lecture 02 - inventory management

8/11/2019 Lecture 02 - Inventory Management

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Quality in Supply Chain Design

Lecture 2: Inventory Management


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Source

Supplier

Supplier

Distributo r

Distributor

Retailer

End-User

Converte r

Converter Consumers

Information Flow

Funds/Demand Flow

Value-Added Services

Material Flow

Reuse/Maintenance/After Sales Service Flow

What Is a Supply Chain?

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Supply Chain ManagementSimchi- Levis Definition:

Supply chain management is a set ofapproaches utilized to efficientlyintegrate suppliers, manufacturers, warehouses,and stores, so thatmerchandise is produced and distributed at theright quantities , to the right locations , and at the

right time , in order tominimize system wide costs while satisfyingservice level requirements.

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SCM Challenges:

Optimization, integration and synchronization withdevelopment chaincomplex, large scale network

facilities with difference, conflicting objectivesdynamic systems

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Why Is Inventory Required?

Uncertainty in customer demandShorter product lifecyclesMore competing products

Uncertainty in suppliesQuality/Quantity/Costs

Delivery lead timesIncentives for larger shipments

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Inventory Costs

CostsOrder cost:Product costTransportation cost

Inventory holding cost, or inventory carrying cost:

Property taxes, and insurance on inventories Maintenance costs Obsolescence cost Opportunity costs

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How Much Does It Cost?Distribution and inventory costs are quite substantialTotal U.S. Manufacturing Inventories ($m):

1992-01-31: $m 808,7731996-08-31: $m 1,000,774

2006-05-31: $m 1,324,108Inventory-Sales Ratio (U.S. Manufacturers):

1992-01-01: 1.562006-05-01: 1.25

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GMs production and distribution network 20,000 supplier plants133 parts plants31 assembly plants11,000 dealers

Freight transportation costs: $4.1 billion (60% formaterial shipments)GM inventory valued at $7.4 billion (70%WIP; RestFinished Vehicles)Decision tool to reduce:

combined corporate cost of inventory and transportation.26% annual cost reduction by adjusting:

Shipment sizes (inventory policy)Routes (transportation strategy)

How Much Does It Cost?

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Holding the right amount at the righttime is difficult!--- Challenging

Dell Computer was sharply off in its forecast ofdemand, resulting in inventory write-downs1993 stock plunge

IBMs ineffective inventory management1994 shortages in the ThinkPad line

Ciscos declining sales 2001 $ 2.25B excess inventory charge

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Inventory Management

Inventory Management Decisions:What to order?When to order?How much is the optimal order quantity?

Approach includes a set of techniquesINVENTORY POLICY !!

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12

OutlineIntroduction

The Needs, the Costs, and the Challenges

Single Stage Inventory ControlEconomic Lot Size ModelDemand Uncertainty

Single PeriodSingle Period ModelInitial Inventory

Multiple Order OpportunitiesContinuous Review Policy

Periodic Review PolicyService Level Optimization


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Model Description (Assumptions)

D items per day: Constant demand rateQ items per order: Order quantities are fixedK , fixed setup cost, incurred every time the warehouseplaces an order.h , inventory carrying cost accrued per unit held ininventory per day that the unit is held.Lead time = 0(the time that elapses between the placement of anorder and its receipt)Initial inventory = 0Planning horizon is long (infinite).

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Economic Lot Size Model

Inventory level as a function of time

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Deriving EOQ(Economic Order Quantity)

Total cost at every cycle:

Average inventory holding in a cycle: Q/ 2Cycle time T = Q/D

Average total cost per time unit:

2

hTQ K

2

hQQ

KD

h KD

Q 2*

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Economic lot size model : Costs

Economic lot size model: total cost per unit time

h KD

Q 2*

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Sensitivity Analysis

b .5 .8 .9 1 1.1 1.2 1.5 2

Increase

in cost 25% 2.5% 0.5% 0 .4% 1.6% 8.9% 25%

Total inventory cost relatively insensitive to order quantities

Actual order quantity: QQ is a multiple b of the optimal order quantity Q*.For a given b , the quantity ordered is Q = bQ *

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What Did We Optimized?

Trade-off between:Ordering costsStorage costs

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OutlineIntroduction

The Needs, the Costs, and the Challenges






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Demand Uncertainty

The forecast is always wrongIt is difficult to match supply and demandThe longer the forecast horizon, the worse theforecast

It is even more difficult if one needs to predictcustomer demand for a long period of time Aggregate forecasts are more accurate.

More difficult to predict customer demand forindividual SKUsMuch easier to predict demand across all SKUswithin one product family

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Single Period: The Model

Short lifecycle productsOne ordering opportunity onlyOrder quantity to be decided before demand

occursOrder Quantity > Demand => Dispose excessinventoryOrder Quantity < Demand => Lose sales/profits

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Single Period: The Approach

Using historical dataidentify a variety of demand scenariosdetermine probability each of these scenarios willoccur

Given a specific inventory policydetermine the profit associated with a particularscenariogiven a specific order quantity

weight each scenarios profit by the likelihood that it willoccurdetermine the average, or expected, profit for a particularordering quantity.

Order the quantity that maximizes the averageprofit.

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Swimsuit: Single Period Model Example

Probabilistic forecast

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Additional Information

Fixed production cost: $100,000Variable production cost per unit: $80.During the summer season, selling price: $125per unit.Salvage value: Any swimsuit not sold during thesummer season is sold to a discount store for$20.

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Two ScenariosManufacturer produces 10,000 units whiledemand ends at 12,000 swimsuitsProfit= 125(10,000) - 80(10,000) - 100,000= $350,000Manufacturer produces 10,000 units whiledemand ends at 8,000 swimsuitsProfit= 125(8,000) + 20(2,000) - 80(10,000) -100,000= $140,000

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Probability of Profitability Scenarioswith Production = 10,000 Units

Probability of demand being 8000 units = 11%Probability of profit of $140,000 = 11%Probability of demand being 12000 units = 27%

Probability of profit of $350,000 = 27%

Total profit = Weighted average of profitscenarios

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Order Quantity that MaximizesExpected Profit

Average profit as a function of production quantity

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What Did We Optimized?

Expected (average) Profit

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Risk-Reward Tradeoffs

Optimal production quantity maximizes averageprofit is about 12,000Producing 9,000 units or producing 16,000 unitswill lead to about the same average profit of$294,000.If we had to choose between producing 9,000units and 16,000 units, which one should wechoose?

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Risk-Reward Tradeoffs

A frequency histogram of profit

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Risk-Reward TradeoffsProduction Quantity = 9000 units

Profit is:either $200,000 with probability of about 11 %or $305,000 with probability of about 89 %

Production quantity = 16,000 units.

Distribution of profit is not symmetrical.Losses of $220,000 about 11% of the timeProfits of at least $410,000 about 50% of the time

With the same average profit , increasing the productionquantity:

Increases the possible riskIncreases the possible reward

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Observations

The optimal order quantity is not necessarilyequal to forecas t, or average demand. As the order quantity increases, average profittypically increases until the production quantity

reaches a certain value, after which the averageprofit starts decreasing.Risk/Reward trade-off: As we increase theproduction quantity, both risk and reward

increases.

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Outline

IntroductionThe Needs, the Costs, and the Challenges





Wh If h M f H I i i l


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What If the Manufacturer Has an InitialInventory?

Trade-off between:Using on-hand inventory to meet demand and avoidpaying fixed production cost: need sufficientinventory stock

Paying the fixed cost of production and not have asmuch inventory

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Initial Inventory Solution

Profit and the impact of initial inventory

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Manufacturer Initial Inventory = 5,000

If nothing is produced, average profit =225,000 ( from the figure: 125k+100k ) + 5,000 x80 = 625,000If the manufacturer decides to produce

Production should increase inventory from 5,000 unitsto 12,000 units.

Average profit =

371,000 (from the figure) + 5,000 80 =771,000

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Manufacturer Initial Inventory =


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No need to produce anythingaverage profit > profit achieved if we produce toincrease inventory to 12,000 units

If we produce, the most we can make onaverage is a profit of $370,700.

Same average profit with initial inventory of 8,500units and not producing anything.If initial inventory < 8,500 units => produce to raisethe inventory level to 12,000 units.If initial inventory is at least 8,500 units, we shouldnot produce anything

Manufacturer Initial Inventory =10,000

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38

Outline

IntroductionThe Needs, the Costs, and the Challenges






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Multiple Order Opportunities

TWO POLICIESContinuous review policyinventory is reviewed continuouslyan order is placed when the inventory reaches a particular levelor reorder point.inventory can be continuously reviewed (computerized inventorysystems are used)

Periodic review policyinventory is reviewed at regular intervalsappropriate quantity is ordered after each review.it is impossible or inconvenient to frequently review inventoryand place orders if necessary.

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Continuous Review Policy: ModelDaily demand is random and follows a normaldistribution .Every time the distributor places an order from themanufacturer, the distributor pays a fixed cost, K , plusan amount proportional to the quantity ordered.

Inventory holding cost is charged per item per unit time.Inventory level is continuously reviewed, and if an orderis placed, the order arrives after the appropriate leadtime .If a customer order arrives when there is no inventoryon hand to fill the order (i.e., when the distributor isstocked out), the order is lost.The distributor specifies a required service level .

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AVG = Average daily demand faced by thedistributor STD = Standard deviation of daily demand facedby the distributor L = Replenishment lead time from the supplierto the distributor in days h = Cost of holding one unit of the product forone day at the distributor

= service level. This implies that theprobability of stocking out is 1 -

Continuous Review Policy

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(Q,R) policy whenever inventory level falls to areorder level R , place an order for Q unitsWhat is the value of R?


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Average demand during lead time: L x AVGSafety stock:

A combination of lead time and demanduncertainty

Reorder Level, R:

Order Quantity, Q:

LSTD z

LSTD z AVG L

h AVG K

Q 2

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Service Level & Safety Factor, z

ServiceLevel

90% 91% 92% 93% 94% 95% 96% 97% 98% 99% 99.9%

z 1.29 1.34 1.41 1.48 1.56 1.65 1.75 1.88 2.05 2.33 3.08

z is chosen from statistical tables to ensurethat the probability of stockouts during lead time is exactly 1 -

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Service Level & Safety Factor, z

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http://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svg


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Inventory Level Over Time

LSTD z Inventory level before receiving an order =

Inventory level after receiving an order =

Average Inventory =

LSTD z Q

LSTD z Q2

Inventory level as a function of time in a ( Q ,R ) policy

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Continuous Review Policy Example A distributor of TV sets that orders from amanufacturer and sells to retailersFixed ordering cost = $4,500Cost of a TV set to the distributor = $250

Annual inventory holding cost = 18% of productcostReplenishment lead time = 2 weeksExpected service level = 97%

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Month Sept Oct Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug

Sales 200 152 100 221 287 176 151 198 246 309 98 156

Continuous Review Policy Example

Average monthly demand = 191.17

Standard deviation of monthly demand = 66.53

Average weekly demand = Average Monthly Demand/4.3

Standard deviation of weekly demand

= Monthly standard deviation/ 4.3

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Parameter Av erage weeklydemand

Standarddevia t ion ofweekly demand

Averagedemanddur ing leadt ime

Safetys tock

Reorderpo in t

Value 44.58 32.08 89.16 86.20 176

87.052

25018.0Weekly holding cost

Optimal order quantity 67987.

58.44500,42Q

Average inventory level 679/2 + 86.20 = 426

Continuous Review Policy Example

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Outline

IntroductionThe Needs, the Costs, and the ChallengesSingle Stage Inventory Control

Economic Lot Size ModelDemand Uncertainty



Variable Lead TimesPeriodic Review Policy

Service Level Optimization


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Inventory level is reviewed periodically at regularintervals

An appropriate quantity is ordered after each reviewTwo Cases:

Short Intervals (e.g. Daily)(s, S) policy

Longer Intervals (e.g. Weekly or Monthly)May make sense to always order after an inventory level review.Determine a target inventory level, the base-stock levelDuring each review period, the inventory position is reviewedOrder enough to raise the inventory position to the base-stock level.Base-stock level policy

Periodic Review Policy

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(s,S) policyCalculate the Q and R values as if this were acontinuous review modelSet s equal to R Set S equal to R+Q .

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Base-Stock Level PolicyDetermine a target inventory level, the base-stock levelEach review period, review the inventoryposition and order enough to raise the inventoryposition to the base-stock level

Assume:r = length of the review periodL = lead time

AVG = average daily demandSTD = standard deviation of this daily demand.

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Average demand during an interval of r + Ldays=

Safety Stock= Lr STD z

AVG Lr )(

Base-Stock Level Policy

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Inventory level as a function of time in a periodicreview policy

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Ordering Receiving Next Receiving


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Summary: Economic Lot Size Model


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Summary: Lead Time


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Base-stock Level


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Summary: Safety Stock


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Q+R

Safety Stock

Average Inventory

R


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Ordering Receiving Next Receiving


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Assume:distributor places an order for TVs every 3 weeksLead time is 2 weeksBase-stock level needs to cover 5 weeks

Average demand = 44.58 x 5 = 222.9

Safety stock =Base-stock level = 223 + 136 = 359 Average inventory level =

Base-Stock Level Policy Example

58.329.1

17.203508.329.1258.443

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3 weeks cycle + 2 weeks lead time


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Outline




Multiple Order OpportunitiesContinuous Review PolicyPeriodic Review Policy



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Optimal inventory policy assumes a specificservice level target.What is the appropriate level of service?

May be determined by the downstream customerRetailer may require the supplier, to maintain a specificservice levelSupplier will use that target to manage its own inventory

Facility may have the flexibility to choose theappropriate level of service


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Service levelinventoryversusinventory level

as a functionof lead time

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Trade-OffsEverything else being equal:

the higher the service level, the higher the inventorylevel.for the same inventory level, the longer the lead timeto the facility, the lower the level of service providedby the facility.the lower the inventory level, the higher the impact ofa unit of inventory on service level and hence onexpected profit

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Retail StrategyGiven a target service level across all productsdetermine service level for each SKU so as tomaximize expected profit .Everything else being equal, service level will behigher for products with:

high profit marginhigh volumelow variabilityshort lead time

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Target inventory level = 95% across allproducts.Service level > 99% for many products withhigh profit margin, high volume and low

variability.Service level < 95% for products with low profitmargin, low volume and high variability.

Profit Optimization and Service Level

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Outline




Multiple Order OpportunitiesContinuous Review PolicyPeriodic Review Policy



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Materials of some slides are taken from David Simchi-Levi; Philip Kaminsky; Edith Simchi-Levi."Designing and Managing the Supply Chain". McGraw-Hill Higher Education, 2008. ISBN-13:9780073341521 (ISBN-10: 0073341525)Used by Permission.

lecture 02 - inventory management

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