inventory mamagement

7/30/2019 inventory mamagement

1/62

1-1

Click to editMaster subtitlestyle

McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter 2

InventoryManagementand Risk Pooling


2/62

1-2

CASE: Steel Worksl Background of case and intentl Overview of businessl What does data tell you about Specialty?l How much inventory might you expect?l What opportunities are there for Custom?l Wrap up

Stephen C. Graves Copyright 2003All Rights Reserved


3/62

1-3

Background & Intentl Abstraction from summer consulting jobl Intent is to examine a realistic, but

simplified inventory context and perform adiagnosis of problem poor service andtoo much inventory



4/62

1-4

Custom Productsl Rapid growth, 1/3 of total sales ($133 MM)l One customer per productl Very high marginsl High service levell 3 plants, co-located with R&D center l Each product produced at a single plant



5/62

1-5

Specialty Productsl Rapid growth, 2/3 of total sales ($267 MM)l 6 product familiesl 3 plants, each producing 2 product familiesl 130 customers, 120 productsl Few big customersl Highly volatile demandl High service level



6/62

1-6

Consultant Recommendationl Drop low volume productsl Improve forecastsl Consolidate warehouses



7/621-7

What Does Data Tell You? cv

DB R10 15.5 13.2 0.85DB R12 1008 256 0.25DB R15 2464 494 0.20DF R10 97 92.5 0.95

DF R12 18.5 11.4 0.62DF R15 55 80 1.46DF R23 35.5 45.9 1.29



8/621-8

What Does Data Tell You?l Durabend R12:

l One customer accounts for 97% of demandl 7 products:

l High volume (2) is not very volatilel Low volume (5) is very volatile



9/621-9

How Much Inventory Should You Expect?

l Assume base stock model with periodicreview

l Review period = r = ?l Lead time = L = ?

[ ]2

E I r z r L

= + +



10/621-10

Cyclestock

Saf.Stock

E[I] Act.Inv.

DB R10 15.5 13.2 8 26 34 72DB R12 1008 256 504 510 1014 740

DB R15 2464 494 1232 990 2222 1875

DF R10 97 92.5 49 185 234 604

DF R12 18.5 11.4 9 23 32 55

DF R15 55 80 28 160 188 388

DF R23 35.5 45.9 18 92 110 190

S 1848 1986 3834 3824

Assumes r = 1; L=0.25; and z = 1.8

Cycle stock = r /2 Safety stock = z r+L



11/621-11

What Are the Opportunities atCustom?

l Combine production and inventory for common items, e. g. DF R23

l Produce monthly: reduce setups by half and pool safety stocks

l Produce twice a month: same number of setups but cut cycle stock and review

period in half



12/621-12

Wrap Upl Realistic diagnostic exercisel In real life: not as clean, more data and

more considerationsl Yet simple models and principles can

provide valuable guidance



13/621-13

2.1 IntroductionWhy Is Inventory Important?

Distribution and inventory (logistics) costsare quite substantial Total U.S. Manufacturing Inventories ($m):l 1992-01-31: $m 808,773l 1996-08-31: $m 1,000,774l 2006-05-31: $m 1,324,108

Inventory-Sales Ratio (U.S. Manufacturers):l 1992-01-01: 1.56l 2006-05-01: 1.25


14/621-14

l GMs production and distribution networkl 20,000 supplier plantsl 133 parts plantsl 31 assembly plantsl 11,000 dealers

l Freight transportation costs: $4.1 billion (60% for material shipments)l GM inventory valued at $7.4 billion (70%WIP; Rest

Finished Vehicles)l Decision tool to reduce:

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

l Shipment sizes (inventory policy)l Routes (transportation strategy)

Why Is Inventory Important?


15/621-15

Why Is Inventory Required?

l Uncertainty in customer demandl Shorter product lifecyclesl More competing products

l Uncertainty in suppliesl Quality/Quantity/Costs/Delivery Times

l Delivery lead times

l Incentives for larger shipments


16/621-16

Holding the right amount at theright time is difficult!

l Dell Computers was sharply off in its forecast of demand, resulting in inventory write-downs

l 1993 stock plungel Liz Claibornes higher-than-anticipated excess

inventoriesl 1993 unexpected earnings decline,

l IBMs ineffective inventory managementl 1994 shortages in the ThinkPad line

l Ciscos declining salesl 2001 $ 2.25B excess inventory charge

d


17/621-17

Inventory Management-DemandForecasts

l Uncertain demand makes demandforecast critical for inventory relateddecisions:l What to order?l When to order?l How much is the optimal order quantity?

l Approach includes a set of techniquesl INVENTORY POLICY!!


18/621-18

Supply Chain Factors in InventoryPolicy

l Estimation of customer demandl Replenishment lead timel The number of different products being consideredl The length of the planning horizonl Costsl Order cost:

l Product costl Transportation cost

l Inventory holding cost, or inventory carrying cost:l State taxes, property taxes, and insurance on inventoriesl Maintenance costsl Obsolescence costl Opportunity costs

l Service level requirements


19/621-19

2.2 Single Stage InventoryControl

l Single supply chain stagel Variety of techniques

l Economic Lot Size Modell Single Period Modelsl Multiple Order Opportunitiesl Continuous Review Policyl Variable Lead Timesl Periodic Review Policyl Service Level Optimization


20/621-20

Economic Lot Size Model

FIGURE 2-3:Inventory level as a function of time


21/62

1-21

Assumptionsl D items per day: Constant demand ratel Q items per order: Order quantities are fixed, i.e., each

time the warehouse places an order, it is for Q items.l K, fixed setup cost, incurred every time the warehouse

places an order.l h, inventory carrying cost accrued per unit held ininventory per day that the unit is held (also known as,

holding cost )l Lead time = 0

(the time that elapses between the placement of anorder and its receipt)l Initial inventory = 0l Planning horizon is long (infinite).


22/62

1-22

Deriving EOQl Total cost at every cycle:

l Average inventory holding cost in acycle: Q/ 2

l Cycle time T = Q/D l Average total cost per unit time:

2

hTQ K +

2

hQQ

KD+

h KD

Q2* =


23/62

1-23

EOQ: Costs

FIGURE 2-4:Economic lot size model: total cost per unittime


24/62

1-24

Single Period Models

Short lifecycle productsl One ordering opportunity onlyl Order quantity to be decided before

demand occursl Order Quantity > Demand => Dispose excess

inventoryl Order Quantity < Demand => Lose sales/profits


25/62

1-25

Single Period Modelsl

Using historical datal identify a variety of demand scenariosl determine probability each of these scenarios will

occur l Given a specific inventory policy

l determine the profit associated with a particular scenario

l given a specific order quantityl weight each scenarios profit by the likelihood that it will

occur l determine the average, or expected, profit for a particular

ordering quantity.l Order the quantity that maximizes the average

profit.


26/62

1-26

Single Period Model Example

FIGURE 2-5:Probabilistic forecast


27/62

1-27

Additional Informationl Fixed production cost: $100,000l Variable production cost per unit: $80.l During the summer season, selling price:

$125 per unit.l Salvage value: Any swimsuit not sold

during the summer season is sold to a

discount store for $20.


28/62

1-28

Two Scenarios

l Manufacturer produces 10,000 units whiledemand ends at 12,000 swimsuitsProfit = 125(10,000) - 80(10,000) - 100,000 = $350,000

l Manufacturer produces 10,000 units whiledemand ends at 8,000 swimsuitsProfit

= 125(8,000) + 20(2,000) - 80(10,000) -100,000 = $140,000


29/62

1-29

Relationship Between OptimalQuantity and Average Demand

l Compare marginal profit of selling an additional unit andmarginal cost of not selling an additional unit

l Marginal profit/unit =Selling Price - Variable Ordering (or, Production) Cost

l Marginal cost/unit =Variable Ordering (or, Production) Cost - Salvage Value

l If Marginal Profit > Marginal Cost => Optimal Quantity > Average Demand

l If Marginal Profit < Marginal Cost => Optimal Quantity < Average Demand


30/62

1-30

For the Swimsuit Examplel Average demand = 13,000 units.l Optimal production quantity = 12,000 units.

l Marginal profit = $45l Marginal cost = $60.

l Thus, Marginal Cost > Marginal Profit=> optimal production quantity < average

demand.


31/62

1-31

Multiple Order OpportunitiesREASONSl To balance annual inventory holding costs and annual fixed order

costs.l To satisfy demand occurring during lead time.l To protect against uncertainty in demand.

TWO POLICIESl Continuous review policy

l inventory is reviewed continuouslyl an order is placed when the inventory reaches a particular level or reorder point.l inventory can be continuously reviewed (computerized inventory systems are

used)

l Periodic review policyl inventory is reviewed at regular intervalsl appropriate quantity is ordered after each review.l it is impossible or inconvenient to frequently review inventory and place orders if

necessary.


32/62

1-32

Continuous Review Policyl Daily demand is random and follows a normaldistribution.l Every time the distributor places an order from the

manufacturer, the distributor pays a fixed cost,K , plus anamount proportional to the quantity ordered.

l Inventory holding cost is charged per item per unit time.l Inventory level is continuously reviewed, and if an order

is placed, the order arrives after the appropriate leadtime.

l If a customer order arrives when there is no inventory onhand to fill the order (i.e., when the distributor is stockedout), the order is lost.

l The distributor specifies a requiredservice level .


33/62

1-33

l AVG = Average daily demand faced by thedistributor l STD = Standard deviation of daily demand faced

by the distributor l L = Replenishment lead time from the supplier tothe distributor in daysl h = Cost of holding one unit of the product for

one day at the distributor l = service level. This implies that the probability

of stockingout is 1 -

Continuous Review Policy


34/62

1-34

l (Q,R) policy whenever inventory levelfalls to a reorder levelR , place an order for Q units

l What is the value of R?

Continuous Review Policy


35/62

1-35

Continuous Review Policyl Average demand during lead time:L x

AVGl Safety stock:

l Reorder Level, R:

l Order Quantity, Q:

LSTD z

LSTD z AVG L +

h AVG K

Q

=2


36/62

1-36

Service Level & Safety Factor,z

Service Level 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 -


37/62

1-37

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 Q +2

FIGURE 2-9:Inventory level as a function of time in a ( Q ,R ) policy


38/62

1-38

Continuous Review Policy Examplel A distributor of TV sets that orders from amanufacturer and sells to retailersl Fixed ordering cost = $4,500l Cost of a TV set to the distributor = $250l Annual inventory holding cost = 18% of

product costl Replenishment lead time = 2 weeksl Expected service level = 97%


39/62

1-39

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 = 191.17Standard deviation of monthly demand = 66.53

Average weekly demand = Average Monthly Demand/4.3Standard deviation of weekly demand = Monthly standard deviation/4.3


40/62

1-40

Parameter Average weekly demand

Standard deviation of weekly demand

Averagedemand during lead time

Safety stock

Reorder point

Value 44.58 32.08 89.16 86.20 176

87.052

25018.0=

Weekly holding cost =

Optimal order quantity = 67987.

58.44500,42=

=Q

Average inventory level =679/2 + 86.20 = 426

Continuous Review Policy Example


41/62

1-41

l Average lead time, AVGLl Standard deviation, STDL .

l Reorder Level, R:

222STDL AVGSTD AVGL z AVGL AVG R ++=

Variable Lead Times

222STDL AVGSTD AVGL z + Amount of safety stock=

h AVG K

Q

=2

Order Quantity =


42/62

1-42

l Inventory level is reviewed periodically at regular intervalsl An appropriate quantity is ordered after each reviewl Two Cases:

l Short Intervals (e.g. Daily)l Define two inventory levels s and Sl During each inventory review, if the inventory position falls below s,

order enough to raise the inventory position to S.l (s, S) policy

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

Periodic Review Policy


43/62

1-43

(s,S) policyl Calculate the Q and R values as if this

were a continuous review modell Set s equal to R l Set S equal to R+Q .


44/62

1-44

Base-Stock Level Policyl Determine a target inventory level, the base-stock levell Each review period, review the inventory

position is reviewed and order enough to raise

the inventory position to the base-stock levell Assume:r = length of the review periodL = lead time

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


45/62

1-45

l Average demand during an interval of r +L days=

l Safety Stock= Lr STD z +

AVG Lr + )(

Base-Stock Level Policy


46/62

1-46

Base-Stock Level Policy

FIGURE 2-10:Inventory level as a function of time in a periodicreview policy

B S k L l P li


47/62

1-47

l Assume:l distributor places an order for TVs every 3 weeksl Lead time is 2 weeksl Base-stock level needs to cover 5 weeks

l Average demand = 44.58 x 5 = 222.9l Safety stock =l Base-stock level = 223 + 136 = 359l Average inventory level =

l Distributor keeps 5 (= 203.17 / 44.58) weeks of supply.

Base-Stock Level PolicyExample

58.329.1

17.20 3508.329.12

58.443 =+


48/62

1-48

l Optimal inventory policy assumes aspecific service level target.l What is the appropriate level of service?

l May be determined by the downstreamcustomer

l Retailer may require the supplier, to maintain aspecific service level

l Supplier will use that target to manage its own

inventoryl Facility may have the flexibility to choose theappropriate level of service

Service Level Optimization

S i L l O ti i ti


49/62

1-49

Service Level Optimization

FIGURE 2-11:Service levelinventory versusinventory level asa function of leadtime


50/62

1-50

Trade-Offsl Everything else being equal:

l the higher the service level, the higher theinventory level.

lfor the same inventory level, the longer thelead time to the facility, the lower the level of service provided by the facility.

l the lower the inventory level, the higher the

impact of a unit of inventory on service leveland hence on expected profit


51/62

1-51

Retail Strategyl Given a target service level across allproducts determine service level for each

SKU so as to maximize expected profit.l

Everything else being equal, service levelwill be higher for products with:l high profit marginl high volumel low variabilityl short lead time

P fi O i i i d S i


52/62

1-52

Profit Optimization and ServiceLevel

FIGURE 2-12:Service level optimization by SKU

P fit O ti i ti d S i


53/62

1-53

l Target inventory level = 95% across allproducts.

l Service level > 99% for many products

with high profit margin, high volume andlow variability.l Service level < 95% for products with low

profit margin, low volume and highvariability.

Profit Optimization and ServiceLevel


54/62

1-54

Risk Poolingl Demand variability is reduced if one

aggregates demand across locations.l More likely that high demand from one

customer will be offset by low demandfrom another.l Reduction in variability allows a decrease

in safety stock and therefore reducesaverage inventory.


55/62

1-55

Demand Variationl Standard deviation measures how much

demand tends to vary around the averagel Gives an absolute measure of the variability

l Coefficient of variation is the ratio of standard deviation to average demandl Gives a relative measure of the variability,

relative to the average demand

Acme Risk Pooling Case


56/62

1-56

Acme Risk Pooling Casel Electronic equipment manufacturer and

distributor l 2 warehouses for distribution in New York andNew Jersey (partitioning the northeast marketinto two regions)

l Customers (that is, retailers) receiving itemsfrom warehouses (each retailer is assigned awarehouse)

l Warehouses receive material from Chicagol Current rule: 97 % service levell Each warehouse operate to satisfy 97 % of

demand (3 % probability of stock-out)

N Id


57/62

1-57

l Replace the 2 warehouses with a singlewarehouse (located some suitable place) andtry to implement the same service level 97 %

l Delivery lead times may increasel But may decrease total inventory investment

considerably.

New Idea


58/62

1-58

Historical DataPRODUCT A

Week 1 2 3 4 5 6 7 8

Massachusetts 33 45 37 38 55 30 18 58

New Jersey 46 35 41 40 26 48 18 55

Total 79 80 78 78 81 78 36 113

PRODUCT BWeek 1 2 3 4 5 6 7 8

Massachusetts 0 3 3 0 0 1 3 0

New Jersey 2 4 3 0 3 1 0 0Total 2 6 3 0 3 2 3 0


59/62

1-59

Summary of Historical DataStatistics Product Average Demand Standard Deviation

of DemandCoefficient of Variation

Massachusetts A 39.3 13.2 0.34

Massachusetts B 1.125 1.36 1.21

New Jersey A 38.6 12.0 0.31

New Jersey B 1.25 1.58 1.26

Total A 77.9 20.71 0.27

Total B 2.375 1.9 0.81


60/62

1-60

Inventory LevelsProduct Average

DemandDuring LeadTime

Safety Stock Reorder Point

Q

Massachusetts A 39.3 25.08 65 132

Massachusetts B 1.125 2.58 4 25

New Jersey A 38.6 22.8 62 31

New Jersey B 1.25 3 5 24

Total A 77.9 39.35 118 186

Total B 2.375 3.61 6 33


61/62

1-61

Savings in Inventoryl Average inventory for Product A:

l At NJ warehouse is about 88 unitsl At MA warehouse is about 91 unitsl In the centralized warehouse is about 132 unitsl Average inventory reduced by about 36 percent

l Average inventory for Product B:l At NJ warehouse is about 15 unitsl At MA warehouse is about 14 unitsl In the centralized warehouse is about 20 unitsl Average inventory reduced by about 43 percent

Critical Points


62/62

l The higher the coefficient of variation, the greater thebenefit from risk pooling

l The higher the variability, the higher the safety stockskept by the warehouses. The variability of the demandaggregated by the single warehouse is lower

l The benefits from risk pooling depend on the behavior of the demand from one market relative to demand fromanother

l risk pooling benefits are higher in situations wheredemands observed at warehouses are negativelycorrelated

l Reallocation of items from one market to another easily accomplished in centralized systems. Notpossible to do in decentralized systems wherethey serve different markets

Critical Points

Date post:	04-Apr-2018
Category:	Documents
Upload:	udhai-pratap-singh
View:	214 times
Download:	0 times

inventory mamagement

Documents