Inventory Management and Risk Pooling (1)

Designing & Managing the Supply Chain

Chapter 3

Byung-Hyun Ha

bhha@pusan.ac.kr

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

2hQ

QKD

Cycle time (T)

(Q)

DQT

TDQ

2hTQK

EOQ: A View of Inventory Trade-off between order cost and holding cost

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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

hKDQ 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

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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

$0

$100,000

$200,000

$300,000

$400,000

8000 12000 16000 20000

Order Quantity

Prof

it

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

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it

Swimsuit Production Solution Risk and reward

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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 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?

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Case: Swimsuit Production Initial inventory and profit

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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 cost

s associated with ordering, transportation, or manufacturing