inventory,risk pooling

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Inventory Management, Supply Contracts

and Risk Pooling

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Inventory Management, Supply Contracts Inventory Management, Supply Contracts and Risk Poolingand Risk Pooling

Learning Objectives: Introduction to Inventory Management. The Effect of Demand Uncertainty:

Economic Order QuantityReorder PointsService levels (s,S) PolicyPeriodic Review PolicySupply ContractsRisk Pooling

Centralized vs. Decentralized Systems. Practical Issues in Inventory Management.

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Types of Inventory & the Flow of MaterialsTypes of Inventory & the Flow of Materials

S

s

S

Supplier C

S

Supplier D

S

s

Supplier A

Supplier B

Work in Process

Finished Goods

Warehouse Y Warehouse Z

Customer Demand Customer Demand Customer Demand

Warehouse X

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Role of Inventory in Supply ChainRole of Inventory in Supply Chain

Where do we hold inventory? Suppliers and manufacturers Warehouses and distribution centers Retailers

Types of Inventory WIP Raw materials Finished goods Distribution Inventories Maintenance, Repair, and Operational Suppliers (MROs) Transit Inventories

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Why do we hold inventory?

Unexpected changes in demand: Short life cycles for a number of products. Presence of many competing products.

Presence of significant uncertainty in the quantity and quality of supply and supplier costs.

Reducing uncertainty due to delivery lead time. Serving decoupling of operations. Allowing flexibility in production scheduling. Reducing purchase ordering and material handling costs. Taking advantage of quantity discounts by bulk purchases

and transportation costs. Satisfying MRO Needs. Hedging the future price increases.

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By effectively managing inventory: Xerox eliminated $700 million inventory from its supply

chain. Wal-Mart became the largest retail company utilizing

efficient inventory management. GM has reduced parts inventory and transportation costs

by 26% annually. In 1984, GM’s distribution network consisted of:

20,000 Supplier plants. 133 Parts plants. 31 Assembly plants. 11, 000 dealers. Freight transportation costs were about US44.1 billion with 60% for

material shipments. Inventory valued at US$7.4 billion: 70% of this is WIP and the rest is

finished vehicles.

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By not managing inventory successfully:

In 1994, “IBM continues to struggle with shortages in their ThinkPad line” (WSJ, Oct 7, 1994).

In 1993, “Liz Claiborne said its unexpected earning decline is the consequence of higher than anticipated excess inventory” (WSJ, July 15, 1993).

In 1993, “Dell Computers predicts a loss; Stock plunges. Dell acknowledged that the company was sharply off in its forecast of demand, resulting in inventory write downs” (WSJ, August 1993).

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Objectives of Inventory Management

Maximize customer service,

Maximize operational efficiency of the plant, and

Minimize investment in inventories.

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Understanding InventoryUnderstanding Inventory

The inventory policy is affected by:

Demand Characteristics Replenishment Lead Time Number of Products Objectives

Service level Minimize costs

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Inventory Cost StructureInventory Cost Structure

Cost Structure: Order costs Setup and teardown costs. Production control costs. Purchase order costs. Lost capacity cost. Holding Costs

Insurance & Security Warehouse rental, heat & lights Maintenance and Handling State and Property Taxes Opportunity Costs Losses due to Pilferage, Spoilage, Damage, or

Obsolescence

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Economic Lot Size ModelEconomic Lot Size Model

Two major questions are of interest in formulating and solving the economic order quantity (EOQ) model.

How much should be ordered when the inventory for a given item is to be replenished?

When the order for a given item should be placed?

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Economic Lot Size ModelEconomic Lot Size Model

Assumptions Made in EOQ Model:

Demand is known and constant, without seasonality. Order processing costs are known and constant (do

not vary with quantity ordered). Carrying cost rate is known and constant. Total carrying cost is a linear function of carrying cost

rate and quantity ordered. Item cost per unit is known and constant (no quantity

discounts). The entire lot is delivered at one time, instantaneously

(zero lead time).

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R = Reorder pointQ = Economic order quantityL = Lead time

L L

Q QQ

R

Time

Numberof unitson hand

1. You receive an order quantity Q.

2. Your start using them up over time. 3. When you reach down to

a level of inventory of R, you place your next Q sized order.

4. The cycle then repeats.

Cost Minimization Goal

Ordering Costs

HoldingCosts

Order Quantity (Q)

COST

Annual Cost ofItems (DC)

Total Cost

QOPT

By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the Qopt inventory order point that minimizes total costs

By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the Qopt inventory order point that minimizes total costs

Basic Fixed-Order Quantity (EOQ) Model Formula

H 2

Q + S

Q

D + DC = TC H

2

Q + S

Q

D + DC = TC

Total Annual =Cost

AnnualPurchase

Cost

AnnualOrdering

Cost

AnnualHolding

Cost+ +

TC=Total annual costD =DemandC =Cost per unitQ =Order quantityS =Cost of placing an order or setup costR =Reorder pointL =Lead timeH=Annual holding and storage cost per unit of inventory

TC=Total annual costD =DemandC =Cost per unitQ =Order quantityS =Cost of placing an order or setup costR =Reorder pointL =Lead timeH=Annual holding and storage cost per unit of inventory

Deriving the EOQ Using calculus, we take the first derivative of

the total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the optimized (cost minimized) value of Qopt

Using calculus, we take the first derivative of the total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the optimized (cost minimized) value of Qopt

Q = 2DS

H =

2(Annual D em and)(Order or Setup Cost)

Annual Holding CostOPTQ =

2DS

H =

2(Annual D em and)(Order or Setup Cost)

Annual Holding CostOPT

Reorder point, R = d L_

Reorder point, R = d L_

d = average daily demand (constant)

L = Lead time (constant)

_

We also need a reorder point to tell us when to place an order

We also need a reorder point to tell us when to place an order

EOQ Example (1) Problem Data

Annual Demand = 1,000 unitsDays per year considered in average

daily demand = 365Cost to place an order = $10Holding cost per unit per year = $2.50Lead time = 7 daysCost per unit = $15

Given the information below, what are the EOQ and reorder point?

Given the information below, what are the EOQ and reorder point?

EOQ Example (1) Solution

Q = 2DS

H =

2(1,000 )(10)

2.50 = 89.443 units or OPT 90 unitsQ =

2DS

H =

2(1,000 )(10)

2.50 = 89.443 units or OPT 90 units

d = 1,000 units / year

365 days / year = 2.74 units / dayd =

1,000 units / year

365 days / year = 2.74 units / day

Reorder point, R = d L = 2.74units / day (7days) = 19.18 or _

20 units Reorder point, R = d L = 2.74units / day (7days) = 19.18 or _

20 units

In summary, you place an optimal order of 90 units. In the course of using the units to meet demand, when you only have 20 units left, place the next order of 90 units.

In summary, you place an optimal order of 90 units. In the course of using the units to meet demand, when you only have 20 units left, place the next order of 90 units.

EOQ Example (2) Problem Data

Annual Demand = 10,000 unitsDays per year considered in average daily demand = 365Cost to place an order = $10Holding cost per unit per year = 10% of cost per unitLead time = 10 daysCost per unit = $15

Determine the economic order quantity and the reorder point given the following…

Determine the economic order quantity and the reorder point given the following…

EOQ Example (2) Solution

Q =2DS

H=

2(10,000 )(10)

1.50= 365.148 units, or OPT 366 unitsQ =

2DS

H=

2(10,000 )(10)

1.50= 365.148 units, or OPT 366 units

d =10,000 units / year

365 days / year= 27.397 units / dayd =

10,000 units / year

365 days / year= 27.397 units / day

R = d L = 27.397 units / day (10 days) = 273.97 or _

274 unitsR = d L = 27.397 units / day (10 days) = 273.97 or _

274 units

Place an order for 366 units. When in the course of using the inventory you are left with only 274 units, place the next order of 366 units.

Place an order for 366 units. When in the course of using the inventory you are left with only 274 units, place the next order of 366 units.

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EOQ: Optimal Order QuantityEOQ: Optimal Order Quantity

Example: Suppose that an annual demand for an outdoor carpet is 20,000yds. The cost of placing an order is estimated at $50 per order, whereas the carrying cost rate per year is 20% and the item cost is $10. How many yards of outdoor carpet should be stocked?

D=20,000ydss=$50i=0.20c=10

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EOQ Model: An ExampleEOQ Model: An Example

EOQ = Q* = 25020000/(0.2010)

= 1000 yds.

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The company must order 1000 yards when ever it orders. At this EOQ

Annual order processing costs =50(20000/ Q*) = 50(20000/1000) = $1000

Annual Carrying Costs=(0.2010)(Q*/2) = (0.2010)(1000/2) = $1000

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Annual TIC*= Annual order processing costs + Annual carrying costs

= $1000 + $1000

= $2000

Annual TC* = Annual order processing costs + Annual carrying costs + Item Costs

= $1000+$1000+1020000

= $202000

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The Effect of The Effect of Demand UncertaintyDemand 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.

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Demand ForecastDemand Forecast

The 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.

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SnowTime Sporting GoodsSnowTime Sporting Goods

Fashion items have short life cycles, high variety of competitors.

SnowTime Sporting Goods 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 13,100, but there is a chance that demand will be greater or less than this.

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Supply Chain Time LinesSupply Chain Time Lines

Jan 00 Jan 01 Jan 02

Feb 00 Sep 00 Sep 01

Design Production Retailing

Feb 01Production

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SnowTime Demand ScenariosSnowTime Demand Scenarios

Demand Scenarios

0%5%

10%15%20%25%30%

Sales

P

robability

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SnowTime CostsSnowTime Costs

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, D demand

Profit =Revenue - Variable Cost - Fixed Cost + Salvage

*the amount expected to be realized upon the sale or other disposition of the asset when it is no longer useful to the program

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SnowTime ScenariosSnowTime Scenarios

Scenario One: Suppose you make 12,000 jackets and demand

ends up being 13,000 jackets. Profit = 125(12,000) - 80(12,000) - 100,000 =

$440,000

Scenario Two: Suppose you make 12,000 jackets and demand

ends up being 11,000 jackets. Profit = 125(11,000) - 80(12,000) - 100,000 +

20(1000) = $ 335,000

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SnowTime Best SolutionSnowTime Best Solution

Find the order quantity that maximizes the average profit.

Question: Will this quantity be less than, equal to, or greater than average demand?

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What to Make?What to Make?

Question: Will this quantity be less than, equal to, or greater than average demand?

Average demand is 13,100.Look at marginal cost Vs. marginal profit

If a extra jacket sold during the season: Marginal profit = 125-80 = $45

If it is not sold during the season:Marginal cost = 80-20 = $60

So Snow Time should make less than average demand.

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SnowTime Expected ProfitSnowTime Expected Profit

Expected Profit

$0

$100,000

$200,000

$300,000

$400,000

8000 12000 16000 20000

Order Quantity

Pro

fit

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Expected Profit

$0

$100,000

$200,000

$300,000

$400,000

8000 12000 16000 20000

Order Quantity

Pro

fit

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SnowTime: Important ObservationsSnowTime: Important Observations

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.

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Key Insights From This ModelKey Insights From This Model

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. In other words, the probability of large gains and of large losses increases.

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Supply ContractsSupply Contracts

Buyers and suppliers usually agree on supply contracts. These contracts are very powerful tools that can used to ensure adequate supply and demand for goods.

In a supply contract the buyer and seller may agree on: Pricing and volume discounts. Minimum and maximum purchase quantities. Delivery lead times. Product or material quality. Product return policies.

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Manufacturer Manufacturer DC Retail DC

Stores

Fixed Production Cost =$100,000

Variable Production Cost=$35

Selling Price=$125

Salvage Value=$20

Wholesale Price =$80


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Demand ScenariosDemand Scenarios

Demand Scenarios

0%5%

10%15%20%25%30%

Sales

P

roba

bilit

y

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Retailer Expected ProfitRetailer Expected Profit

Expected Profit

0

100000

200000

300000

400000

500000

6000 8000 10000 12000 14000 16000 18000 20000

Order Quantity

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Retailer Expected ProfitRetailer Expected Profit

Expected Profit

0

100000

200000

300000

400000

500000

6000 8000 10000 12000 14000 16000 18000 20000

Order Quantity

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Supply Contracts (Cont.)Supply Contracts (Cont.)

Retailer optimal order quantity is 12,000 units. Retailer’s expected profit is $470,000 See the

Figure on previous slide). Manufacturer profit is $440,000 (= 12000(80-35)-

100000). Supply Chain Profit is $910,000 (470000+440000).

Is there anything that the retailer and manufacturer can do to increase the profit of both?

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Supply Contracts (Cont’d)Supply Contracts (Cont’d)

Buy-Back Supply Contracts. Revenue-Sharing Contracts. Global Optimization. Quantity-Flexibility Contracts. Sales Rebate Contracts.

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Stores



Selling Price=$125

Salvage Value=$20



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Retailer Profit Buy Back=$55)Retailer Profit Buy Back=$55)

Buy-Back Contracts:

Suppose the manufacturer offers to buy back unsold jackets from the retailer for $55.

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Retailer Profit Buy Back=$55) Retailer Profit Buy Back=$55)

0

100,000

200,000

300,000

400,000

500,000

600,000

Order Quantity

Re

tail

er

Pro

fit

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Retailer Profit (Buy Back=$55)Retailer Profit (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

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Manufacturer Profit (Buy Back=$55)Manufacturer Profit (Buy Back=$55)

0

100,000

200,000

300,000

400,000

500,000

600,000

Production Quantity

Ma

nu

factu

rer

Pro

fit

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Manufacturer Profit (Buy Back=$55)Manufacturer Profit (Buy Back=$55)

0

100,000

200,000

300,000

400,000

500,000

600,000

Production Quantity

Ma

nu

fact

ure

r P

rofi

t

$471,900

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Buy-Back SC Profit (Buy back = 55)Buy-Back SC Profit (Buy back = 55)

Under buy back at $55:

Retailer’s profit = $513,800.

Manufacturer’s profit = $471,900.

SC profit = 513,800+471,900 = $985700.

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Revenue-Sharing Contracts:

In revenue-sharing contracts, buyer shares some of its revenue with the seller, in turn for a discount on the wholesale price.

In this type a contract, manufacturer agrees to reduce the whole price from $80 to $60, and in return, the retailer provides 15% of the product revenue to the manufacturer.

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Stores



Selling Price=$125

Salvage Value=$20



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Retailer Profit (Wholesale Price $60, RS Retailer Profit (Wholesale Price $60, RS 15%)15%)

0

100,000

200,000

300,000

400,000

500,000

600,000

Order Quantity

Re

tail

er

Pro

fit

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Retailer Profit (Wholesale Price $60, RS Retailer Profit (Wholesale Price $60, RS 15%)15%)

0

100,000

200,000

300,000

400,000

500,000

600,000

Order Quantity

Re

tail

er

Pro

fit

$504,325

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Manufacturer Profit (Wholesale Price $60, Manufacturer Profit (Wholesale Price $60, RS 15%)RS 15%)

0

100,000

200,000

300,000

400,000

500,000

600,000

700,000

Production Quantity

Ma

nu

fact

ure

r P

rofi

t

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Manufacturer Profit (Wholesale Price $60, Manufacturer Profit (Wholesale Price $60, RS 15%)RS 15%)

0

100,000

200,000

300,000

400,000

500,000

600,000

700,000

Production Quantity

Ma

nu

fact

ure

r P

rofi

t

$481,375

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Revenue-Sharing SC Profit (Wholesale Price Revenue-Sharing SC Profit (Wholesale Price $60, RS 15%)$60, RS 15%)

Under this RS Contract:

Retailer’s profit = $504,325.

Manufacturer’s profit = $481,375.

SC profit = 504,325+481,375 = $985,700.

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Strategy Retailer Manufacturer TotalSequential Optimization 470,700 440,000 910,700 Buyback 513,800 471,900 985,700 Revenue Sharing 504,325 481,375 985,700

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Global Optimization:

Both the manufacturer and the retailer are considered as two members of the same organization, causing the transfer of money between the two parties is ignored.

In this case, the supply chain marginal profit is $90=$125-$35, and the marginal loss is $15 = $35-$20.

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Stores



Selling Price=$125

Salvage Value=$20



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Supply Chain ProfitSupply Chain Profit

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

Production Quantity

Su

pp

ly C

ha

in P

rofi

t

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Supply Chain ProfitSupply Chain Profit

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

Production Quantity

Su

pp

ly C

ha

in P

rofi

t $1,014,500

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Strategy Retailer Manufacturer TotalSequential Optimization 470,700 440,000 910,700 Buyback 513,800 471,900 985,700 Revenue Sharing 504,325 481,375 985,700 Global Optimization 1,014,500

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Supply Contracts: Key InsightsSupply Contracts: 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.

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Supply Contracts: Case StudySupply 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

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Supply Contracts: Case StudySupply 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)

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Other ContractsOther Contracts

Quantity Flexibility ContractsSupplier provides full refund for returned

items as long as the number of returns is no larger than a certain quantity

Sales Rebate ContractsSupplier provides direct incentive for the

retailer to increase sales by means of a rebate paid by the supplier for any item sold above a certain quantity

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SnowTime Costs: Initial InventorySnowTime Costs: Initial Inventory

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, D demand

Profit =Revenue - Variable Cost - Fixed Cost +

Salvage

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Expected Profit

$0

$100,000

$200,000

$300,000

$400,000

8000 12000 16000 20000

Order Quantity

Pro

fit

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Initial InventoryInitial Inventory

Suppose that one of the jacket 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 7000 units remaining, what should SnowTime do? What should they do if there are 10,000 remaining?

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(s, S) Policies(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 costs associated with ordering, transportation, or manufacturing.

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Market Two

Risk PoolingRisk Pooling

Consider these two systems:

Supplier

Warehouse One

Warehouse Two

Market One

Market Two

Supplier Warehouse

Market One

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Risk PoolingRisk Pooling

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?

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Risk Pooling:Risk Pooling:Important ObservationsImportant Observations

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

What other kinds of risk pooling will we see?

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Risk Pooling:Risk Pooling:Types of Risk PoolingTypes of Risk Pooling

Risk Pooling Across Markets Risk Pooling Across Products Risk Pooling Across Time

Daily order up to quantity is: LTAVG + z AVG LT

10 1211 13 14 15

Demands

Orders

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To Centralize Or Not To CentralizeTo Centralize Or Not To Centralize

What is the effect on:Safety stock?Service level?Overhead?Lead time?Transportation Costs?

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Centralized Decision: Supplier

Warehouse

Retailers

Centralized SystemsCentralized Systems

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Factors that Drive Reduction in InventoryFactors that Drive Reduction in Inventory

Top management emphasis on inventory reduction (19%).

Reduce the Number of SKUs in the warehouse (10%).

Improved forecasting (7%). Use of sophisticated inventory management

software (6%). Coordination among supply chain members

(6%). Others.

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Factors that Drive Inventory Turns Factors that Drive Inventory Turns IncreaseIncrease

Better software for inventory management (16.2%).

Reduced lead time (15%). Improved forecasting (10.7%). Application of SCM principles (9.6%). More attention to inventory management (6.6%). Reduction in SKU (5.1%). Others.

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End of the Session

Thank You

inventory,risk pooling

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