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? Types of 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, Dell’s 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 “>” or “<“ 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)
Q=TD -> T=Q/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. The three principles of all forecasting techniques:
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: Scenario Two:
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, (1000) = $ 335,000

26. Find order quantity that maximizes weighted average profit.
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. Look at marginal cost vs. marginal profit
What to Make?
Average demand is 13,100
Look at marginal cost vs. marginal profit
if extra swimsuit sold, profit is = 45
if not sold, cost is = 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 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:
×80=625,000

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 Level s Time Inventory Position
Lead
Time s
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:  2 = 89.2
Safety Stock is:  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 / = 679
Order-up-to level: s + Q = = 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: Warehouse One Market One
Supplier
Warehouse Two
Market 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 )
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 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?

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 11 12 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. Three rules of forecasting
The forecast is always wrong.
The longer the forecast horizon, the worse the forecast.
Aggregate forecasts are more accurate.

78. Categories (See section 3.7)
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.