Inventory Management and Risk Pooling

Designing & Managing the Supply Chain

Chapter 3

Byung-Hyun Ha

bhha@pusan.ac.kr

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

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 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, supplier costs and delivery times.

Delivery lead time and capacity limitations even with no uncertainty

Economies of scale (transportation cost)

Single Warehouse Inventory Example

Contents Economy lot size model News vendor model

• Effect of demand uncertainty

• Supply contract

Multiple order opportunities• Continuous review policy

• Periodic review policy

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, and opportunity costs

Service level requirements

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

Economy Lot Size Model

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

Economy Lot Size Model

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

Economy Lot Size Model

Optimal order quantity Economic order quantity (EOQ)

Important insights Tradeoff between setup 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 25.0% 2.5% 0.5% - 0.4% 1.6% 8.0% 25.0%

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

Effect of Demand Uncertainty

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

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 Production quantity (Q)

Demand Scenarios

0%5%

10%15%20%25%30%

8000

1000

0

1200

0

1400

0

1600

0

1800

0

Sales

P

roba

bilit

y

Case: Swimsuit Production

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

…

Swimsuit Production Solution

Problem Find optimal order quantity Q* that maximizes expected profit

Notation di – ith possible demand where di < di+1

• (d1, d2, d3, d4, d5, d6) = (8K, 10K, 12K, 14K, 16K, 18K)

pi – probability 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) – CQ – F + VEI(Q)

Swimsuit Production Solution

Expected sales Case 1: Q d1

Case 2: dk < Q dk+1, k=1,…,5

Case 3: d6 Q

Expected left over inventory (why?) EI(Q) = Q – ES(Q)

QQES )(

6

11

)(ki

i

k

iii pQdpQES

6

1

)(i

iidpQES

6

1

},min{)(i

ii QdpQES

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

Question Average demand is 13,000 Will optimal quantity be less than, equal to, or greater than

average demand? Note that fixed production cost is sunk cost

• We have to pay in all cases

Swimsuit Production Solution

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) – CQ – F + VEI(Q)

= SES(Q) – C{ES(Q) + EI(Q)} – F + VEI(Q)= (S – C)ES(Q) – (C – V)EI(Q) – F

So we will make less than average

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

0

1200

0

1300

0

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0

1500

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1600

0

Production Quantity

Pro

fit

Case: Swimsuit Production

Initial inventory and profit

0

100000

200000

300000

400000

500000

5000

6000

7000

8000

9000

1000

0

1100

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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

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

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

Demand Scenario and Retailer Profit

Demand Scenarios

0%5%

10%15%20%25%30%

Sales

P

roba

bilit

y

Expected Profit

0

100000

200000

300000

400000

500000

6000 8000 10000 12000 14000 16000 18000 20000

Order Quantity

Demand Scenario and Retailer Profit

Sequential supply chain Retailer optimal order quantity is 12,000 units Retailer expected profit is $470,700 Manufacturer profit is $440,000 Supply Chain Profit is $910,700

Is there anything that the distributor and manufacturer can do to increase the profit of both? Global optimization?

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

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1200

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1300

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1400

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1600

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1700

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1800

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Order Quantity

Re

tail

er

Pro

fit

$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

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1300

0

1400

0

1500

0

1600

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1700

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0

Production Quantity

Ma

nu

fact

ure

r P

rofi

t $471,900

Buy-Back Contracts

Sequential supply chain Retailer optimal order quantity is 12,000 units Retailer expected profit is $470,700 Manufacturer profit is $440,000 Supply chain profit is $910,700

With buy-back contracts Retailer optimal order quantity is 14,000 units Retailer expected profit is $513,800 Manufacturer expected profit is $471,900 Supply chain profit is $985,700

Manufacture sharing some of risk!

Revenue-Sharing Contracts

Wholesale price from $80 to $60, RS 15%

0

100,000

200,000

300,000

400,000

500,000

600,000

6000

7000

8000

9000

1000

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1100

0

1200

0

1300

0

1400

0

1500

0

1600

0

1700

0

1800

0

Order Quantity

Re

tail

er

Pro

fit

$504,325

0

100,000

200,000

300,000

400,000

500,000

600,000

700,000

6000

7000

8000

9000

1000

0

1100

0

1200

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1300

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1400

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1500

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Production Quantity

Ma

nu

fact

ure

r P

rofi

t

$481,375retailer

manufacturer

Supply chain profit is $985,700

Other Types of Supply Contracts

Quantity-flexibility contracts Supplier providing full refund for returned (unsold) items up to a

certain quantity

Sales rebate contracts Direct incentive to retailer by supplier for any item sold above a c

ertain quantity

…

Consult Cachon 2002

Global Optimization

What is the most profit both the supplier and the buyer 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

Su

pp

ly C

ha

in P

rofi

t $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

Su

pp

ly C

ha

in P

rofi

t $1,014,500

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 the

optimal decision Consult Ch14 of Winston, “Game theory”

Key Insights Effective supply contracts allow supply chain partners to replace

sequential optimization by global optimization Buy Back and Revenue Sharing contracts achieve this objective

through risk sharing

Supply Contracts: Case Study

Example: Demand for a movie newly released video cassette 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

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 rental income, the breakeven point is 6 rental per copy

The impact of revenue sharing on Blockbuster was dramatic 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)

Multiple Order Opportunities

Situation Often, there are multiple reorder opportunities A central distribution facility which orders from a manufacturer

and 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

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 out during 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

Reminder: The Normal Distribution

0 10 20 30 40 50 60

Average = 30

Standard Deviation = 5

Standard Deviation = 10

A View of (s, S) Policy

Time

Inve

ntor

y L

evel

S

s

0

LeadTimeLeadTime

Inventory Position

(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)

(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 safety stoc

k) zSTDLT

where z is chosen from statistical tables to ensure that the probability of stock-outs during lead-time is 100% - 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

(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 level SL = 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 at warehouse and in the pipeline

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

Order-up-to level thus equals: Reorder Point + Q = 176+679 = 855

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

Inve

ntor

y L

evel

Time

Base-stock Level

0

Inventory Position

r r

L L L

Inve

ntor

y L

evel

Time

Base-stock Level

0

Inventory Position

r r

L L L

Time

Base-stock Level

0

Inventory Position

r r

L L L

Periodic Review

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

ck level. The base-stock level includes two components:

• Average demand during r+L days (the time until the next order arrives):

(r+L)*AVG

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

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 better

service? Why? What are the factors that affect these answers?

Market Two

Supplier

Warehouse One

Warehouse Two

Market One

Market Two

Supplier Warehouse

Market One

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, $1.10

in centralized system 1 week lead time

Week 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

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%

Risk Pooling: Important Observations

Centralizing inventory control reduces both safety stock and average inventory level for the same service level.

This works best for High coefficient of variation, which increases required safety

stock. Negatively correlated demand. Why?

What other kinds of risk pooling will we see?

Centralized vs. Decentralized Systems

Trade-offs that need to be considered in comparing centralized and decentralized systems Safety stock Service level Overhead costs Customer lead time Transportation costs

Inventory in Supply Chain

Centralized distribution systems How much inventory should managem

ent keep at each location?

A good strategy: The retailer raises inventory to level Sr

each period The supplier raises the sum of inventor

y in the retailer and supplier warehouses and in transit to Ss

If there is not enough inventory in the warehouse to meet all demands from retailers, it is allocated so that the service level at each of the retailers will be equal.

Supplier

Warehouse

Retailers

Practical Issues

Top seven effective strategies Periodic inventory reviews Tight management of usage rates, lead times, and safety stock Reduced safety stock levels Introduce or enhance cycle counting practice ABC approach Shift more inventory, or inventory ownership, to suppliers Quantitative approaches

Forecasting

Recall the three rules

Nevertheless, forecast is critical

General overview: Judgment methods Market research methods Time series methods Causal methods

Forecasting

Judgment methods Assemble the opinion of experts Sales-force composite combines salespeople’s estimates Panels of experts – internal, external, both Delphi method

• Each member surveyed

• Opinions are compiled

• Each member is given the opportunity to change his opinion

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.

Forecasting

Time series methods Past data is used to estimate future data Examples include

• Moving averages – average of some previous demand points.

• Exponential Smoothing – more recent points receive more weight

• Methods for data with trends:

• Regression analysis – fits line to data

• Holt’s method – combines exponential smoothing concepts with the ability to follow a trend

• Methods for data with seasonality

• Seasonal decomposition methods (seasonal patterns removed)

• Winter’s method: advanced approach based on exponential smoothing

• Complex methods (not clear that these work better)

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

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?

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