Inventory Management and Risk Pooling (2)

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

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

0

1200

0

1300

0

1400

0

1500

0

1600

0

1700

0

1800

0

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

0

1300

0

1400

0

1500

0

1600

0

1700

0

1800

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

0

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

0

1300

0

1400

0

1500

0

1600

0

1700

0

1800

0

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)

A Multi-Period Inventory Model

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.

Intuitively, how will the above assumptions effect our policy?

(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?

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

Inventory Management

Best Practice Periodic inventory reviews Tight management of usage rates, lead times and safety stock ABC approach Reduced safety stock levels 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

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

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.

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)

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