Ch14(Inventory Control)

8/18/2019 Ch14(Inventory Control)

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©The McGraw-Hill Companies,

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Chapter 14

Inventory Control


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• Inventory System Defined• Inventory Costs

• Independent vs. Dependent Demand

• Single-Period Inventory Model• Multi-Period Inventory Models: Basic Fixed-rder

!uantity Models

• Multi-Period Inventory Models: Basic Fixed-"ime

Period Model

• Miscellaneous Systems and Issues

B#$C"I%$S


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Inventory System

Defined • Inventory is t&e stoc' of any item or resource

used in an organi(ation and can include: ra)

materials* finis&ed products* component

parts* supplies* and )or'-in-process

• +n inventory system is t&e set of policies and

controls t&at monitor levels of inventory and

determines )&at levels s&ould ,e maintained*)&en stoc' s&ould ,e replenis&ed* and &o)

large orders s&ould ,e


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Purposes of Inventory

. "o maintain independence of operations

. "o meet variation in product demand

/. "o allo) flexi,ility in production sc&eduling

0. "o provide a safeguard for variation in ra)

material delivery time

1. "o ta'e advantage of economic purc&ase-

order si(e


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Inventory Costs

• 2olding 3or carrying4 costs – Costs for storage* &andling* insurance* etc

• Setup 3or production c&ange4 costs

– Costs for arranging specific e5uipment setups* etc• rdering costs – Costs of someone placing an order* etc

• S&ortage costs

– Costs of canceling an order* etc


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E(1

)

Independent vs. Dependent Demand

Independent Demand (Demand for the final end-product or demand not related to other items)

DependentDemand

(Derived demand

items forcomponent

parts,subassemblies,raw materials,

etc)

Finis&ed

product

Component parts



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Inventory Systems• Single-Period Inventory Model

– ne time purc&asing decision 3$xample: vendorselling t-s&irts at a foot,all game4

– See's to ,alance t&e costs of inventory overstoc'and under stoc'

• Multi-Period Inventory Models

– Fixed-rder !uantity Models

• $vent triggered 3$xample: running out of

stoc'4 – Fixed-"ime Period Models

• "ime triggered 3$xample: Mont&ly sales call ,ysales representative4



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Single-Period Inventory Model

uo

u

C C

C P

+

≤uo

u

C C

C P

+

≤

sold beunit will that the!robabilit

esti"atedunderde"ando# unit perCostCesti"atedo$erde"ando# unit perCostC

%&here

u

o

=

==

P

"&is model states t&at )e

s&ould continue to increase

t&e si(e of t&e inventory so

long as t&e pro,a,ility of

selling t&e last unit added is

e5ual to or greater t&an t&eratio of: Cu6Co7Cu

"&is model states t&at )e

s&ould continue to increaset&e si(e of t&e inventory so

long as t&e pro,a,ility of

selling t&e last unit added is

e5ual to or greater t&an t&eratio of: Cu6Co7Cu



1'

Single Period Model $xample

• ur olle*e bas+etball tea" is plain* in atourna"ent *a"e this wee+end, -ased on our paste.periene we sell on a$era*e 2/4'' shirts with astandard de$iation o# 35', &e "a+e 01' on e$er

shirt we sell at the *a"e/ but lose 05 on e$er shirtnot sold, ow "an shirts should we "a+e #orthe *a"eC

u = 89 and C

o 81; P < 89 6 389 7 814 .==>

?.==> .0/ 3use @AMSDIS"3.==>4 or +ppendix $4

t&erefore )e need *099 7 .0/3/194 *11 s&irts



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Multi-Period Models:

Fixed-rder !uantity Model Model

+ssumptions 3Part 4

• Demand for t&e product is constant and

uniform t&roug&out t&e period

• ead time 3time from ordering to receipt4 is

constant

• Price per unit of product is constant


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Basic Fixed-rder !uantity Model and

Aeorder Point Be&avior

R = Reorder pointQ = Economic order quantityL = Lead time

! !!

A

Time

Number

of unitson hand

1, ou reei$e an order uantit ,

2, our start usin*the" up o$er ti"e, 3, &hen ou reah down to

a le$el o# in$entor o# /

ou plae our ne.t

sied order,

4, he le then repeats,



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Cost Minimi(ation oal

Ordering Costs

oldingCosts

Order !uantit" (!)

CO#T

$nnual Cost of

Items (DC)

Total Cost

QOPT

%" adding the item, holding, and ordering costs

together, we determine the total cost curve, which inturn is used to find the !opt inventor" order point that

minimi&es total costs

%" adding the item, holding, and ordering costs

together, we determine the total cost curve, which inturn is used to find the !opt inventor" order point that

minimi&es total costs

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Basic Fixed-rder !uantity

3$!4 Model Formula

125 9:

5; 9;C



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Deriving t&e $!

sing calculus* )e ta'e t&e first derivative of t&e

total cost function )it& respect to !* and set t&e

derivative 3slope4 e5ual to (ero* solving for t&e

optimi(ed 3cost minimi(ed4 value of !opt

sing calculus* )e ta'e t&e first derivative of t&e

total cost function )it& respect to !* and set t&e

derivative 3slope4 e5ual to (ero* solving for t&e

optimi(ed 3cost minimi(ed4 value of !opt

5 <2;:

1 <

2(=nnual ;e"and)(rder or :etup Cost)

=nnual 1oldin* Cost!8

5 <2;:

1 <

2(=nnual ;e"and)(rder or :etup Cost)

=nnual 1oldin* Cost!8

eorder point/ < d > ? eorder point/ < d > ?

d < a$era*e dail de"and (onstant)

> < >ead ti"e (onstant)

?

'e also need areorder point totell us when toplace an order

'e also need areorder point totell us when toplace an order

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$! $xample 34 Pro,lem Data

$nnual Demand ,*** unitsDa"s per "ear considered in average

dail" demand +Cost to place an order .*

olding cost per unit per "ear ./0*1ead time 2 da"sCost per unit .

3iven the information below, what are the 4O! andreorder point5

3iven the information below, what are the 4O! andreorder point5

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$! $xample 34 Solution

<2;:

<

2(1/''' )(1')

2,5' < 89,443 units or! E9 units

<2;:

<

2(1/''' )(1')

2,5' < 89,443 units or! E9 units

d <1/''' units @ ear

365 das @ ear < 2,74 units @ dad <

1/''' units @ ear

365 das @ ear

< 2,74 units @ da

eorder point/ < d > < 2,74units @ da (7das) < 19,18 or ?

.9 unitseorder point/ < d > < 2,74units @ da (7das) < 19,18 or ?

.9 units

In summar", "ou place an optimal order of 6* units0 Inthe course of using the units to meet demand, when"ou onl" have /* units left, place the ne7t order of 6*units0

In summar", "ou place an optimal order of 6* units0 Inthe course of using the units to meet demand, when"ou onl" have /* units left, place the ne7t order of 6*units0


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$! $xample 34 Solution

<2;:

<

2(1'/''' )(1')

1,5'< 365,148 units/ or! /== units

< 2;:

< 2(1'/''' )(1')

1,5'< 365,148 units/ or! /== units

d <

1'/''' units @ ear

365 das @ ear < 27,397 units @ dad <

1'/''' units @ ear

365 das @ ear < 27,397 units @ da

< d > < 27,397 units @ da (1' das) < 273,97 or ?

.>0 units < d > < 27,397 units @ da (1' das) < 273,97 or ?

.>0 units

;lace an order for + units0 'hen in the course ofusing the inventor" "ou are left with onl" /2< units,place the ne7t order of + units0

;lace an order for + units0 'hen in the course ofusing the inventor" "ou are left with onl" /2< units,place the ne7t order of + units0

21Fixed "ime Period Model )it& Safety



21Fixed-"ime Period Model )it& Safety

Stoc' Formula

order)onite"s(inludesle$elin$entorurrent



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Multi-Period Models: Fixed-"ime Period

Model:

Determining t&e %alue of "7

( )σ σ

σ

σ σ

> di 1

>

d

> d

2

<

:ine eah da is independent and is onstant/

< ( >)

i

2

=

∑( )σ σ

σ

σ σ

> di 1

>

d

> d

2

<

:ine eah da is independent and is onstant/

< ( >)

i

2

=

∑

• "&e standard deviation of a se5uence ofrandom events e5uals t&e s5uare root of t&esum of t&e variances

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$xample of t&e Fixed-"ime Period Model

+verage daily demand for a product is 9

units. "&e revie) period is /9 days* and leadtime is 9 days. Management &as set a policy

of satisfying E= percent of demand from items

in stoc'. +t t&e ,eginning of t&e revie)period t&ere are 99 units in inventory. "&e

daily demand standard deviation is 0 units.

iven t&e information ,elo)* &o) many unitss&ould ,e ordered

iven t&e information ,elo)* &o) many units

s&ould ,e ordered

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$xample of t&e Fixed-"ime Period Model:

Solution 3Part 4

( ) ( )σ σ > d2 2 < ( >) < 3' 1' 4 < 25,298( ) ( )σ σ > d 2 2 < ( >) < 3' 1' 4 < 25,298

"&e value for G(H is found ,y using t&e $xcel

@AMSI@% function* or as )e )ill do &ere* using

+ppendix D. By adding 9.1 to all t&e values in

+ppendix D and finding t&e value in t&e ta,le t&at

comes closest to t&e service pro,a,ility* t&e G(H

value can ,e read ,y adding t&e column &eadingla,el to t&e ro) la,el.

"&e value for G(H is found ,y using t&e $xcel

@AMSI@% function* or as )e )ill do &ere* using

+ppendix D. By adding 9.1 to all t&e values in+ppendix D and finding t&e value in t&e ta,le t&at

comes closest to t&e service pro,a,ility* t&e G(H

value can ,e read ,y adding t&e column &eading

la,el to t&e ro) la,el.

So* ,y adding 9.1 to t&e value from +ppendix D of 9.01EE*

)e &ave a pro,a,ility of 9.E1EE* )&ic& is given ,y a ( .>1

So* ,y adding 9.1 to t&e value from +ppendix D of 9.01EE*

)e &ave a pro,a,ility of 9.E1EE* )&ic& is given ,y a ( .>1

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$xample of t&e Fixed-"ime Period Model:

Solution 3Part 4

or644,272/


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Price-Brea' Model Formula

Costoldin*=nnual

Cost):etuporder;e"and)(r 2(=nnual <

iC

2;:

i percentage of unit cost attributed to carr"ing inventor"C cost per unit

#ince ?C@ changes for each price-brea=, the formulaabove will have to be used with each price-brea= costvalue

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Price-Brea' $xample Pro,lem Data

3Part 4

+ company &as a c&ance to reduce t&eir inventoryordering costs ,y placing larger 5uantity orders using

t&e price-,rea' order 5uantity sc&edule ,elo). &at

s&ould t&eir optimal order 5uantity ,e if t&is company

purc&ases t&is single inventory item )it& an e-mail

ordering cost of 80* a carrying cost rate of J of t&e

inventory cost of t&e item* and an annual demand of

9*999 units

+ company &as a c&ance to reduce t&eir inventoryordering costs ,y placing larger 5uantity orders using

t&e price-,rea' order 5uantity sc&edule ,elo). &at

s&ould t&eir optimal order 5uantity ,e if t&is company

purc&ases t&is single inventory item )it& an e-mail

ordering cost of 80* a carrying cost rate of J of t&e

inventory cost of t&e item* and an annual demand of

9*999 units

Order Quantity'units( Price)unit'*(+ to ,-.// *01,+,-2++ to 3-/// 01++.-+++ or more 1/4

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Price-Brea' $xample Solution 3Part 4

units1/826<','2(1,2')

4)2(1'/''')( <

iC

2;:


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Price-Brea' $xample Solution 3Part /4

#ince the feasible solution occurred in the first price-brea=, it means that all the other true !opt values occur

at the beginnings of each price-brea= interval0 'h"5

#ince the feasible solution occurred in the first price-brea=, it means that all the other true !opt values occur

at the beginnings of each price-brea= interval0 'h"5

+ 04,9 ,2++ .+++ Order Quantity

Totalannualcosts

#o the candidatesfor the price-brea=s are B/,/**, and


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Miscellaneous Systems:

ptional Aeplenis&ment System

a7imum Inventor" 1evel,

$ctual Inventor" 1evel, I

9 - I

I

! minimum acceptable order 9uantit"

If 9 E !, order 9, otherwise do not order an"0

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Miscellaneous Systems:

Bin Systems

Two-%in #"stem

;ull Empty

Order One


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+BC Classification System

• Items 'ept in inventory are not of e5ualimportance in terms of:

– dollars invested

– profit potential

– sales or usage volume

– stoc'-out penalties

+

3+

9+

3+

9+

= -C

5 o!* alue

5 o!>se

#o, identif" inventor" items based on percentage of totaldollar value, where ?$@ items are roughl" top 8, ?%@items as ne7t + 8, and the lower *8 are the ?C@ items

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Inventory +ccuracy and Cycle Counting

Defined

• Inventory accuracy refers to &o) )ell t&e

inventory records agree )it& p&ysical

count

• Cycle Counting is a p&ysical inventory-

ta'ing tec&ni5ue in )&ic& inventory is

counted on a fre5uent ,asis rat&er t&an

once or t)ice a year

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End o# Chapter 14

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Ch14(Inventory Control)