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

2. 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

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
WIP (work in process) / raw materials / 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, Capacity limitations
Economies of scale (transportation cost)

6. Key Factors Affecting Inventory Policy
Customer demand Characteristics
Replenishment lead Time
Number of Products
Service level requirements
Cost Structure
Order cost
Fixed, variable
Holding cost
Taxes, insurance, maintenance, handling, obsolescence, and opportunity costs
Objectives: minimize costs

7. EOQ: A View of Inventory
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

8. EOQ: A View of Inventory
Inventory level
Total inventory cost in a cycle of length T
Average total cost per unit of time
(Q)
Cycle time (T)

9. EOQ: A View of Inventory
Trade-off between order cost and holding cost
Total Cost
Holding Cost
Order Cost

10. EOQ: A View of Inventory
Optimal order quantity
Important insights
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
Order Quantity
50%
80%
90%
100%
110%
120%
150%
200%
Cost Increase
125%
103%
101%
102%
108%

11. 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
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

12. 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

13. 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
Q is production quantity

14. Case: Swimsuit Production
Scenario One:
Suppose you make 10,000 swimsuits and demand ends up being 12,000 swimsuits.
Profit = 125(10,000) - 80(10,000) - 100,000 = $350,000
Scenario Two:
Suppose you make 10,000 swimsuits and demand ends up being 8,000 swimsuits.
Profit = 125(8,000) - 80(10,000) - 100, (2,000) = $140,000

15. Swimsuit Production Solution
Find order quantity that maximizes weighted average profit
Question: Will this quantity be less than, equal to, or greater than average demand?
Average demand is 13,000
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) = 45(8,000) - 60(2,000) - 100,000 = $140,000
So we will make less than average

16. Swimsuit Production Solution
Quantity that maximizes average profit

17. 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?

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

19. 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)

20. 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?

21. 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?

22. Case: Swimsuit Production
Initial inventory and profit

23. 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