discounts, the retailer will have
    an incentive to order more.
  • Study example 3-4 and explain how does it works.

42
Quantity-flexibility contracts
  • The supplier provides full unsold items as long
    as the number of returns is no larger than a
    certain quantity.
  • How is it different from buy-back contracts?

43
Sales rebate contracts
  • Sales rebate (discounts) contacts provide a
    direct incentive to the retailer to increase
    sales by means of a rebate paid by the supplier
    for any item sold above a certain quantity.

44
Global optimization
  • What is the best strategy for the entire supply
    chain?
  • The difficulty with global optimization is that
    it requires the firm to surrender decision-making
    power to an unbiased decision maker.
  • See example 3-5 on page 56
  • Its main drawback is that it does not provide a
    mechanism to allocate supply chain profit between
    the partners.
  • See example 3-6 on page 57

45
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
  • Continuous review policy and periodic review
    policy

46
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, what will a good policy look like?


47
Continuous review policy
  • Known parameters
  • AVG average daily demand faced by the
    distributor
  • STD Standard deviation of daily demand faced by
    the distributor
  • L Replenishment lead time from the supplier to
    the distributor in days
  • h Cost of holding one unit of the product for
    one day at the distributor
  • ? service level

48
Continuous review policy
  • Inventory position
  • The actual inventory at the warehouse plus items
    ordered by the distributor that have not yet
    arrived minus items that are backordered.

49
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

50
A View of (s, S) Policy
S
Inventory Position
Inventory Level
Lead Time
s
0
Time
51
Analysis
  • The reorder point has two components
  • To account for average demand during lead
    time
  • L ? AVG
  • To account for deviations from average (we call
    this safety stock) z ? STD ? ?L
  • where z is chosen from statistical tables to
    ensure that the probability of stockouts during
    leadtime is (1-?).

52
Analysis
  • Reorder level (s)
  • L ? AVG z ? STD ? ?L
  • It needs to satisfy
  • Probability Demand during lead time ? L ? AVG
    z ? STD ? ?L (1-?)
  • Refer to Table 3-2 on page 59 for z values.

53
Analysis
  • Use EOQ model
  • Q
  • S Q s
  • Average inventory level (S s)

54
Reminder The Normal Distribution
Standard Deviation 5
Standard Deviation 10
Average 30
55
The distributor holds inventory to
  • Satisfy demand during lead time
  • Protect against demand uncertainty
  • Balance fixed costs and holding costs

56
Distributor of the TV sets
  • 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

57
Distributor of the TV sets
  • 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 the service
    requirement
  • s LT?AVG z ? AVG ? ?L
  • What about the order up to level?


58
Distributor of the TV sets
  • 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 L ?AVG. Why?
  • There is variability, so we need safety stock
  • z ? STD ? ?L

59
Distributor of the TV sets
  • 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 quantity Q?(2 ?4500 ? 44.6 / 0.87 679
  • Order-up-to level s Q 175 679 855

60
Periodic review policy
  • Base-stock level
  • Each review period, the inventory position is
    reviewed and the warehouse orders enough to raise
    the inventory position to the base-stock level.
  • Assume that orders are placed every r period of
    time.

61
Periodic review policy
62
Periodic review policy
  • Average demand during an interval of r L(r
    L) ? AVG
  • Safety stock
  • z ? STD ? ? (r L)
  • Expected level of inventory after receiving an
    order
  • r ? AVG z ? STD ? ? (r L)
  • Example 3-8 on page 63

63
Risk Pooling
  • Consider these two systems

Market One
Warehouse One
Supplier
Market Two
Warehouse Two
Market One
Warehouse
Supplier
Market Two
64
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?

65
Risk Pooling Example
  • Compare the two systems (Read the case on page.
    64-66)
  • 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

66
Risk Pooling Example
67
Risk Pooling Example
68
Risk Pooling Example
69
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 reduces
    required safety stock.
  • Negatively correlated demand. Why?
  • What other kinds of risk pooling will we see?

70
Risk Pooling Types 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 ? ?L

Orders
10
12
11
13
14
15
Demands
71
To Centralize or not to Centralize
  • Safety stock
  • Safety stock decreases as a firm moves from a
    decentralized to a centralized system.
  • Depend on CV and correlation
  • Service level
  • Given the same total safety stock, the service
    level provided by the centralized system is
    higher.
  • Overhead
  • Typically, these costs are much greater in a
    decentralized system.

72
To Centralize or not to Centralize
  • Lead time
  • The response time for a decentralized system is
    much shorter.
  • Transportation Costs
  • Outbound costs are higher for the centralized
    system.
  • Inbound costs are higher for the decentralized
    system.

73
Centralized Systems
  • Centralized Decision

Supplier
Warehouse
Retailers
74
Centralized Distribution Systems
  • Question How much inventory should management
    keep at each location?
  • A good strategy
  • The retailer raises inventory to level s each
    period
  • The supplier raises the sum of inventory in the
    retailer and supplier warehouses and in transit
    to S
  • 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.

75
Practical issues
  • Periodic inventory review policy
  • Tight management of usage rates, lead times and
    safety stock
  • Reduced safety stock levels
  • Introduce or enhance cycle counting practice
  • ABC approach
  • Shift more inventory, or inventory ownership, to
    suppliers
  • Quantitative approaches inventory turnover rate

76
Practical issues
Practical issues
77
Forecasting
  • Three rules of forecasting
  • The forecast is always wrong.
  • The longer the forecast horizon, the worse the
    forecast.
  • Aggregate forecasts are more accurate.

78
Forecasting
  • Categories (See section 3.7)
  • Judgment methods
  • Market research methods
  • Time-series methods
  • Causal methods

79
Summary
  • Matching supply and demand in the supply chain is
    a critical challenge.
  • Unfortunately, the existence the three
    forecasting rules.
  • Globally optimal inventory policies, in which the
    best possible policy for the entire supply chain
    is implemented, are the best course of action.
  • Well-designed supply contracts frequently make
    this global optimization possible.
Write a Comment
User Comments (0)
About PowerShow.com