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
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


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
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
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