class 4 module 4

7/28/2019 Class 4 Module 4

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Inventory Management

Inventory Costs

Inventory VisibilityAssessing Effectiveness of Inventory ManagementApproaches to Managing InventoryInventory Models


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Inventory Management (Henry C. Co) 2

Short-range decisions about supplies,inventories, production levels, staffingpatterns, schedules, and distribution -operations infrastructure

4 Rs Right MaterialRight AmountRight PlaceRight Time.


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Motivations

Economies of ScaleUncertainties


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Economies of ScaleOver-investment

Ties up capacity and financial resourcesInventory carrying cost, obsolescence,etc.

Insufficient/late availability causesIdle personnel or equipment whencomponents ran outLost sales/customer-goodwill if items are

out-of-stock.


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UncertaintiesSafety stock (demand or supplyuncertainty)In-transit inventories (lead times)Hedge inventories


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Drivers


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Approximately 16 % of total assets areinvested in inventories (1986)

In manufacturing firms, 25 to 35% of total assetsof typical are tied in inventories

Materials average share in a manufacturers

cost of goods sold40% in 194550% in 1960> 60% Today

Spare parts (service parts) inventories of atypical manufacturer

~ $ 5 million - $ 15 million


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Consequently distribution andinventory (logistics) costs are quitesubstantialValue of inventories in U.S. ~ $ 1

trillion (1993)


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Basic definitionsAn inventory is an accumulation of acommodity that will be used to satisfysome future demand.Inventories of the following form:

Raw materialComponentsSemi-finished goodsSpare partsPurchased products in retailing.


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Functional classificationCycle Inventories: Produce or buy inlarger quantities than needed.

Economies of scaleQuantity discounts

Restrictions (technological,transportation,) inventory

time

cycle stock

a cycle


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Anticipation stock: Low demand in onepart of the year build up stockfor the high demand season

Low demand season

AverageAnticipation stock


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Hedge inventories : expect changes inthe conditions (price, strike, supply,etc.)

Pipeline (or work-in-process)inventories: goods in transit, betweenlevels of a supply chain, between workstations.


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Service OperationsNo tangible items to purchase orinventory, materials management is of minor concernOperations that provide repair or

refurbishment services carry inventoryof replacement parts and suppliesExamples:

Automobile service centers carryautomotive partsHospitals carry inventory of food, linens,medicine, and medical supplies


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Functions of InventoryTo meet anticipated demandTo smooth production requirementsTo decouple components of theproduction-distribution

To protect against stock-outsTo take advantage of order cyclesTo help hedge against price increases

or to take advantage of quantitydiscounts


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Pressures to Cut InventoryInterest/opportunity costStorage and handlingProperty taxes

Insurance premiumsShrinkageINVENTORIES HIDE PROBLEMS!


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Quantityon hand

Q

Receiveorder

Placeorder

Receiveorder

Placeorder

Receiveorder

Lead time

Reorder point

Usagerate

Profile of Inventory Level Over Time


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Profile of Frequent Orders


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The Classic EOQ Model


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The Economic Order Quantity (EOQ)The total cost curve reaches its minimum

where the carrying and ordering costs areequal.EOQ represents trade-off between fixed costassociated with production or procurementagainst inventory holding costs.D = Rate of demand, units/yearS = Fixed cost of procurement, $/orderv = Variable cost of procurement.

h = Cost/unit time of holding each unit of inventory, $/unit/yearQ = Quantity ordered, units


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The Classical EOQ ModelThe total cost curve reaches itsminimum where the carrying andordering costs are equal.

Q O

A n n u a

l C o s

t

TC Q H DQ

S 2

Ordering Costs

Order Quantity (Q)(optimal order quantity)


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Using calculus, we take the derivativeof the total cost function (TC) and setthe derivative (slope) equal to zeroand solve for Q.

CostHoldingAnnualCost)Setupor der Demand)(Or 2(Annual

=H

2DS =Q OPT


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A grocery store pays $100 for each delivery of milk fromthe dairy. They sell 200 gallons per week. Each galloncosts the store $2, and they sell it for $3. They earn a 15%return on cash that is invested in milk. They have a largerefrigerator that holds up to 2,000 gallons. It costs them$10,000 per year to maintain.

D ~ 200(52) = 10,400 gallons per year.h ~ 15%($2) = $.30 per gallon per year

S ~ $100

Q* = 2,633 Roughly one replenishment every 9 weeks?!?!

Example


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Suppose that the refrigerator held only 100 gallons. Howmuch would it be worth to expand capacity to 200 gallons?

415,10$2

1003$.

100

400,10100$)100(TC

230,5$2

2003$.

200400,10

100$)200(TC

$5,185 per year in operational savings from doublingfreezer size.


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A bank has determined that it costs $30 to replenish thecash in one of its suburban ATMs. Customers take cashout of the ATM at a rate of $2000 per day (365 days per year). The bank earns a 10% return on cash that is not

sitting in an ATM. Let us define $1000 to be a basic unitof cash.

D ~ $2K(365) = $730K per year.h ~ 10%($1K) = $100 per $K per year S ~ $30

Q* = $20.9K Roughly one replenishment every 10 days.

Example


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Potential Analytical ErrorsUsing different time units for holdingcost versus the rate of demand.Determining the true opportunity costassociated with holding inventory.

(Physical costs as well as financial.)Dealing with operational constraints.


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When to Reorder?Reorder Point R When the quantityon hand of an item drops to thisamount, the item is reorderedSafety Stock SS Stock that is held in

excess of expected demand due tovariable demand rate and/or leadtime.Service Level - Probability thatdemand will not exceed supply duringlead time.


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LT

Expected demand

during lead time

Maximum probabledemand during leadtime

Reorder point R

Q u a n

t i t y

Safety stock


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Reorder Point

R

Risk of a stock-out

Service level =

probability of no stock-out

Expecteddemand

Safety-stock

0 z

Quantity

z-scale

U


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Determining Reorder Point RThe Average lead time demand is equal tothe average rate of demand (D) multipliedby the length of the lead time (L).

The amount of safety stock is influenced bythe variability of demand, and our

preference for avoiding inventory versussatisfying all of the demand.If distribution of demand is stable over time,and the demand in one interval of time isstatistically independent from that in another

interval, then the standard deviation of leadtime demand is proportional to the squareroot of the length (L) of the lead time:

DLU

L L


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Standard Deviation of Lead-time Demand

If daily demand has mean 100, and standard

deviation 40, and the lead time L= 9 days:Then Lead Time Demand has mean = 900,and the standard deviation of lead timedemand =120 (=SQRT[9] * 40).

If annual demand has mean 1040, andstandard deviation 600, and the lead time L= 2 weeks: Then Lead Time Demand hasmean = 40 (= 1040*(2/52) and the

standard deviation of lead time demand =117.67 (=SQRT[2/52]*600.


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Safety StockSafety stock determines the expected

amount of unsatisfied demandWhenever the amount of demandduring the lead time exceeds R, theexcess represents the amount of unsatisfied demand. The expectedamount of unsatisfied demand is:

where g(x) represents the distribution of Lead Time Demand.

R

dxxgR x


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A Retail Stocking ProblemDaily demand (7 days/wk) is normally

distributed with mean = 60, standarddeviation = 30.Orders can be placed at any time, and willbe filled in exactly 6 days.

It costs $10 to place and order, and eachunit costs $5.Annual holding costs are 10% of the value of the item.We want to determine an efficient inventorypolicy that allows us to satisfy 99% of demand from inventory.


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936

50$.10$3656022

h DS

Q

48.73630L L

First, we need to determine how much to

order at a time:

Thus, our average cycle stock is 936/2

=468.In order to determine the re-order point, weneed to know the length of the lead time (6days), and the standard deviation of leadtime demand.


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127.048.7301.9361

L

P Q z E

Now, to satisfy 99% of demand from inventory, we need:

From the table in the lecture note, we can see thatE(z) = .127 implies that z = .77 (or so).

We can now calculate the re-order point, which consistsof expected lead time demand plus safety stock .

417)48.73(77.660L z dL R


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Batch Production


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Suppose a machine produces a

product at a production rate = p; e.g.,p = 200 units/day.Suppose the demand rate of thisproduct is d; e.g., d = 80 units/day.Since p > d, inventory will increase at(p-d) or (200-80 = 120) units/day.Suppose the current inventory is 0.

In 10 days, the inventory level would be10 days * 120 unit/day = 1,200 units.In 20 days, the inventory level would be20 days * 60 unit/day = 2,400 units.etc.


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Suppose the machine produces a batch of this

product, then stop, then resumes production at somelater time when the inventory of this item is low. Thisis call batch production.Batch production is very common in industry.

When a machine is used to produce two or more

products, one product at a time.One decision the production manager has to make iswhen to start producing each product, and when tostop.

The run time is the amount of time the machine is

producing a batch.For example, producing at 200 units/day, if we want toproduce 2,000 units per batch, the run time is2,000/200 = 10 days. Here, batch size Q = 2,000 units,the run time t = 10 days.


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Maximum Inventory LevelIf the current inventory level is 0, what is theinventory at the end of the run time?

Since inventory will be rising at (200- 80 =120)units/day, in 10 days, the inventory level will be 10days * 120 unit/day = 1,200 units.The inventory at the end of the run time is themaximum inventory. It is equal to (p-d)*t = (200

units/day - 80 units/day)*10 days = 1,200 units.Why is it that the machine produced 2,000 units in10 days, and the maximum inventory level is only1,200?

Answer: We consumed d*t = 80 units/day * 10 days =800 units.

After completing a batch, how long will it take todeplete the inventory?

Answer: It will take (p-d)*t/d = 1,200/80 = 15 days todeplete the inventory. This is the off-time.


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Number of Runs Per YearIf the annual demand of this productis D = 24,000 units, how many runs of this item do we produce each year?

Answer: Since we are producing Q =2,000 units per batch, there will be D/Q =24,000/2,000 = 12 batches per year.In other words, there are D/Q = 12 cyclesper year. In each cycle, there is a periodof time the machine is producing theproduct (the run time), and a period toallow the inventory to deplete (the off time).


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Average InventoryWhat is the average inventory level?

During the run time, the inventory level rises from0 to the maximum level of (p-d)*t = 1,200 units(see page 4).During the off time, the inventory level drops froma maximum of (p-d)*t units to 0.The average inventory level therefore = [0 + (p-d)*t ]/2 = (0 + 1,200)/2 = 600 units.

Since p*t = Q, then t = Q/p. We can rewritethe expression for the average inventory as

(p-d)*t/2 = (p-d)*(Q/p)/2 = (1-d/p)Q/2.


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Tradeoff Batch size = production rate * run time. Large batchsize means long run time, and high averageinventory.On the contrary, if the batch size is small, the runtime is short, and we need to run many batches peryear.What is the average inventory if the batch size equalsthe annual demand D = 24,000 units? How manybatches do we have to run per year?

Answer: The average inventory = (1-d/p)Q/2 = (1-80/200) (24,000)/2 = 7,200 units. We need to run onebatch per year.

What is the average inventory if the batch size equalsthe weekly demand of 480 units (assuming 50weeks/year)? How many batches do we have to runper year?

Answer: 144 units; Run 50 batches per year.


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pd H

S DQ

1

2*

Optimal Tradeoff Suppose the cost to carry one unit of inventory forone year is H. Since the average inventory level is(1-d/p)Q/2, the annual inventory-carrying cost isH*(1-d/p) Q/2.Suppose the cost to set-up the machine to produce abatch is S. Since we need to run D/Q batches per

year (see page 5), the annual set-up cost is S*D/Q.Adding the two costs, we have H*(1-d/p) Q/2 +S*D/Q. Using calculus, the optimal batch size is


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IllustrationAnnual demand D = 24,000 units.Production rate p = 200 units/day.Demand rate d = 80 units/day (25days/month).

Set-up cost S = $100.Inventory-carrying cost H =$2/unit/year.

The optimal batch size =2,000 units.


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The machine will produce D/Q = 12 batches

a year.Run time t = Q/p = 2,000/200 = 10 days.Maximum inventory = (p-d)*t = (100-40)*20 = 1,200 units.

Off time = 1,200 units/ 80 units/day = 15days.In other words, the machine will run thisproduct for 10 days, stop (to do somethingelse) for 15 days, before running this itemagain.


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The New Boy Problem

Johnson & Pike, 1999
http://localhost/var/www/apps/conversion/tmp/EBZDownloads/SCM(Johnson&Pyke)Newsboy.pdfhttp://localhost/var/www/apps/conversion/tmp/EBZDownloads/SCM(Johnson&Pyke)Newsboy.pdf


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A-B-C Classification

% of total number of SKUs

% of totalannual

$ usage

20 40 60

80100

80

A specific unit of stock to be controlledis called a Stock Keeping Unit (SKU)


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20 % of SKUs account for 80 % of total annual usage

Large number of cheap itemsA few very expensive items

1. A (most important) [ First 5-10 % of items]

2. B (intermediate important) [ 50 % of items]

3. C (least important) [40-45 % of items only ~ 20 % of value]


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Inventory Management:Then and Now


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Innovations in informationtechnology and computer networking

tracking customer demandproduction ~ demand

1. Electronic Data Interchange2. Efficient Consumer Response (ECR)3. Vendor Managed Inventory (VMI)

How to utilize available information ?


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Electronic Data InterchangeComputer to computer transmission of data (orders, invoices, payments, etc.)Fast and reliable tracking of inventorylevels, outstanding customer orders,

backorders.Shorter lead times for orderprocessing, more reliable due-datequotation.


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Efficient Consumer Response (ECR)Distributors and suppliers work

together so that information andgoods can be exchanged quickly,efficiently and reliably

Efficient store assortmentEfficient replenishmentEfficient promotionEfficient product introduction

Wegmans, Spartan Stores, HP, IBM,Compaq


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Vendor Managed Inventory (VMI)

Supplier manages the inventory on itscustomers shelf (when and how much

to order)


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Framework for Inventory Management

Large number of itemsLarge manufacturer ~ 500,000 itemsRetailer ~ 100,000

Items show different characteristics

Demand can occur in many ways:Unit by unit, in cases, by the dozen, etc.


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Decision making in production and

inventory management involvesdealing with large number of items,with very diverse characteristics andwith external factors.We want to resolve:

How often the inventory status (of anitem) should be determined ?

When a replenishment order should beplaced ?How large the replenishment order shouldbe ?


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Vendor-Managed Inventory


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Forecasting & ReplenishmentApproaches

1. Traditional Aggregate Forecasting andReplenishment (AFR),

2. Vendor-Managed Inventory (VMI),3. Jointly Managed Inventory (JMI).


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The Aggregate Forecasting andReplenishment (AFR) Approach


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Current Planning and Forecasting PracticesMost companies generate multiple, independentdemand forecasts for different purposes.Most forecasting is done at a high level of detail thatfocuses on a product category or family, a market orregion, and a period of weeks or months.Forecast accuracy is not measured frequently.Operational forecasts usually focus on interactionbetween two nodes on the value chain. Theseforecasts are not time-phased across the value chain.Manufacturing usually pushes inventory to itsdistribution centers based on manufacturingeconomics and not on forecasted consumer demand

pull.

f


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The Manufacturing Approach1. Assemble data : The core data used for forecasting

involve historical shipments, syndicated data, andsales forecasts. Typically, the data is aggregated tothe product family or brand level, by week ormonth, and by market region. Data inaccuracy iscompensated for or buried through the aggregationprocess.

2. Forecast Sales : The available data inputs andplans from marketing that focus on influencingdemand are used to generate an aggregatedconsumer demand forecast. Best practice is to usethis forecast to drive integrated planning across thecorporation. Frequently, this does not happen. Thedesire for meeting short term financial targets oftenpreempts the best forecasting algorithms when itcomes to driving operational planning.


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3. Forecast Orders : The aggregated consumerforecast drives a coordinated effort to create a

supply plan that supports the designated level of sales. In todays environment, the demand andsupply is matched by planning the customer orderflow and finished goods inventory flow intodistribution centers. Conventional distributionrequirements planning (DRP) systems are

sometimes used to facilitate a customer-pull-basedprocess through to manufacturing. However, manycompanies are still driven by push-based processes,where manufacturing sends distribution centerswhat it believes is appropriate to make and stock.This lack of integrated supply planning driveshigher inventory levels, lower order fill rates, andincreased expedited activity in manufacturing,which in turn create the out-of-stock and customersatisfaction problems described in the "BusinessOpportunity" chapter.


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4. Order Generation : As the execution phase begins,a purchase order is placed by a retailer. Oneprimary driver of the ordering process isreplenishment activity. The key input to this iswarehouse withdrawals by stores. Other inputsinvolve the basic ordering parameters that factorinventory targets and transportation costs into

ordering quantities. The third primary driver ispromotional activity. Frequently, retailers maintaina separate ordering process and separate buyersfor promotions. Replenishment buyers andpromotional buyers do not commonly share plansor coordinate their purchases, which represents anopportunity for CPFR to improve the practice andadd value.


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5. Order Fulfillment : Once retail orders are received,manufacturers look to the available inventory anddetermine whether the order will be filledcompletely. If an allocation needs to take place, themanufacturer notifies the retailer. This contactmarks the first collaboration within the process.Frequently, the first notification of a shortage

occurs when the retail receiver opens the back of the truck. In either case, given the short ordercycles, the retailer and the manufacturer have littlerecourse for remedying the shortage. If the retailerhas been carrying enough inventory, the consumermay not be disappointed. If not, sales are lost.Either outcome is costly.

Th R il A h


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The Retailer Approach1. Assemble Data : Historical sales, syndicated data,

and inputs from suppliers on promotional plans andchanging product offerings are the key datasources. Other inputs involving store openings orclosing and retail promotional activity level are theprimary forecast drivers.

2. Forecast Sales : The assembled data leads to a

category or merchandising sales plan. The level of detail varies but is generally high, categorized bymajor market areas. Independent sales forecastsmay be generated by procurement, logistics, andstore operations to support operating plans. As withthe manufacturing approach, the financial plan mayprevail over the consumer sales forecast when itcomes to operational planning.


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3. Forecast Orders : The forecasting of material flowis concentrated around distribution center (DC)inventory and processing. Many retailers do notforecast for regular replenishment business.However, they attempt to predict orders forseasonal and promotional activity because of theoperational impact on their business. Mostbusinesses expect 100% responsiveness frommanufacturers in meeting orders within short time

frames.


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4. Order generation : Orders often are placedindependently by replenishment, promotional, andseasonal buyers. Each has targeted inventory andsales plans to support. While lead times may varyfor the different processes, the level of coordinationwith manufacturers on supply capability isexception driven (in other words, coordination only

takes place when a problem or special need comesup).5. Order Receiving : Demand and supply come

together for the retailer on the receiving dock. Atthis point, there is little time to react to shortages.


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The Vendor-ManagedInventory (VMI) Approach


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A key technology component that has made VMIpossible is the ability of supply-chain applications tomanage inventories at retailer locations.

Demand and supply now come together at the retailreceiving location.This is frequently the distribution center, yet store-levelVMI is also common.

VMI practices and technology provide a broader viewof the inventory-holding locations and pipelineactivity, which gives the manufacturer betterinformation for planning inventory deployment acrossthe pipeline.It also allows the manufacturer to be more customer specific in its planning and to plan at a much lowerlevel of detail.

The key process activities in VMI residei il i h h d f


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primarily with the vendor or manufacturer1. Assemble Data : The primary data driver for VMI

programs focused on distribution centers is

warehouse withdrawal data from retailerdistribution centers. Some companies complementthis with point-of-sale (POS) data so that store-level activity and inventory have greater visibility.Store-level VMI uses POS data as its primary driver.Complementary data on retail and manufacturer

promotional plans and other drivers of volumevariability also need to be available.2. Forecast Sales : The primary forecasting effort for

most VMI programs is warehouse withdrawals fromthe retail distribution center. Store-level VMI isconsumer focused. Retail customer-specific salesneed to be reconciled with the overall market salesin the complementary aggregate forecastingprocess.


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3. Forecast Orders : Order forecasting is controlledby the manufacturer and generally works toagreed-on retail inventory targets andtransportation cost objectives. This allows themanufacturer to plan inventory for specificcustomers.

4. Order Generation : The manufacturer controls the

generation of purchase orders. These are driven bythe store replenishment pull on the distributioncenter or actual consumer demand for store-levelVMI. Since the manufacturer controls the process,the customer usually receives priority service whenshortages occur.

5. Order Fulfillment : The manufacturer fills productprimarily out of inventory. Promotions may positionmanufacturers to produce to promotional orders.

Limitations of VMI


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Limitations of VMIThe overall level of collaboration is limited.The level of detail for planning is stillgenerally high.The focus on warehouse withdrawals fordistribution-center VMI is not as effective asa store-level consumer focus.

Most companies fail to leverage customer-specific data effectively for planningmanufacturing production. Instead, theycontinue to make to stock.In some cases, reserving finished goods

inventory in the manufacturers distributioncenters actually causes shortages to othercustomers.


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Lack of integration of systems, particularly for storelevel VMI, creates operational challenges due tolimited visibility into inventory and orders.Another disadvantage is that retailers have higherexpectations of VMI because the pipeline is morevisible and the manufacturer has more control.Industry results show, however, that many retailers

have been disappointed and canceled these programs.The blame for inadequate performance is frequentlyequally shared between trading partners. To be mosteffective, VMI programs depend on strongpartnerships with active communication, informationsharing, joint problem solving, and commitments tocontinued development.


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The Jointly ManagedInventory (JMI) Approach


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This method focuses on collaboratively planning andexecuting the business at a much lower level of

detail.This allows an increased focus on the consumer and onexploiting opportunities frequently hidden in theaggregated data.

JMI uses teams of people working only with keyaccounts.

Frequently, team members are located geographicallyclose to each other, which allows frequent face-to-facemeetings.This fosters open communication between functionalcounterparts, which in turn furthers processcustomization.

The improved understanding of each othersoperations and increased interaction that resultshelps develop trust between the trading partners.


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The five functional steps described earlierare also part of the JMI process.

Normally, these are guided by the previouslycompleted joint business planning.JMI, however, involves a much more intense joint-planning effort and coordination of executionbefore the process steps begin.

The level of customization of the processsteps is driven by the capabilities of eachtrading partner, with a focus that is muchmore consumer centric .

The JMI approach also increases theintegration of planning and execution withineach company.

Limited Trading Partner Relationships


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Limited Trading-Partner RelationshipsMuch of the lower level detail work is

done manually or on an ad-hoc basis.Team members need to filter throughgreat quantities of data to identifyopportunities.

Cost of locating JMI team membersteams close together is high.Tools and processes currentlyavailable for inter-enterprise

computing in a real-time environmentare limited and those available are notscaleable.

Aggregate Forecasting Vendor Managed Inventory Jointly managed Inventory


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gg g g g y y g y

Joint Business Planning Limited joint-business plandevelopment

Limited joint-business plandevelopment

Heavy emphasis on joint-business planning and coordinatedexecution planning

Assemble Data Syndicated data and historicalsales POS, warehouse withdrawal data,syndicated data POS data by product, store, andweek; syndicated data

Sales Forecasting Sales forecast done at a high levelof detail: category, week or month, market or region

Sales forecast generated by: product, customer DC, byweek. Store-level VMI is by

product, store, week

Sales forecast generated at thestore level by product byweek. Identifies micro-marketing and micro-merchandisingopportunities

Order Forecasting Primarily focused onmanufacturing support to itsown distribution centers.Frequently not done byretailers

Focused on retailer DC driven byinventory and transportationcost targets; store-levelVMI focused on storeinventory; still focused onsupply coming fromsupplier DC

Time-phased replenishment of stores, retail DCs, andsupplier DCs

Order Generation Generated by retailer expecting

100% fulfillment fromsupplier

Generated by supplier based on

the pull from storereplenishment or consumer demand for store-level VMI

Could be generated by either

party based on store-levelsales that are time-phased tosupply capabilities

Order Fulfillment Supplier provides what isavailable at its DC

Supplier fills orders from its DCs,giving priority to VMIcustomers

Supplier fills orders from its DCsor manufacturing,depending on the extent of integrated planning

class 4 module 4

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