1. Inventory Management and Risk Pooling
Designing & Managing the Supply Chain
Chapter 3
Byung-Hyun Ha

2. Outline Introduction to Inventory Management
Effect of Demand Uncertainty
(s,S) Policy
Supply Contracts
Continuous/Periodic Review Policy
Risk Pooling
Centralized vs. Decentralized Systems
Managing Inventory in Supply Chain
Practical Issues in Inventory Management
Forecasting

3. Case: JAM USA, Service Level Crisis
Background
Subsidiary of JAM Electronics (Korean manufacturer)
Established in 1978
Five Far Eastern manufacturing facilities, each in different countries
2,500 different products, a central warehouse in Korea for FGs
A central warehouse in Chicago with items transported by ship
Customers: distributors & original equipment manufacturers (OEMs)
Problems
Significant increase in competition
Huge pressure to improve service levels and reduce costs
Al Jones, inventory manage, points out:
Only 70% percent of all orders are delivered on time
Inventory, primarily that of low-demand products, keeps pile up

4. Case: JAM USA, Service Level Crisis
Reasons for the low service level:
Difficulty forecasting customer demand
Long lead time in the supply chain
About 6-7 weeks
Large number of SKUs handled by JAM USA
Low priority given the U.S. subsidiary by headquarters in Seoul
Monthly demand for item xxx-1534

5. Inventory Where do we hold inventory? Types of Inventory
Suppliers and manufacturers / warehouses and distribution centers / retailers
Types of Inventory
Raw materials / WIP (work in process) / finished goods
Reasons of holding inventory
Unexpected changes in customer demand
The short life cycle of an increasing number of products.
The presence of many competing products in the marketplace.
Uncertainty in the quantity and quality of the supply, supplier costs and delivery times.
Delivery lead time and capacity limitations even with no uncertainty
Economies of scale (transportation cost)

6. Single Warehouse Inventory Example
Contents
Economy lot size model
News vendor model
Effect of demand uncertainty
Supply contract
Multiple order opportunities
Continuous review policy
Periodic review policy

7. Single Warehouse Inventory Example
Key factors affecting inventory policy
Customer demand characteristics
Replenishment lead time
Number of products
Length of planning horizon
Cost structure
Order cost
Fixed, variable
Holding cost
Taxes, insurance, maintenance, handling, obsolescence, and opportunity costs
Service level requirements

8. Economy Lot Size Model Assumptions
Constant demand rate of D items per day
Fixed order quantities at Q items per order
Fixed setup cost K when places an order
Inventory holding cost h per unit per day
Zero lead time
Zero initial inventory & infinite planning horizon

9. Economy Lot Size Model Inventory level
Total inventory cost in a cycle of length T
Average total cost per unit of time
(Q)
Cycle time (T)

10. Economy Lot Size Model Trade-off between order cost and holding cost
Total Cost
Holding Cost
Order Cost

11. Economy Lot Size Model Optimal order quantity Important insights
Economic order quantity (EOQ)
Important insights
Tradeoff between setup 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
Order Quantity
50%
80%
90%
100%
110%
120%
150%
200%
Cost Increase
25.0%
2.5%
0.5% -
0.4%
1.6%
8.0%

12. 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

13. Effect of Demand Uncertainty
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
News vendor model
Incorporating demand uncertainty and forecast demand into analysis
Characterizing impact of demand uncertainty on inventory policy

14. Case: Swimsuit Production
Fashion items have short life cycles, high variety of competitors
Swimsuit production
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

15. Case: Swimsuit Production
Information
Production cost per unit (C) = $80
Selling price per unit (S) = $125
Salvage value per unit (V) = $20
Fixed production cost (F) = $100,000
Production quantity (Q)

16. Case: Swimsuit Production
Possible scenarios
Make 10,000 swimsuits, demand ends up being 12,000
Profit = 125(10,000) - 80(10,000) - 100,000 = $350,000
Make 10,000 swimsuits, demand ends up being 8,000
Profit = 125(8,000) - 80(10,000) - 100, (2,000) = $140,000 …

17. Swimsuit Production Solution
Problem
Find optimal order quantity Q* that maximizes expected profit
Notation
di – ith possible demand where di < di+1
(d1, d2, d3, d4, d5, d6) = (8K, 10K, 12K, 14K, 16K, 18K)
pi – probability that ith possible demand occurs
(p1, p2, p3, p4, p5, p6) = (0.11, 0.11, 0.28, 0.22, 0.18, 0.10)
ES(Q) – expected sales when producing Q
EI(Q) – expected left over inventory when producing Q
EP(Q) – expected profit when producing Q
Expected profit
EP(Q) = SES(Q) – CQ – F + VEI(Q)

18. Swimsuit Production Solution
Expected sales
Case 1: Q  d1
Case 2: dk < Q  dk+1, k=1,…,5
Case 3: d6  Q
Expected left over inventory (why?)
EI(Q) = Q – ES(Q)

19. Swimsuit Production Solution
Quantity that maximizes average profit

20. Swimsuit Production Solution
Question
Average demand is 13,000
Will optimal quantity be less than, equal to, or greater than average demand?
Note that fixed production cost is sunk cost
We have to pay in all cases

21. Swimsuit Production Solution
Look at marginal cost vs. marginal profit
If extra swimsuit sold, profit is = 45
If not sold, cost is = 60
In case of Scenario Two (make 10,000, demand 8,000)
Profit = 125(8,000) - 80(10,000) - 100, (2,000) = 125(8,000) - 80(8, ,000) - 100, (2,000) = 45(8,000) - 60(2,000) - 100,000 = $140,000
That is,
EP(Q) = SES(Q) – CQ – F + VEI(Q) = SES(Q) – C{ES(Q) + EI(Q)} – F + VEI(Q) = (S – C)ES(Q) – (C – V)EI(Q) – F
So we will make less than average

22. Swimsuit Production Solution
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?

23. Swimsuit Production Solution
Risk and reward
Consult Ch13 of Winston, “Decision making under uncertainty”

24. Case: Swimsuit Production
Key insights
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 (the probability of large gains and of large losses increases)

25. Case: Swimsuit Production
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
Question: If there are 5,000 units remaining, what should Swimsuit production do?

26. Case: Swimsuit Production
Analysis for initial inventory and profit
Solid line: average profit excluding fixed cost
Dotted line: same as expected profit including fixed cost
Nothing produced
225,000 (from the figure) + 80(5,000) = 625,000
Producing
371,000 (from the figure) + 80(5,000) = 771,000
If initial inventory was 10,000?

27. Case: Swimsuit Production
Initial inventory and profit

28. Case: Swimsuit Production
(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

29. Supply Contracts Assumptions for Swimsuit production Supply contracts
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

30. Supply Contracts Condition Wholesale Price =$80 Selling Price=$125
Manufacturer
Manufacturer DC
Retail DC
Stores
Fixed Production Cost =$100,000
Variable Production Cost=$35
Wholesale Price =$80
Selling Price=$125
Salvage Value=$20

31. Demand Scenario and Retailer Profit

32. 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?

33. Buy-Back Contracts
Buy back=$55
retailer
manufacturer

34. Buy-Back Contracts Sequential supply chain With buy-back contracts
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!

35. Revenue-Sharing Contracts
Wholesale price from $80 to $60, RS 15%
Supply chain profit is $985,700
retailer
manufacturer

36. 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

37. 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 profit=$90, marginal loss=$15
Optimal production quantity=16,000
Drawbacks
Decision-making power
Allocating profit

38. Global Optimization Revised buy-back contracts Equilibrium point!
Wholesale price=$75, buy-back price=$65
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

39. 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

40. 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)

41. Multiple Order Opportunities
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

42. 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.
(s, S) Policy
Whenever the inventory position drops below a certain level (s) we order to raise the inventory position to level S

43. Reminder: The Normal Distribution

44. A View of (s, S) Policy

45. (s, S) Policy Notations Policy Inventory Position
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)

46. (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LT where 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

47. (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, Q=679
Order-up-to level thus equals:
Reorder Point + Q = = 855

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

49. 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 r+L days (the time until the next order arrives): (r+L)*AVG
Safety stock during that time: z*STD* r+L

50. 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?

51. 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

52. Risk Pooling Example
Risk Pooling Performance

53. 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?

54. Centralized vs. Decentralized Systems
Trade-offs that need to be considered in comparing centralized and decentralized systems
Safety stock
Service level
Overhead costs
Customer lead time
Transportation costs

55. 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.

56. Practical Issues Top seven effective strategies
Periodic inventory reviews
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

57. Forecasting Recall the three rules Nevertheless, forecast is critical
General overview:
Judgment methods
Market research methods
Time series methods
Causal methods

58. Forecasting Judgment methods Assemble the opinion of experts
Sales-force composite combines salespeople’s 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

59. Forecasting 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.

60. Forecasting 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
Holt’s method – combines exponential smoothing concepts with the ability to follow a trend
Methods for data with seasonality
Seasonal decomposition methods (seasonal patterns removed)
Winter’s method: advanced approach based on exponential smoothing
Complex methods (not clear that these work better)

61. Forecasting 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

62. Forecasting Selecting appropriate forecasting technique
What is purpose of forecast? How is it to be used?
What are dynamics of system for which forecast will be made?
How important is past in estimating future?

63. Summary Matching supply and demand Inventory management
Reducing cost and providing required service level
Taking into account holding and setup cost, lead time, forecast demand, and information about demand variability
Demand aggregation
Globally optimal inventory policies
Global optimization