inventory management and risk pooling (1) designing & managing the supply chain chapter 3...
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Inventory Management and Risk Pooling (1)
Designing & Managing the Supply Chain
Chapter 3
Byung-Hyun Ha
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 (OE
Ms)
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
Time
Inventory
OrderSize
Avg. Inven
EOQ: A View of Inventory
Inventory level
Total inventory cost in a cycle of length T
Average total cost per unit of time
Time
Inventory
OrderSize
Avg. Inven
2
hQ
Q
KD
Cycle time (T)
(Q)
D
QT
TDQ
2
hTQK
EOQ: A View of Inventory
Trade-off between order cost and holding cost
0
20
40
60
80
100
120
140
160
0 500 1000 1500
Order Quantity
Co
st
Total Cost
Order Cost
Holding Cost
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
h
KDQ
2*
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
0%5%
10%15%20%25%30%
8000
1000
0
1200
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1400
0
1600
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1800
0
Sales
P
roba
bilit
y
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
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Pro
fit
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
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Pro
fit
Swimsuit Production Solution
Risk and reward
0%
20%
40%
60%
80%
100%
Revenue
Pro
ba
bili
ty
Q=9000
Q=16000
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 l
ast 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?
0
100000
200000
300000
400000
500000
5000
6000
7000
8000
9000
1000
0
1100
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1200
0
1300
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0
Production Quantity
Pro
fit
Case: Swimsuit Production
Initial inventory and profit
0
100000
200000
300000
400000
500000
5000
6000
7000
8000
9000
1000
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Production Quantity
Pro
fit
Case: Swimsuit Production
(s, S) policies For some starting inventory levels, it is better to not start producti
on 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 cost
s associated with ordering, transportation, or manufacturing