Inventory Management and Risk Pooling (1)
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Transcript Inventory Management and Risk Pooling (1)
Inventory Management and Risk
Pooling (1)
Designing & Managing the Supply Chain
Chapter 3
Byung-Hyun Ha
[email protected]
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
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
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
Inventory
Where do we hold 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)
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
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
Inventory
Order
Size
Avg. Inven
Time
EOQ: A View of Inventory
Inventory level
Q TD
Q
T
D
Inventory
Order
Size
(Q)
Avg. Inven
Time
Cycle time (T)
Total inventory cost in a cycle of length T
hTQ
K
2
Average total cost per unit of time
KD hQ
Q
2
EOQ: A View of Inventory
Trade-off between order cost and holding cost
160
140
Total Cost
120
Cost
100
Holding Cost
80
60
Order Cost
40
20
0
0
500
1000
Order Quantity
1500
EOQ: A View of Inventory
Optimal order quantity
2KD
Q
h
*
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%
100%
101%
102%
108%
125%
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
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
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
Demand Scenarios
Sales
00
0
18
00
0
16
00
0
14
00
0
12
00
0
10
00
30%
25%
20%
15%
10%
5%
0%
80
Probability
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) - 100,000 + 20(2,000) =
$140,000
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 125-80 = 45
if not sold, cost is 80-20 = 60
In case of Scenario Two (make 10,000, demand 8,000)
• Profit = 125(8,000) - 80(10,000) - 100,000 + 20(2,000)
= 45(8,000) - 60(2,000) - 100,000 = $140,000
So we will make less than average
Swimsuit Production Solution
Quantity that maximizes average profit
Expected Profit
$400,000
Profit
$300,000
$200,000
$100,000
$0
8000
12000
16000
Order Quantity
20000
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 16000 units lead to about the
same average profit, so which do we prefer?
Expected Profit
$400,000
Profit
$300,000
$200,000
$100,000
$0
8000
12000
16000
Order Quantity
20000
Swimsuit Production Solution
Risk and reward
Probability
100%
80%
60%
Q=9000
40%
Q=16000
20%
-3
00
00
0
-1
00
00
0
10
00
00
30
00
00
50
00
00
0%
Revenue
Consult Ch13 of Winston, “Decision making under uncertainty”
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)
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?
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?
500000
300000
200000
100000
Production Quantity
16000
15000
14000
13000
12000
11000
10000
9000
8000
7000
6000
0
5000
Profit
400000
Case: Swimsuit Production
Initial inventory and profit
500000
300000
200000
100000
Production Quantity
16000
15000
14000
13000
12000
11000
10000
9000
8000
7000
6000
0
5000
Profit
400000
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