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Inventory Management and Risk

Pooling

Designing & Managing the Supply Chain

Chapter 3Byung-Hyun Ha

[email protected]
mailto:[email protected]:[email protected]

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Outline

Introduction to Inventory Management

Effect of Demand Uncertainty

(s,S) Policy

Supply Contracts

Continuous/Periodic Review Policy

Risk Pooling

Centralized vs. Decentralized Systems

Managing Inventory in Supply Chain Practical Issues in Inventory Management

Forecasting

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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

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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

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Inventory

Where do we hold inventory? Suppliers and manufacturers / warehouses and distribution

centers / retailers

Types of Inventory Raw materials / WIP (work in process) / 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, suppliercosts and delivery times.

Delivery lead time and capacity limitations even with nouncertainty

Economies of scale (transportation cost)

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Single Warehouse Inventory Example

Key factors affecting inventory policy Customer demand characteristics

Replenishment lead time

Number of products

Length of planning horizon

Cost structure

Order cost

Fixed, variable

Holding cost

Taxes, insurance, maintenance, handling, obsolescence, andopportunity costs

Service level requirements

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Economy Lot Size Model

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

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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

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Trade-off between order cost and holding cost

0

20

40

60

80

100

120

140

160

0 500 1000 1500

Order Quantity

Cost

Total Cost

Order Cost

Holding Cost

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Optimal order quantity Economic order quantity (EOQ)

Important insights

Tradeoff between setup costs and holding costs whendetermining order quantity. In fact, we order so that these costsare equal per unit time

Total cost is not particularly sensitive to the optimal orderquantity

h

KDQ

2*

Order Quantity 50% 80% 90% 100% 110% 120% 150% 200%

Cost Increase 25.0% 2.5% 0.5% - 0.4% 1.6% 8.0% 25.0%

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Most companies treat the world as if it werepredictable

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 aforecast, 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

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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

News vendor model

Incorporating demand uncertainty and forecast demand into

analysis

Characterizing impact of demand uncertainty on inventory policy

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Case: Swimsuit Production

Fashion items have short life cycles, high variety ofcompetitors

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 probabilisticforecast

The forecast averages about 13,000, but there is a chance that

demand will be greater or less than this

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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 Production quantity (Q)

Demand Scenarios

0%5%

10%15%

20%25%30%

8000

1000

0

1200

0

1400

0

1600

0

1800

0

Sales

Probability

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Possible scenarios Make 10,000 swimsuits, demand ends up being 12,000

Profit = 125(10,000) - 80(10,000) - 100,000 = $350,000

Make 10,000 swimsuits, demand ends up being 8,000

Profit = 125(8,000) - 80(10,000) - 100,000 + 20(2,000) = $140,000

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Swimsuit Production Solution

Problem Find optimal order quantity Q*that maximizes expected profit

Notation

diith possible demand where di< di+1

(d1, d2, d3, d4, d5, d6) = (8K, 10K, 12K, 14K, 16K, 18K) piprobability that ith possible demand occurs

(p1,p2,p3,p4,p5,p6) = (0.11, 0.11, 0.28, 0.22, 0.18, 0.10)

ES(Q)expected sales when producing Q

EI(Q)expected left over inventory when producing Q

EP(Q)expected profit when producing Q

Expected profit

EP(Q) = SES(Q)CQF+ VEI(Q)

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Expected sales Case 1: Qd1

Case 2: dk< Qdk+1, k=1,,5

Case 3: d6Q

Expected left over inventory (why?)

EI(Q) = QES(Q)

QQES )(

6

11

)(ki

i

k

i

ii pQdpQES

6

1

)(i

iidpQES

6

1

},min{)(i

ii QdpQES

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Quantity that maximizes average profit

Expected Profit

$0$100,000

$200,000

$300,000

$400,000

8000 12000 16000 20000

Order Quantity

Profit

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Question Average demand is 13,000

Will optimal quantity be less than, equal to, or greater thanaverage demand?

Note that fixed production cost is sunk cost

We have to pay in all cases

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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)= 125(8,000) - 80(8,000 + 2,000) - 100,000 + 20(2,000)= 45(8,000) - 60(2,000) - 100,000 = $140,000

That is,

EP(Q) = SES(Q)CQF+ VEI(Q)= SES(Q)C{ES(Q) + EI(Q)}F+ VEI(Q)

= (SC)ES(Q)(CV)EI(Q)F

So we will make less than average

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Tradeoff between ordering enough to meet demandand 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 thesame average profit, so which do we prefer?

Expected Profit

$0

$100,000

$200,000

$300,000

$400,000

8000 12000 16000 20000

Order Quantity

Profit

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Risk and reward

0%

20%

40%60%

80%

100%

-30000

0

-10000

0

10000

0

30000

0

50000

0

Revenue

Probab

ility

Q=9000Q=16000

Consult Ch13 of Winston, Decision making under uncertainty

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Key insights The optimal order quantity is not necessarily equal to average

forecast demand

The optimal quantity depends on the relationship betweenmarginal profit and marginal cost

As order quantity increases, average profit first increases andthen decreases

As production quantity increases, risk increases (the probabilityof large gains and of large losses increases)

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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

10000

11000

12000

13000

14000

15000

16000

Production Quantity

Profit

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Initial inventory and profit

0

100000

200000

300000

400000

500000

5000

6000

7000

8000

9000

10000

11000

12000

13000

14000

15000

16000

Production Quantity

Profit

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(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

sis the reorder point, and Sis the order-up-to level

The difference between the two levels is driven by the fixedcosts associated with ordering, transportation, or manufacturing

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Supply Contracts

Assumptions for Swimsuit production In-house manufacturing

Usually, manufactures and retailers

Supply contracts

Pricing and volume discounts Minimum and maximum purchase quantities

Delivery lead times

Product or material quality

Product return policies

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Supply Contracts

Manufacturer Manufacturer DC Retail DC

Stores

Selling Price=$125

Salvage Value=$20

Wholesale Price =$80

Fixed Production Cost =$100,000

Variable Production Cost=$35

Condition

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Demand Scenario and Retailer Profit

Demand Scenarios

0%

5%10%15%

20%25%30%

8000

1000

0

1200

0

1400

0

1600

0

1800

0

Sales

Probability

Expected Profit

0

100000

200000

300000

400000

500000

6000 8000 10000 12000 14000 16000 18000 20000

Order Quantity

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Demand Scenario and Retailer Profit

Sequential supply chain Retailer optimal order quantity is 12,000 units

Retailer expectedprofit is $470,700

Manufacturer profit is $440,000

Supply Chain Profit is $910,700

Is there anything that the distributor andmanufacturer can do to increase the profit of both?

Global optimization?

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Buy-Back Contracts

Buy back=$55

0

100,000

200,000

300,000

400,000

500,000

600,000

6000

7000

8000

9000

1000

0

1100

0

1200

0

1300

0

1400

0

1500

0

1600

0

1700

0

1800

0

Order Quantity

RetailerProfit

$513,800

retailer

manufacturer

0

100,000

200,000

300,000

400,000

500,000

600,000

6000

7000

8000

9000

1000

0

1100

0

1200

0

1300

0

1400

0

1500

0

1600

0

1700

0

1800

0

Production Quantity

ManufacturerProfit $471,900

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Buy-Back Contracts

Sequential supply chain Retailer optimal order quantity is 12,000 units


Manufacturer profit is $440,000

Supply chain profit is $910,700

With buy-back contracts

Retailer optimal order quantity is 14,000 units


Manufacturer expectedprofit is $471,900 Supply chain profit is $985,700

Manufacture sharing some of risk!

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Global Optimization

What is the most profit both the supplier and thebuyer can hope to achieve?

Assume an unbiased decision maker

Transfer of money between the parties is ignored

Allowing the parties to share the risk!

Marginal profit=$90, marginal loss=$15

Optimal production quantity=16,000

Drawbacks

Decision-making power Allocating profit

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

6000

7000

8000

9000

1000

0

1100

0

1200

0

1300

0

1400

0

1500

0

1600

0

1700

0

1800

0

Production Quantity

SupplyChainP

rofit $1,014,500

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

6000

7000

8000

9000

1000

0

1100

0

1200

0

1300

0

1400

0

1500

0

1600

0

1700

0

1800

0

Production Quantity

SupplyChainP

rofit $1,014,500

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Global Optimization

Revised buy-back contracts Wholesale price=$75, buy-back price=$65

Global optimum

Equilibrium point!

No partner can improve his profit by deciding to deviate from theoptimal decision

Consult Ch14 of Winston, Game theory

Key Insights

Effective supply contracts allow supply chain partners to replacesequential opt im izat ionby glob al op timizat ion

Buy Back and Revenue Sharing contracts achieve this objectivethrough r isk shar ing

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Supply Contracts: Case Study

Example: Demand for a movie newly released videocassette typically starts high and decreases rapidly

Peak demand last about 10 weeks

Blockbuster purchases a copy from a studio for $65

and rent for $3 Hence, retailer must rent the tape at least 22 times before

earning profit

Retailers cannot justify purchasing enough to cover

the peak demand In 1998, 20% of surveyed customers reported that they could not

rent the movie they wanted

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Supply Contracts: Case Study

Starting in 1998 Blockbuster entered a revenue-sharing agreement with the major studios

Studio charges $8 per copy

Blockbuster pays 30-45% of its rental income

Even if Blockbuster keeps only half of the rentalincome, the breakeven point is 6 rental per copy

The impact of revenue sharing on Blockbuster wasdramatic

Rentals increased by 75% in test markets Market share increased from 25% to 31% (The 2nd largest

retailer, Hollywood Entertainment Corp has 5% market share)

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Multiple Order Opportunities

Situation Often, there are multiple reorder opportunities

A central distribution facility which orders from a manufacturerand delivers to retailers

The distributor periodically places orders to replenish its inventory

Reasons why DC holds inventory

Satisfy demand during lead time

Protect against demand uncertainty

Balance fixed costs and holding costs

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Continuous Review Inventory Model

Assumptions Normally distributed random demand

Fixed order cost plus a cost proportional to amount ordered

Inventory cost is charged per item per unit time

If an order arrives and there is no inventory, the order is lost

The distributor has a required service level

expressed as the likelihood that the distributor will not stock outduring lead time.

(s, S) Policy

Whenever the inventory position drops below a certain level (s)we order to raise the inventory position to level S

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Reminder: The Normal Distribution

0 10 20 30 40 50 60

Average = 30

Standard Deviation = 5

Standard Deviation = 10

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A View of (s, S) Policy

Time

InventoryL

evel

S

s

0

Lead

Time

Lead

Time

Inventory Position

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(s, S) Policy

Notations AVG = average daily demand

STD = standard deviation of daily demand

LT = replenishment lead time in days

h = holding cost of one unit for one day

K = fixed cost

SL = service level (for example, 95%)

The probability of stocking out is 100% - SL (for example, 5%)

Policy

s= reorder point, S = order-up-to level

Inventory Position

Actual inventory + (items already ordered, but not yet delivered)

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(s, S) Policy - Analysis

The reorder point (s) has two components: To account for average demand during lead time:

LTAVG

To account for deviations from average (we call this safetystock)

zSTDLTwhere zis chosen from statistical tables to ensure that theprobability of stock-outs during lead-time is100% - SL.

Since there is a fixed cost, we order more than up to

the reorder point:Q=(2KAVG)/h

The total order-up-to level is:S= Q+ s

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(s, S) Policy - Example

The distributor has historically observed weekly demand of:

AVG= 44.6 STD= 32.1

Replenishment lead time is 2 weeks, and desired service levelSL = 97%

Average demand during lead time is: 44.6 2 = 89.2

Safety Stock is: 1.88 32.1 2 = 85.3

Reorder point is thus 175, or about 3.9 weeks of supply atwarehouse and in the pipeline

Weekly inventory holding cost: .87 Therefore, Q=679

Order-up-to level thus equals:

Reorder Point + Q = 176+679 = 855

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Periodic Review

Periodic review model Suppose the distributor places orders every month

What policy should the distributor use?

What about the fixed cost?

Base-Stock Policy

Inventory

Level

Time

Base-stock

Level

0

Inventory

Position

r r

L L L

Inventory

Level

Time

Base-stock

Level

0

Inventory

Position

r r

L L L

Time

Base-stock

Level

0

Inventory

Position

r r

L L L

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Periodic Review

Base-Stock Policy Each review echelon, inventory position is raised to the base-

stock level.

The base-stock level includes two components:

Average demand during r+Ldays (the time until the next order

arrives):(r+L)*AVG

Safety stock during that time:z*STD* r+L

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Risk Pooling

Consider these two systems: For the same service level, which system will require more

inventory? Why?

For the same total inventory level, which system will have betterservice? Why?

What are the factors that affect these answers?

Market Two

Supplier

Warehouse One

Warehouse Two

Market One

Market Two

Supplier Warehouse

Market One

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Risk Pooling Example

Compare the two systems: two products

maintain 97% service level

$60 order cost

$.27 weekly holding cost

$1.05 transportation cost per unit in decentralized system, $1.10in centralized system

1 week lead timeWeek 1 2 3 4 5 6 7 8

Prod A,

Market 1

33 45 37 38 55 30 18 58

Prod A,

Market 2

46 35 41 40 26 48 18 55

Prod B,

Market 1

0 2 3 0 0 1 3 0

Product B,

Market 2

2 4 0 0 3 1 0 0

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Risk Pooling Example

Risk Pooling Performance

Warehouse Product AVG STD CV s S Avg.

Inven.

%

Dec.

Market 1 A 39.3 13.2 .34 65 197 91

Market 2 A 38.6 12.0 .31 62 193 88

Market 1 B 1.125 1.36 1.21 4 29 14

Market 2 B 1.25 1.58 1.26 5 29 15

Cent. A 77.9 20.7 .27 118 304 132 36%

Cent B 2.375 1.9 .81 6 39 20 43%

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Risk Pooling: Important Observations

Centralizing inventory control reduces both safetystock and average inventory level for the sameservice level.

This works best for

High coefficient of variation, which increases required safetystock.

Negatively correlated demand. Why?

What other kinds of risk pooling will we see?

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Centralized vs. Decentralized Systems

Trade-offs that need to be considered in comparingcentralized and decentralized systems

Safety stock

Service level

Overhead costs

Customer lead time

Transportation costs

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Inventory in Supply Chain

Centralized distribution systems How much inventory should

management keep at each location?

A good strategy:

The retailer raises inventory to level Sreach period

The supplier raises the sum ofinventory in the retailer and supplierwarehouses and in transit to Ss

If there is not enough inventory in thewarehouse to meet all demands fromretailers, it is allocated so that theservice level at each of the retailers willbe equal.

Supplier

Warehouse

Retailers

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Forecasting

Recall the three rules

Nevertheless, forecast is critical

General overview:

Judgment methods

Market research methods

Time series methods

Causal methods

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Forecasting

Judgment methods Assemble the opinion of experts

Sales-force composite combines salespeoples estimates

Panels of expertsinternal, external, both

Delphi method

Each member surveyed

Opinions are compiled

Each member is given the opportunity to change his opinion

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Forecasting

Market research methods Particularly valuable for developing forecasts of newly introduced

products

Market testing

Focus groups assembled

Responses tested Extrapolations to rest of market made

Market surveys

Data gathered from potential customers

Interviews, phone-surveys, written surveys, etc.

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Forecasting

Time series methods Past data is used to estimate future data

Examples include

Moving averagesaverage of some previous demand points.

Exponential Smoothingmore recent points receive more weight

Methods for data with trends: Regression analysisfits line to data

Holts method combines exponential smoothing concepts withthe ability to follow a trend

Methods for data with seasonality

Seasonal decomposition methods (seasonal patterns removed) Winters method: advanced approach based on exponential

smoothing

Complex methods (not clear that these work better)

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Forecasting

Causal methods Forecasts are generated based on data other than the data

being predicted

Examples include:

Inflation rates

GNP Unemployment rates

Weather

Sales of other products

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Forecasting

Selecting appropriate forecasting technique What is purpose of forecast? How is it to be used?

What are dynamics of system for which forecast will be made?

How important is past in estimating future?

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Summary

Matching supply and demand

Inventory management

Reducing cost and providing required service level

Taking into account holding and setup cost, lead time, forecast

demand, and information about demand variability Demand aggregation

Globally optimal inventory policies

Global optimization

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