1

생산운영관리

재고관리(Inventory Management) (Ch. 12)

Hansoo Kim (���)

Dept. of Management Information SystemsYUST

2

OM Overview

Class Overview (Ch. 0)

Project Management

(Ch. 17)

Strategic Capacity Planning (Ch. 5, 5S)

Operations, Productivity, and Strategy

(Ch. 1, 2)

Mgmt of Quality/ Six Sigma Quality

(Ch. 9, 10)

Supply Chain Management

(Ch 11)

Location Planning and Analysis

(Ch. 8)

Demand Mgmt Forecasting

(Ch 3)

Inventory Management

(Ch. 12)

Aggregated Planning

(Ch. 13)

Queueing/ Simulation

(Ch. 18)

MRP & ERP (Ch 14)

JIT & Lean Mfg System

(Ch. 15)

Term Project

Process Selection/

Facility Layout; LP (Ch. 6, 6S) X X X X X

X X X X

X X

일정계획 !  6/12 : 재고관리 !  6/14 : 총괄생산계획 !  6/19 : MRP/ERP !  6/21 : Final Exam

3 4

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5

Question 1 ? !  년간�수요, Annual Demand (D) = 1000 units/yr !  주문�비용, Ordering Cost (S) = $10/order !  재고�보관비�비율, Inventory Carrying rate (I) = 5% !  년간�작업일�수, Working days in a year = 250 days/year !  단위�가격, Unit Price (P) = $10/unit !  배송�시간, Lead Time (L) = 5 days

몇�개를�주문해야�년간�재고비용이�최소화�되는가? (Order Quantity to minimize annual inventory cost?) 평균�년간�주문�회수는�얼마인가? (Average number of orders?) 평균�주문�주기는�얼마인가? (Average ordering period?) �발주�시점은�언제인가? (Reorder point?)

6

Question 2 ?

!  당신은�할인�혜택을�받으시겠습니까? (Will you take discount or not?) 몇�개를�주문해야�할까요? (How many quantity to be ordered?)

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7

재고란? (What is Inventory?)

!  제품의 저장(Stock of materials) !  생산력의 저장(Stored capacity)

"  �¸ï�£�É¿Z���ÛX�dÌ��¸íÛ_�ª_��Êm�

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재고가 필요한 이유 (Why Inventory?)

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9

재고의 종류 (Types of Inventory)

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!  완제품$재고���484=30/��99/=��#  è��E`î�à×�Ôë�

10

자재의 흐름 �!,>0<4,6��69A��

비사용$Raw$Material$

가공중$WIP$

판매가능$Finished$Goods$

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재고의 문제점 �(Problems caused by inventory)

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70>�

#  ÍP�çÔÃ�¬uº�

#  생산공정의$문제를$숨김$Hides$production$problems$

12

Scrap

Work in process inventory level (hides problems)

Unreliable Vendors

Capacity Imbalances

재공품(WIP)이 많이 있는 경우

NO PROBLEM!!! Really?

13

Scrap

암초에 걸리기 시작… 문제가 드러남!

Unreliable Vendors

Capacity Imbalances

WIP

재고 수준을 낮춘다면?

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재고의 분류 (Inventory Classifications)

재고 (Inventory)

생산과정 (Process stage)

수요유형 (Demand Type)

수량과 용량 (Number & Value)

기타 (Other)

부품(Raw Material) 재공품(WIP)

완제품 (Finished Goods)

독립적 (Independent)

종속적 (Dependent)

A아이템 (A Items) B아이템 ( B Items)

유지 (Maintenance)

생산운영 (Operating)

© 1984-1994 T/Maker Co.

15

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ABC 접근법� (ABC Analysis)

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ABC 분석에 의한 재고 분류

Class % $ Vol % Items A 80 15 B 15 30 C 5 55

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ABC 분석에 의한 재고 분류 (예제)

1 $ 60 90 2 350 40 3 30 130 4 80 60 5 30 100 6 20 180 7 10 170 8 320 50 9 510 60

10 20 120

PART UNIT COST ANNUAL USAGE

Example 10.1 18

ABC 분석에 의한 재고 분류

Example 10.1

1 $ 60 90 2 350 40 3 30 130 4 80 60 5 30 100 6 20 180 7 10 170 8 320 50 9 510 60

10 20 120

PART UNIT COST ANNUAL USAGE TOTAL % OF TOTAL % OF TOTAL PART VALUE VALUE QUANTITY % CUMMULATIVE

9 $30,600 35.9 6.0 6.0 8 16,000 18.7 5.0 11.0 2 14,000 16.4 4.0 15.0 1 5,400 6.3 9.0 24.0 4 4,800 5.6 6.0 30.0 3 3,900 4.6 10.0 40.0 6 3,600 4.2 18.0 58.0 5 3,000 3.5 13.0 71.0

10 2,400 2.8 12.0 83.0 7 1,700 2.0 17.0 100.0

$85,400

A

B

C

19

ABC 분석에 의한 재고 분류

100 –

80 –

60 –

40 –

20 –

0 – | | | | | | 0 20 40 60 80 100

% of Quantity

% o

f Val

ue

A

B C

20

Example 1

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독립재고와 종속재고�(Independent vs. Dependent Demand)

!  독립재고(Independent/demand)��/07,8/�19<�4>07�4=�48/0:08/08>�91�/07,8/�19<�,8C�9>30<�4>07��02��484=30/�299/=��

!  종속재고(Dependent/demand)��/07,8/��19<�4>07�4=�/0:08/08>�?:98�>30�/07,8/��19<�=970�9>30<�4>07�

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Item Materials With Independent Demand

Materials With Dependent Demand

Demand Source Company Customers Parent Items

Material Type Finished Goods WIP & Raw Materials

Method of Estimating Demand

Forecast & Booked Customer Orders

Calculated

Planning Method EOQ & ROP MRP

독립재고와 종속재고

It makes no sense to independently forecast dependent demands.

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재고관련 비용들…

!  재고�보관비�(Holding or Carrying Cost) #  재고를 보관하는데 드는 비용 #  시간이 길 수록 비용이 증가한다

!  주문비�(Ordering Cost) #  물건을 주문하고 수령하는데 드는 비용

!  준비비�(Setup Cost) #  생산에 앞서 설비를 준비하는데 드는 비용

!  판매유실�비용�(Lost Sales Cost) #  판매기회 상실에 따는 기회비용 및 잠재비용

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재고 보관비 �(Holding or Carrying Cost) 재고를�유지하고�보관하는데�드는�비용�일반적으로�재고�수량과�비례적�관계��

!  열화 (Obsolescence ) !  보험 (Insurance) !  관리 (Extra staffing ) !  이자 (Interest) !  도난 (Pilferage) !  손상 (Damage) !  보관 (Warehousing) !  Etc.

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주문비 �(Ordering Cost) 물건을�주문하고�수령하는데�드는�비용�일반적으로�제품의�수량과�관련이�없다��

!  공급관련�비용 (Supplies) !  양식 (Forms) !  주문처리 (Order processing) !  사무적�지원 (Clerical support ) !  Etc.

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준비비�(Setup Cost)

생산에�앞서�설비를�준비하는데�드는�비용��

!  Clean-up costs !  Re-tooling costs !  Adjustment costs !  Etc.

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!  정량발주�모델�(Fixed order-quantity models) #  경제적 주문 수량

(Economic order quantity (EOQ)) #  경제적 생산 수량

(Production order quantity (POQ)) #  대량할인

(Quantity discount)

!  확률적�모델�(Probabilistic models)

!  정기발주�모델�(Fixed order-period models)

Help answer the inventory planning questions!

재고모델�(Inventory Models)

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EOQ 모델의 가정

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!  °G�£·sÀ�«uÕ�Éa�

!  £·_�°Ù�UÆíL���í��oq��£·¾À�ÆÓía��

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!  F�Ø�À�î��¯��cja�

!  £s�ïÅÀ�®a�

���

재고$주문$사이클$

Figure$10.1$

보유량$

재주문점$

사용률$

발주량$사용률$리드타임$재주문점$

입고$ 출고$ 입고$ 출고$ 입고$

���

주문량과$재고수준과의$관계$

평균재고$

평균재고$

발주횟수가$증가하면$평균재고는$감소$

발주횟수가$감소하면$평균재고는$증가$

� �

EOQ$모델$얼마를$주문해야$하는가?$

#</0<�;?,8>4>C�

�88?,6��9=>�

(9>,6��9

=>��?<@0

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비용$

주문량$

최저$총비용$

총비용곡선$

32

!  More units must be stored if more are ordered

Purchase Order Description Qty. Microwave 1

Order quantity

Purchase Order Description Qty. Microwave 1000

Order quantity

왜 재고유지비는 증가하는가? (Why Holding Costs Increase)

���

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왜$재고$주문비는$감소하는가?$$

(*3C�#</0<��9=>=��0.<0,=0�� 재고비용�모델링

34

35

EOQ 구하는 법

1.  주문비�(혹은�준비비)에�대한�식을�구한다�(Develop an expression for setup or ordering costs)

2.  보관비에�대한�식을�구한다�(Develop an expression for holding cost)

3.  준비비와�보관비가�동일하게�수식을�세운다�(Set setup cost equal to holding cost)

4.  수식을�풀면, EOQ가�계산�된다�(Solve the resulting equation for the best order quantity)

36

계산

!  Holding Cost:

!  Ordering Costs: s per order, so

!  Calculation

DhQ

hQ

Q

2cost holdingunit

2cost holding annual

2inventory average

=

=

=

QsQDs

=

=

cost setupunit

cost setup annual

?Q

Cost Setup Annual2

cost holding Annual

=

===QDs

DhQ

37

예제) !  Demand, D = 1000 racks per year

!  Price, P = $250

!  Ordering Cost, s = $500 (estimated from supplier’s pric

ing)

!  Holding Cost, h = $35 per unit per year, or

H = IP, I = annual interest rate for inventory carryin

g cost. Then, I = 1.4 %

38

EOQ모델의 비용 그래프

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

20.00

0 100 200 300 400 500

Order Quantity (Q)

Cost

($/u

nit)

hQ/2D

A/Qc

Y(Q)

Q*=169

S/Q P/

39

최적주문량 (Optimal Order Quantity) 주문수 (Expected Number of Orders) 주문사이클의 길이 (Expected Time Between Orders)

Working Days / Year

Working Days / Year

= = × ×

= =

= =

=

= ×

Q* D S H

N D Q*

T N

d D

ROP d L

2

D = 연간주문량(Demand per year) S = 주문비용 (Setup (order) cost per order) H = 유지비용 (Holding (carrying) cost ) d = 일당주문량(Demand per day) L = 리드타임(Lead time in days)

EOQ Model Equations

40

재발주점과 리드타임 �(The Reorder Point (ROP) Curve)

Q*

ROP (Units)

Slope = units/day = d

Lead time = L Time (days)

Inven

tory l

evel

(unit

s)

41

예제 !  년간�수요�(D) = 1000 units/yr !  주문비�(S) = $10/order !  재고�보관비�비율�(I) = 5% !  년간�작업일수�= 250 days/year !  단위�가격�(P) = $10/unit !  리드타임�(L) = 5 days

EOQ?, 년간�총�비용? 평균�년간�발주�회수�(N)? 평균�발주�주기�(T)? 재발주점�(ROP)?

unitsLdR

daysT

timesQDN

IPHDSQ

2052501000

505250

52001000

2001005.01010002

)(2

*

*

**

*

=⋅=⋅=

==

===

=⋅

⋅⋅=

==

42

Robustness of EOQ (Eg. 6)

!  What if D is changed to 1500 units/yr (50% under-estimate)?

!  Total Cost (Q=200)? !  Total Cost (Q=244.9)? !  How much different?

24595.2445.010150022

100$5.0220010

2001000

2)(

* ≈=⋅⋅

==

=+=+=

HDSQ

HQSQDQTC

125$5.0220010

2001500)200( =+=TC

47.122$5.0224510

2451500)245( =+=TC

%247.12247.122125

≈−

43

Production Order Quantity (POQ)Model

!  언제�얼마나�생산해야�하는가에�대한�답을�준다�(Answers how much to order and when to order)

!  제품의�입고가�점진적이다�(Allows partial receipt of material) #  EOQ와는 다른 가정

!  경제적�제품생산량을�결정하는데�유용하다�(Suited for production environment) #  Material produced, used immediately #  Provides production lot size

!  EOQ모델�보다�재고�보관비용이�적게�나타난다(Lower holding cost than EOQ model)

���

EOQ$POQ$(or$EPQ)$Model$When$To$Order$

(470��8@0

8>9

<C� 0@0

6�

��R�¡�E�h§¯�Ä{¬

�Üa�¡���Ä{¬�

Üa�!,B47?7�48@08>9<C�60@06�

���

POQ$Model$Inventory$Levels$

Time$

Inventory$Level$

Production$$Portion$of$Cycle$

Max.$Inventory$$Qã(1-$d/p)$

Q*$

Supply$Begins$

Supply$Ends$

Inventory$level$with$no$demand$

Demand$portion$of$cycle$with$no$supply$

>�%�$�

$�

$��

�$���%�$�%� ��$��

46

D = Demand per year S = Setup cost H = Holding cost d = Demand per day p = Production per day

POQ Model Equations

Optimal Order Quantity

Setup Cost

Holding Cost

= =

-

= *

= *

=

Q H* d

p

Q

D Q

S

p *

1

(

0.5 * H * Q - d p

1

) - d p

1

( )

2*D*S

( ) Maximum inventory level

47

Solution to POQ Model

!  Annual Cost Function:

!  Solution (by taking derivative and setting equal to zero):

DcQPDHQSDQTC +

−+=

2)/1()(

setup holding production

)/1(2*

PDHSDQ−

=

•  tends to EOQ as P →∞ •  otherwise larger than EOQ because replenishment takes longer

48

예제

!  D = 1000 units/yr !  S = $10/order !  H = $0.5/unit*year !  p = 8 units/day, Working Days=250days/yr !  P = 2000 units/yr POQ? Total Cost?

28384.282)2000/10001(5.0

1010002)/1(

2* ≈=−

⋅⋅=

−=

PDHDSPOQ

71.70$2

283)2000/10001(5.0283100010)283( =

⋅−+

⋅=TC

49

!  언제�얼마나�생산해야�하는가에�대한�답을�준다��(Answers how much to order & when to order)

!  대량구매시�할인이�있다. (Allows quantity discounts) #  Reduced price when item is purchased in larger quant

ities #  Other EOQ assumptions apply

!  가격할인과�재고보관�비용에�대한�절충�(Trade-off is between lower price & increased holding cost)

대량할인 모델�Quantity Discount Model

50

대량할인��Quantity Discount Schedule

Discount Number

Discount Quantity Discount (%) Discount Price (P)

1 0 to 999 No discount

$5.00

2 1,000 to 1,999 4 $4.80 3 2,000 and over 5 $4.75

���������?84>=�C<��'�����9</0<�������������

51

대량할인 문제 푸는 방법 1.  각각의�할인에�대해서�EOQ를�사용하여�각각의�최적�주문량을�구한다.

(For each discount, calculate a value for optimal order size Q*, using EOQ formula)

2.  최소치로�변경시킨다. (For any discount, if the order quantity is too low to qualify for the discount, adjust the order quantity upward to the lowest quantity that will qualify for the discount)

3.  비용을�구하는�공식을�사용히여, 각각의�주문량, Q*, 에�대하여�총�비용을�구한다. (Using the preceding total cost equation compute a total cost for every Q*

determined in steps 1 and 2. If you had to adjust Q* upward because it was below the allowable quantity range, be sure to use adjusted value for Q)

4.  이�비용중, 최소의�총�비용을�갖는�주문량, Q*를�선택한다. (Select the Q* that has the lowest total cost, as computed in step 3.

It will be the quantity that will minimize the total inventory cost)

52

Quantity Discount – How Much to Order

PDQHSQDTC ++=

2

���

해답$ì$Price$Discount$Model$

Discount Number Discount Quantity Discount (%) Discount Price (P)

1 0 to 999 No discount $5.00

2 1,000 to 1,999 4 $4.80

3 2,000 and over 5 $3

���������?84>=�C<��'�����9</0<�������������

unitsPISDQ

unitsPISDQ

unitsPISDQ

7182.0*35000*49*22

7142.0*8.45000*49*22

7002.0*55000*49*22

*3$

*8.4$

*5$

===

===

===

adjusting$

50.822,24$,2000

725,24$,1000

700,25$,700

*3$

*8.4$

*5$

==

==

==

TCunitsQ

TCunitsQ

TCunitsQ

���

다른$예제..$Quantity$Discount$Example$

$QUANTITY $PRICE$$

$1$-$49 $$1,400$$

$50$-$89 $1,100$

$90+ $900$

/S$=$$2,500$$

/H$=$$190$per$computer$$

/D$=$200$

Q*$=$$$$$$$$$$$$$$$$=$$$$$$$$$$$$$$$$$$$$$$$$$$$$$=$72.5$PCs$2SD/

H/

2(2500)(200)$

190$

TC$=$$$$$$$$$$$+$$$$$$$$$$$$$+$PD/=$$233,784$$SD/

Q*$HQ*$

2$

For$Q$=$72.5$

TC$=$$$$$$$$$$$+$$$$$$$$$$$$+$PD/=$$194,105$SD/

Q$HQ$

2$

For$Q$=$90$

���

재발주점$계산$예제$

년간수요/,/D/=/10,000/units/year/

년간/작업일수,/Store/open/311/days/year/

일간수요,/d/=/10,000///311/=/32.154/units/day/

리드타임,/L/=/10/days/

/

R/=/dL/=/(32.154)(10)/=/321.54/units/

56

확률적 모형 !  언제�얼마나�생산해야�하는가에�대한�답을�준다�

(Answer how much & when to order) !  수요에�변동이�있을수�있다.

(Allow demand to vary) #  수요는 정규분포를 따른다 (Follows normal distribution) #  Other EOQ assumptions apply

!  봉사수준과�안전재고를�고려한다�(Consider service level & safety stock) #  봉사수준, Service level =

1 - Probability of stockout (품절확률) #  더 높은 봉사수준을 위해서는 더 많은 안전재고가 필요하다

(Higher service level means more safety stock) !  더 많은 안전재고는 더 높은 재발주점을 의미한다.

More safety stock means higher ROP

57

Probabilistic Models When to Order?

Reorder Point (ROP)

Optimal Order

Quantity X

Safety Stock (SS)

Time

Inventory Level

Lead Time

SS ROP

Service Level P(Stockout)

Place order

Receive order

Frequency 서비스 수준

품절 위험

58

안전재고 (Safety Stocks)

$  Safety stock (안전재고) $  수요변동과 리드타임의 변동으로 인해 수요의 기대치보다

초과해서 보관하는 재고. �(buffer added to on hand inventory during lead time)

$  Stockout (품절) $  재고 부족 (an inventory shortage)

$  Service level (봉사 or 서비스 수준) $  리드타임 동안의 재고가 부족하지 않을 확률�

probability that the inventory available during lead time will meet demand

59

Variable Demand with a Reorder Point

Reorder point, R

Q

LT Time

LT

Inve

ntor

y le

vel

0

60

Reorder Point with a Safety Stock

Figure 10.6

Reorder point, R

Q

LT Time

LT

Inve

ntor

y le

vel

0 Safety Stock

61

예제 10

!  재발주점�계산�ROP = d*L + SS, SS=Safety Stock (안전재고) #  d*L=50 units #  H=$5/년, 품절비용 (C)=$40/개, 년간 발주수=6

Number of Units Probability

30 40 50 60 70

0.2 0.2 0.3 0.2 0.1

�07,8/��19<��<09</0<�:0<49/�

Safety Stock Inventory Holding Cost Stockout Cost Total Cost

20

10 0

20*$5=100 10*$5=50

0

0 10*0.1*$40*6=240

10*0.2*$40*6+20*0.1*$40*6=960

$100 $290 $960

62

!  얼마나�주문할�것인가에�대해�답변�(Answers how much to order)

!  주문을�일정한�간격으로�한다�(Orders placed at fixed intervals) #  적정재고 수준까지 주문

(Inventory brought up to target amount)

#  주문량을 그때 그때 달라요. (Amount ordered varies)

!  계속적으로�재고를�관찰하지�않아도�된다. (No continuous inventory count) #  재고 부족현상이 나타날수 있다.

(Possibility of stockout between intervals)

!  보통�공급자가�정기적으로�방문하는�경우�사용�(Useful when vendors visit routinely) #  Example: P&G representative calls every 2 weeks

고정발주시스템�(Fixed Period Model)

63

Inventory Level in a Fixed Period System

Various amounts (Qi) are ordered at regular time intervals (p) based on the quantity necessary to bring inventory up to

target maximum

p p p

Q1 Q2

Q3

Q4

Target maximum

Time

On-H

and I

nven

tory

64

Example 고정발주시스템에서�!  Back order = 3 units !  Product inventory = 0 unit !  Target Value = 50 unit !  이전에�한�주문은�없다. (None of earlier order)

이번에�몇개를�주문해야�하는가? What is Quantity for order in this time period?

Sol) Q = Taget – On-hand Inventory

– Earlier orders not yet received + Back Order = 50 – 0 – 0 + 3 = 53 units

65

Announcement !  HW

#  Review Examples #  Review Solved Problems

66

Good Bye!