Inventory and Economic Order Quantity

8/13/2019 Inventory and Economic Order Quantity

1/7

INVENTORY AND ECONOMIC ORDER QUANTITY MODELS

Types of Demand

Retailers and distributors must manage independent demand items-that is, items for

which demand is influenced by market conditions and isnt related to the inventorydecisions for any other item held in stock. Independent demand inventory includes:

1. wholesale and retail merchandise. service industry inventory!. end-item and replacement part distribution inventories". maintenance, repair and operating #$R%& supplies

$anufacturers and service providers must manage dependent demand items-that is,items that are re'uired as components or inputs to a product or service.

Accountin Cateo!ies of In"ento!y

Inventory e(ists in three aggregate categories, which are useful for accounting purposes.Ra# mate!ia$sare inventories needed for the production of good or services. )hile theyhave arrived from the supplier, no processing has yet been applied to them. %o!&'in'p!ocessconsists of components or sub assemblies used in the manufacture of finalproducts. )I* is also present in service industries. In both cases, one or more phases ofprocessing have been completed. (inis)ed oodsin manufacturing plants, warehouses,and retail outlets are items sold to the firms customers.

Types of In"ento!y

+nother way to look at inventory is to consider how or why it comes into being.

Cycle inventory* he portion of total inventory that varies directly with the lot sie iscalled cycle inventory. etermining how much to order and how often is called $otsi+in. he lot sie and therefore the cycle inventory vary directly with the elapsed timebetween orders. /or e(ample, if orders are placed every three weeks, the average lot siemust e'ual ! weeks of demand and the average cycle inventory will be 1-0 weeks ofdemand.

Safety stock inventory. o provide ade'uate customer service and avoid costs ofunavailable components, companies hold safety stock. afety stock inventory protectsagainst uncertainties in demand, lead-time and supply. o create safety stock, a firmplaces an order for an item earlier than when the items is e(pected to be needed.

Anticipation inventory. Inventory used to absorb uneven rates of demand or supply iscalled anticipation inventory. It is often an attractive alternative to changing the sie ofthe workforce and the use of overtime. + common e(ample is building an inventory for apeak sales season.


2/7

Pipeline inventory. Inventory moving from point to point in the materials flow system iscalled pipeline inventory. *ipeline inventory between two points is determined by thecorresponding lead-time.

Decoupling inventory. Inventory thats serves as a buffer between stages in a production

process that have significantly different operating characteristics #e.g., set up times, lotsies, run lengths, product fle(ibility, etc.&. It also is used to buffer production fromdistribution.

A,C In"ento!y C$assification

Inventories are often classified in order to allocate the appropriate e(tent of managementreview. + typical approach is the +23 classification.

C$ass A itemstypically represent 145 to 45 of the items types or stock keeping units

#67& and as much as 845 of the dollar value of the inventory. hese items areidentified for top management attention.

C$ass , itemstypically represent about !45 of the items types or 67s and 145 to45 of the dollar value of the inventory. hese items receive management attention bye(ception and typically are handled by computer systems.

C$ass C itemstypically represent about 945 of the items types or 67s and as little as95 of the dollar value of the inventory. hese items are handled by crude systems andseldom receive management attention.

In"ento!y -$acement

+ critical decision in the design of supply chains is where to locate the inventories offinished goods.

,aca!d p$acementrefers to the strategy of placing inventory back in the supplychain. he e(treme case is to hold no finished goods inventory and to assemble to orderor build to order. +nother somewhat less e(treme case is to hold inventory in a singlecentralied facility. 2ackwards placement provides the benefits of pooling which reducesrisk and the levels of safety stock re'uired.

(o!#a!d p$acementis the opposite strategy of placing inventory backward in the supplychain, i.e., nearer the customer. he advantages include faster response time tocustomers and, sometimes, reduced transportation costs, both of which can lead toenhanced sales.

In"ento!y Re"ie# Systems

Inventory levels are reviewed or measured either continuously or periodically.


3/7

Continuous Re"ie# .Q/ Systems, sometimes called !eo!de!point .RO-/ systems0track the inventory level each time a withdrawal is made to determine if it is time toreorder. )henever the inventory level falls to or below a !eo!de! point .R/, an order fora fi(ed 'uantity #& is made. +lthough the order sie is fi(ed, the time 1et#een o!de!s

.T,O/will change.

-e!iodic Re"ie# .-/ Systems, review the inventory level at fi(ed periods #e.g., weekly,monthly& in order to determine how large an order to place. +n order is placed to takethe inventory position #on hand inventory ; schedules receipts < backorders& up to apredetermined target level #&. hus in a * system the 2% is constant but the order'uantity will change.

ECONOMIC ORDER QUANTITY

In a continuous review system, ordering too often #in 'uantities too small& increases theannual cost of placing orders. %rdering too infre'uently #in 'uantities too large&increases the annual cost of holding inventory. he economic o!de! 2uantity .EOQ/isthe 'uantity that minimies the sum of these two costs. It is based on the followingassumptions:

1. he demand for the item is constant and known with certainty.. here are no upper or lower limits on the order 'uantity #lot sie&.!. tockouts are not permitted.". here are no 'uantity discounts.9. =ead time and supply are known with certainty> lead time is constant.?. %rder 'uantities for individual items are made independently.

he classic @saw toothA diagram of inventory level over time is illustrated in /igure 1.

/igure 1. Inventory levels over time.


4/7

If we define

3 - total annual #period& cost - fi(ed cost of placing an order - annual #period& demand

B - annual #period& unit cost of holding inventory < order 'uantity #to be determined&

then

HQ

Q

SDC += .

he /igure displays the cost relationships involved in the model:

Cost Versus Order Quantity

0

200

400

600

800

10001200

100 200 300 400 500 600 700 800 900 1000

Q

Cos

Order Cost = (S*D)/Q Holdin Cost = (H*Q)/2 !ot"l Cost

/igure . Inventory cost versus order sie .

he economic order 'uantity is calculated by

H

SDEOQ

= .

MINIMUM ORDER SI3ES AND ORDER ,LOC4 SI3ES

ealing with minimum order sies and order block sies #a number which all order siesmust be a multiple of& is 'uite easy. )e Round C% to +% #allowable order 'uantity&by choosing the multiple of the order block sie that is closest to C% and at least e'ualto minimum order sie

QUANTITY DISCOUNTS


5/7

In many instances, a vendor offers an item at a unit price, which we will call the normalcost and denote by *n, but will make the item available at a reduced unit cost, which wewill call the discount cost and denote by *d, as long as the order sie is at least e'ual tothe discount volume #D&. In such a case we begin by calculating C% and rounding to+%. he cost relationships for the 'uantity discount problem are illustrated in /igure !.

/igure !. 3ost relationships for 'uantity discounts.

herefore, we must compare the total cost per period for +% and D and usewhichever produces the smaller cost. his total cost adds the purchase cost per period tothe order plus holding cost specified previously. hus we calculate

&1# DVAOQIFPDAOQH

AOQ

SDCostDaily nAOQat


6/7

E5AM-LES

uppose demand for final product is as follows:

/441: G8/44: ""/44!: 1G8

3onsider *4!H pokes 4A

%rder cost #&: 14 Bolding 3ost *er ay #B&: 4.4444GJormal 3ost #*n&: 4.494 iscount 3ost #*d&: 4.4"9iscount Dolume #D&: 44,444 $inimum %rder: 4,444%rder block: ,444

ince there are H *4!Hs in each /441 and 4 in each /44 and /44!, weestimate daily volume for *4!H as

K aily Dolume K G8#H&;""#4&;1G8#4& K H49?

9G8,!G4444G.

&H49?#===

H

SDQ

+bove minimum order so round to +% K "4,444ince +% is below D we calculate by #1& by using the first e'uation

!?.!9?84.!984.1H?.1&494#.49?,H

&444,"4#4444G.

444,"4

&49?,H#14=++=++=AOQatCostDaily

and by #&

8H.!?9.!1H44.G!9.4&4"9#.49?,H

&444,44#4444G.

444,44

&49?,H#14=++=++=DVatCostDaily

hen since aily 3ost at D L aily 3ost at +% order 'uantity is set to

discount volume K 44,444.

%rder cycle K DM K 44,444M#H,49?& K 8.! days

3onsider *4"! teel ubing

%rder cost#&: "9 Bolding 3ost *er ay#B&: 4.444!9


7/7

Jormal 3ost #*n&: 4.4 iscount 3ost #*d&: 4.18iscount Dolume #D&: 14,444 $inimum order: 9,444%rder block: 1444

ince there are 1 *4"!s in each /441, ! in each /44 and " in each/44!, we estimate daily volume for *4"! as

K aily Dolume K G8 #1& ; ""#!& ; 1G8#"& K 1,"

91,91H,9?444!9.

&",1"9#===

H

SDQ

+bove minimum order so round to 9H,444ince +% is above D we calculate by #1& by using the second e'uation

,G?.!9,GH.G81.G&18#.",1

&444,9H#444!9.

444,9H

&",1#"9=++=++=AOQatCostDaily

and by #&

,G?.!9,H9.1G4.99&18#.",1

&444,14#444!9.

444,14

&",1#"9=++=++=DVatCostDaily

hen since aily 3ost at +% L aily 3ost at D order 'uantity is set to +%K 9H,444. his could have been anticipated since +% N D.

%rder cycle K+%M K 9H,444M1," K ".? days

Documents

Inventory and Economic Order Quantity