Chapter 3 Inventory Management and Risk Pooling. 結束 2 Outline of the contents Introduction to...

Chapter 3 Inventory Chapter 3 Inventory Management and Risk Management and Risk

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Chapter 3 Inventory Chapter 3 Inventory Management and Risk Management and Risk

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Outline of the Outline of the contentscontents

Introduction to Inventory Management

The Effect of Demand Uncertainty(s,S) PolicyPeriodic Review PolicySupply ContractsRisk Pooling

Centralized vs. Decentralized Systems

Practical Issues in Inventory Management

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InventoryInventory

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

Types of Inventory Raw materials WIP Finished goods

Why do we hold inventory? Economies of scale Uncertainty in supply and demand Lead Time, Capacity limitations

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InventoryInventoryInventoryInventory

Managing inventory in complex supply chains is typically difficult, and may have a significant impact on the customer service level and supply chain system-wide cost.

Inventory in three typesRaw material inventory (where?)Work-in-process inventory (where?)Finished product inventory (where?)

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Why hold Inventory?Why hold Inventory?

Unexpected changes in customer demand. The short life cycle of an increasing number of products. Thus,

historical data may not be available or may be quite limited. The presence of many competing products in the marketplace.

(Discussed in Chapters 5 and 9)

The presence in many situations of a significant uncertaintyuncertainty in the quantity and quality of the supply, supplier costs, and delivery times.A need to hold inventory due to delivery lead times – even if there is no uncertainty in supply or demand.Economies of scale offered by transportation companies that encourage firms to transport large quantities of items, and therefore hold large inventories.

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Managing inventory – examplesManaging inventory – examples

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 .

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Managing inventory – examplesManaging inventory – examples

By not managing inventory successfullyIn 1993, Dell’s stock plunged after the company

predicted a loss. (sharply off in its forecast of demand)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 2001, Cisco took a $2.25B excess inventory charge due to declining scales.

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Two important issues in inventory Two important issues in inventory managementmanagement

Demand forecastingForecast demand is a critical element in

determining order quantity.What is the relationship between forecast

demand and the optimal order quantity?Should the order quantity “=“ or “>” or “<“ the

forecast demand?…..

Order quantity calculation

A single warehouse inventory A single warehouse inventory exampleexample

A single warehouse inventory A single warehouse inventory exampleexample

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Key factors affecting inventory Key factors affecting inventory policy?policy?

Customer demandKnown in advance or may be random (forecasting tools

can be used).

Replenishment lead timeMay be known at the time we place the order or may be

uncertain.

The number of different productsHigh-mix and low volume?

The length of the planning horizon

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Costs (order cost and inventory holding cost)Order cost: the cost of the product and the transportation

costInventory holding cost

State taxes, property taxes, and insurance on inventoriesMaintenance costsObsolescence cost (an item will lose some of its value

because of changes in the market.)Opportunities costs (the return on investment that one

would receive had money been invested in something else (e.g. stock market) instead of inventory.

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Service level requirementsIt is not possible to meat customer orders 100

percent of the time. Managements need to specify an acceptable level of service

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3.2.1 The Economic Lot Size model3.2.1 The Economic Lot Size model

Economic lot size model is used to trade-off the costs between ordering and storage.Assumptions (for a single item and has a unlimited quantity of the product) Demand is constant at a rate of D items per day. Order quantities are fixed at Q items per order. A fixed cost (setup cost) K, incurred every time the warehouse

places an order. An inventory carrying cost, h, also referred to as a holding cost, is

accrued per unit held in inventory per day that the unit is held. The lead time, the time that elapses between the placement of an

order and its receipt, is zero Initial inventory is zero. The planning horizon is long (infinite).

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GoalFind the optimal order policy that minimizes annual

purchasing and carrying costs while meeting all demand.

Realistic system?A known fixed demand over a long horizon is clear

unrealistic.This model will help us to develop inventory policies

that are effective for more complex realistic systems.

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Time

Inventory

OrderSize

Notes:• No Stockouts• Order when no inventory• Order Size determines policy

Avg. Inven

Saw-toothed inventory pattern

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Total costsPurchase Cost is ConstantHolding Cost: (Avg. Inven) × (Holding Cost)Ordering (Setup Cost):

Number of Orders × Order Cost

Goal: Find the order Quantity that minimizes these costs.

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Total inventory cost in a cycle of length T

Average total cost per unit of time

EOQ model:

2

hTQK

2

hQ

Q

KD

h

KDQ 2*

A fixed cost (setup cost)

An inventory holding cost Q/2: average inventoryLevel.

Q=TD -> T=Q/D

Setup cost/unit Holding/unit

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2

hQ

Q

KD

Total Cost

Order Cost

Holding Cost

h

KDQ 2*

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Economic Lot Size model : Important Economic Lot Size model : Important ObservationsObservations

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

See page. 48.

Q = bQ*

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The Effect of Demand UncertaintyThe 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 seasonCompanies 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 ForecastsDemand Forecasts

The three principles of all forecasting techniques:

Forecasting is always wrongThe longer the forecast horizon the worst is the

forecast Aggregate forecasts are more accurate

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Swimsuit productionSwimsuit production

(Read the case on page 49)

Fashion items have short life cycles, high variety of competitors

Swimsuit New designs are completedOne production opportunityBased 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.

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Probabilistic forecastProbabilistic forecast

Demand Scenarios

0%

5%

10%

15%

20%

25%

30%

8000 10000 12000 14000 16000 18000

Sales

Pro

bab

ilit

y

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DataData

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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Example scenariosExample scenarios

Scenario One:Suppose you make 12,000 swimsuits and

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

$440,000

Scenario Two:Suppose you make 12,000 swimsuits and

demand ends up being 11,000 swimsuits.Profit = 125(11,000) - 80(12,000) - 100,000 + 20(1000)

= $ 335,000

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What to make?What to make?

Find order quantity that maximizes weighted average profit.

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

See Excel Spreadsheet for Chapter 3

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What to Make?What to Make?

Average demand is 13,100

Look at marginal cost vs. marginal profitif extra swimsuit sold, profit is 125-80 = 45if not sold, cost is 80-20 = 60

So we will make less than average demand

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Expected ProfitExpected Profit

Expected Profit

$0

$50,000

$100,000

$150,000

$200,000

$250,000

$300,000

$350,000

$400,000

8000 12000 16000 20000Order Quantity

Pro

fit

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Expected ProfitExpected Profit

Expected Profit

$0

$100,000

$200,000

$300,000

$400,000

8000 12000 16000 20000

Order Quantity

Pro

fit

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Important ObservationsImportant 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

Question: 9000 and 16000 units lead to about the same average profit, so which do we prefer?

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Probability of OutcomesProbability of Outcomes

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Cost

Pro

bab

ilit

y

Q=9000

Q=16000

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Key Points from this case studyKey Points from this case study

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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The effect of Initial InventoryThe effect of Initial Inventory

Suppose that one of the swimsuit designs is a model produced last year.Some inventory is left from last yearAssume the same demand pattern as beforeIf only old inventory is sold, no setup cost

From Figure 3-6, the profit can be obtained:225000+5000×80=625,000

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Initial Inventory and ProfitInitial Inventory and Profit

0

100000

200000

300000

400000

500000

Production Quantity

Prof

itFix production costs

225000

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QuestionsQuestions

If there are 7000 units remaining, what should the company do?

What should they do if there are 10,000 remaining?

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Initial Inventory and ProfitInitial Inventory and Profit

0

100000

200000

300000

400000

500000

Production Quantity

Pro

fit

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(s, S)(s, S) Policies 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

Swimsuit case: s = 8,500 and S = 12,000

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Supply contractsSupply contracts

In as supply contract, the buyer and supplier may agree on:Pricing and volume discountsMaximum and minimum purchase quantitiesDelivery lead timesProduct or material qualityProduct return policies

Refer to the Excel spreadsheet (supply contract).

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Swimsuit example againSwimsuit example again

(Read the case of example 3-2 on page 53)

Sequential supply chain: each party determines its own course of action

independent of the other parties.For the earlier example, the retailer assumes all of the

risk, of having more inventory than sales, while the manufacturer takes no risk.

Larger the order is, better it is for the manufacturer but it has a reverse impact to the retailer.

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Buy-back contractsBuy-back contracts

In a buy-back contract, the seller agrees to buy back unsold goods from the buyer for some agreed-upon price.

Study example 3-3 on page 54 and explain how does it work?

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Revenue-sharing contractsRevenue-sharing contracts

For the swimsuit example, if the manufacturer is willing to give discounts, the retailer will have an incentive to order more.

Study example 3-4 and explain how does it works.

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Quantity-flexibility contractsQuantity-flexibility contracts

The supplier provides full unsold items as long as the number of returns is no larger than a certain quantity.

How is it different from buy-back contracts?

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Sales rebate contractsSales rebate contracts

Sales rebate (discounts) contacts provide a direct incentive to 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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Global optimizationGlobal optimization

What is the best strategy for the entire supply chain?The difficulty with global optimization is that it requires the firm to surrender decision-making power to an unbiased decision maker.See example 3-5 on page 56Its main drawback is that it does not provide a mechanism to allocate supply chain profit between the partners.See example 3-6 on page 57

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Multiple reorder opportunitiesMultiple reorder opportunities

Consider a central distribution facility which orders from a manufacturer and delivers to retailers. The distributor periodically places orders to replenish its inventory

Continuous review policy and periodic review policy

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The Multi-Period Inventory ModelThe Multi-Period Inventory Model

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. This is expressed as the the likelihood that the distributor will not stock out during lead time.

Intuitively, what will a good policy look like?

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Continuous review policyContinuous review policy

Known parametersAVG = average daily demand faced by the distributorSTD = Standard deviation of daily demand faced by the

distributorL = Replenishment lead time from the supplier to the

distributor in daysh = Cost of holding one unit of the product for one day

at the distributor = service level

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Continuous review policyContinuous review policy

Inventory position: The actual inventory at the warehouse plus items

ordered by the distributor that have not yet arrived minus items that are backordered.

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The (s,S) PolicyThe (s,S) Policy

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

The reorder point is a function of:The Lead TimeAverage demandDemand variabilityService level

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A View of (s, S) PolicyA View of (s, S) Policy

Time

Inve

ntor

y L

evel

S

s

0

LeadTime

Inventory Position

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AnalysisAnalysis

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

L AVG

To account for deviations from average (we call this safety stock)

z STD L

where z is chosen from statistical tables to ensure that the probability of stockouts during leadtime is (1-).

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AnalysisAnalysis

Reorder level (s)L AVG + z STD L

It needs to satisfy

Probability {Demand during lead time L AVG + z STD L} = (1-)

Refer to Table 3-2 on page 59 for z values.

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AnalysisAnalysis

Use EOQ model

Q =

S = Q + s

Average inventory level = (S + s)

=

h

AVGK 2

LSTDzQ

2

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Reminder:Reminder: The Normal DistributionThe Normal Distribution

0 10 20 30 40 50 60

Average = 30

Standard Deviation = 5

Standard Deviation = 10

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The distributor holds inventory to:The distributor holds inventory to:

Satisfy demand during lead time

Protect against demand uncertainty

Balance fixed costs and holding costs

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Distributor of the TV setsDistributor of the TV sets

The distributor has historically observed weekly demand of:

AVG = 44.6 STD = 32.1Replenishment 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

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In addition to previous costs, a fixed cost K is paid every time an order is placed.

We have seen that this motivates an (s,S) policy, where reorder point and order quantity are different.

The reorder point will be the same as the previous model, in order to meet the service requirement: s = LTAVG + z AVG L

What about the order up to level?

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We have used the EOQ model to balance fixed, variable costs: Q=(2 K AVG)/h

If there was no variability in demand, we would order Q when inventory level was at L AVG. Why?

There is variability, so we need safety stock:

z STD L

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Consider the previous example, but with the following additional info:fixed cost of $4500 when an order is placed$250 product costholding cost 18% of product

Weekly holding cost:h = (.18 250) / 52 = 0.87

Order quantityQ=(2 4500 44.6 / 0.87 = 679

Order-up-to level:s + Q = 175 + 679 = 855

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Periodic review policyPeriodic review policy

Base-stock levelEach review period, the inventory position is

reviewed and the warehouse orders enough to raise the inventory position to the base-stock level.

Assume that orders are placed every r period of time.

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Average demand during an interval of r + L(r + L) AVG

Safety stockz STD (r + L)

Expected level of inventory after receiving an order

r AVG + z STD (r + L)

Example 3-8 on page 63

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Market Two

Risk PoolingRisk Pooling

Consider these two systems:

Supplier

Warehouse One

Warehouse Two

Market One

Supplier Warehouse

Market One

Market Two

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Risk Pooling Risk 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 ExampleRisk Pooling Example

Compare the two systems: (Read the case on page. 64-66)two productsmaintain 97% service level$60 order cost$.27 weekly holding cost$1.05 transportation cost per unit in decentralized

system, $1.10 in centralized system1 week lead time

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Week 1 2 3 4 5 6 7 8Prod A/W1 33 45 37 38 55 30 18 58Prod A/W2 46 35 41 40 26 48 18 55Prod B/W1 0 2 3 0 0 1 3 0Prod B/W2 2 4 0 0 3 1 0 0

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Warehouse Product AVG STD CVMarket 1 A 39.3 13.2 0.34Market 2 A 38.6 12 0.31Market 1 B 1.125 1.36 1.21Market 2 B 1.25 1.58 1.26

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Warehouse Product AVG STD CV s S Avg.Inven.

%Dec.

W 1 A 39.3 13.2 0.34 65 158 91W2 A 38.6 12 0.31 62 154 88W 1 B 1.125 1.36 1.21 4 26 15W2 B 1.25 1.58 1.26 5 27 15

Central A 77.9 20.7 0.27 118 226 132 26%Central B 2.375 1.9 0.81 6 37 20 33%

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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.

This works best for High coefficient of variation, which reduces required

safety stock.Negatively correlated demand. Why?

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 TimeDaily order up to quantity is:

LTAVG + z AVG L

10 1211 13 14 15

Demands

Orders

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To Centralize or not to CentralizeTo Centralize or not to Centralize

Safety stockSafety stock decreases as a firm moves from a

decentralized to a centralized system.Depend on CV and correlation

Service levelGiven the same total safety stock, the service level

provided by the centralized system is higher.

OverheadTypically, these costs are much greater in a

decentralized system.

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To Centralize or not to CentralizeTo Centralize or not to Centralize

Lead timeThe response time for a decentralized system is

much shorter.

Transportation CostsOutbound costs are higher for the centralized

system.Inbound costs are higher for the decentralized

system.

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Centralized Decision

Supplier

Warehouse

Retailers

Centralized SystemsCentralized Systems

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Centralized Distribution SystemsCentralized Distribution Systems

Question: How much inventory should management keep at each location?

A good strategy:The retailer raises inventory to level s each period

The supplier raises the sum of inventory in the retailer and supplier warehouses and in transit to S

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.

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Practical issuesPractical issues

Periodic inventory review policy

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 – inventory turnover rate

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Practical issues

Practical issuesPractical issues

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ForecastingForecasting

Three rules of forecastingThe forecast is always wrong.The longer the forecast horizon, the worse the

forecast.Aggregate forecasts are more accurate.

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ForecastingForecasting

Categories (See section 3.7)Judgment methodsMarket research methodsTime-series methodsCausal methods

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SummarySummary

Matching supply and demand in the supply chain is a critical challenge.Unfortunately, the existence the three

forecasting rules.

Globally optimal inventory policies, in which the best possible policy for the entire supply chain is implemented, are the best course of action.Well-designed supply contracts frequently make this global optimization possible.

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