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Transcript of 1 Introduction to Operations Management Inventory Management (Ch. 12) Hansoo Kim ( 金翰秀 ) Dept....
![Page 1: 1 Introduction to Operations Management Inventory Management (Ch. 12) Hansoo Kim ( 金翰秀 ) Dept. of Management Information Systems, YUST.](https://reader031.fdocuments.in/reader031/viewer/2022012919/56649e6f5503460f94b6c24c/html5/thumbnails/1.jpg)
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Introduction to Operations Management
Inventory Management Inventory Management (Ch. 12)(Ch. 12)
Hansoo Kim ( 金翰秀 )Dept. of Management Information
Systems, YUST
![Page 2: 1 Introduction to Operations Management Inventory Management (Ch. 12) Hansoo Kim ( 金翰秀 ) Dept. of Management Information Systems, YUST.](https://reader031.fdocuments.in/reader031/viewer/2022012919/56649e6f5503460f94b6c24c/html5/thumbnails/2.jpg)
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Schedule
5/27, 29 – Inventory Management 6/5 – 2nd Exam 6/10, 12 – Aggregated Production
Planning 6/17, 19 – MRP 6/26 – 3rd Exam 6/3, 24 – Location Theory
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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 MgmtForecasting
(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
XX XX
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Today’s Outline 재고란 ? (What is inventory?) 재고의 기능 (The function of inventory) 재고비용 항목 (Inventory Costs)
재고보관비 주문비 품절비
재고 모델 (Inventory Model) 정량발주모델
EOQ 모델 EPQ (or POQ) 모델 확률적 모델
정기발주모델
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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?)再발주 시점은 언제인가 ?(Reporder point?)
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Question 2 ?
당신은 할인 혜택을 받으시겠습니까 ?(Will you take discount or not?)몇 개를 주문해야 할까요 ?(How many quantity to be ordered?)
대안 할인 수량 할인률 (%) 할인가격 (P)
1 0 to 999 No discount $5.00
2 1,000 to 1,999 4 $4.80
3 2,000 and over 5 $4.75
년간수요 = 5000 units/yr, 주문비 =49$/order, 재고 보관비 비율 = 20%,
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재고란 ?What is Inventory?
Stock of materials Stored capacity
사용할 수 있으나 , 지금 당장 사용하지는 않는 물자들
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재고가 필요한 이유 (Why Inventory?)
예측하지 못한 수요에 대한 대응Meet unexpected demand
계절적 , 주기적 수요 변화에 대한 대응Smooth seasonal or cyclical demand
생산 공정의 독립성 제고 및 분리Decouple or separate various parts of the production process
가격할인의 잇점 ( 쌀때 왕창 사두자 !) Take advantage of price discounts
대량할인의 잇점Take advantage of quantity discounts
갑작스런 가격 상승에 대한 대비Hedge against price increases
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재고의 종류 (Types of Inventory) 원자재 (Raw Material)
가공되지 않은 구매된 자재 재공재고 (Work-In-Process)
원자재와 완재품 사이의 반제품 상태의 자재 소모품 (Maintenance/repair/operating sup
ply) 유지 보수 혹은 운영을 위해 소모되는 물품
완제품 재고완제품 재고 (Finished Goods) 판매 가능한 최종 제품
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자재의 흐름 (Material Flow)
비사용Raw Material
가공중WIP
판매가능Finished Goods
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재고의 문제점 (Problems caused by inventory) 재고 = 지금 당장 사용할 수 없는 자산
재고 관련 비용의 증가 구매비 , Item cost (if purchased) 주문비 , Ordering (or setup) cost 보관비 , Holding (or carrying) cost
창고 임대비 , 보험료 , 세금 등…
품절 비용 , Shortage Cost Temporary or permanent loss of sales when demand cannot
be met 재고 통제의 어려움 생산공정의 문제를 숨김
Hides production problems
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Scrap
Work in process inventory level(hides problems)
Unreliable Vendors
Capacity Imbalances
재공재고 (WIP) 가 많이 있는 경우
NO PROBLEM!!!Really?
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Scrap
암초에 걸리기 시작…문제가 드러남 !
Unreliable Vendors
Capacity Imbalances
WIP
재고 수준을 낮춘다면 ?
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재고의 분류Inventory Classifications
Inventory
Process stage
Demand Type
Number & Value Other
Raw Material WIP
Finished Goods
Independent Dependent
A Items B Items C Items
Maintenance Operating
© 1984-1994 T/Maker Co.
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재고의 수량과 가치에 따라 세 종류로 나눔Divides on-hand inventory into 3 classes
A class, B class, C class 년간 $ x 부피 ($ volume) 의 단위에 기초
Basis is usually annual $ volume $ volume = Annual demand x Unit cost
ABC 분석에 따른 전략Policies based on ABC analysis
A Class 제품을 집중 관리함
ABC 분석 (ABC Analysis)
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ABC 분석에 의한 재고 분류
Class % $ Vol % ItemsA 80 15B 15 30C 5 55
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ABC 분석에 의한 재고 분류 ( 예제 )
11 $ 60$ 60 909022 350350 404033 3030 13013044 8080 606055 3030 10010066 2020 18018077 1010 17017088 320320 505099 510510 6060
1010 2020 120120
PARTPART UNIT COSTUNIT COST ANNUAL USAGEANNUAL USAGE
Example 10.1Example 10.1
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ABC 분석에 의한 재고 분류
Example 10.1Example 10.1
11 $ 60$ 60 909022 350350 404033 3030 13013044 8080 606055 3030 10010066 2020 18018077 1010 17017088 320320 505099 510510 6060
1010 2020 120120
PARTPART UNIT COSTUNIT COST ANNUAL USAGEANNUAL USAGETOTAL % OF TOTAL % OF TOTALPART VALUE VALUE QUANTITY % CUMMULATIVE
9 $30,600 35.9 6.0 6.08 16,000 18.7 5.0 11.02 14,000 16.4 4.0 15.01 5,400 6.3 9.0 24.04 4,800 5.6 6.0 30.03 3,900 4.6 10.0 40.06 3,600 4.2 18.0 58.05 3,000 3.5 13.0 71.0
10 2,400 2.8 12.0 83.07 1,700 2.0 17.0 100.0
$85,400
AA
BB
CC
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ABC 분석에 의한 재고 분류
100 100 –
80 80 –
60 60 –
40 40 –
20 20 –
0 0 –| | | | | |00 2020 4040 6060 8080 100100
% of Quantity% of Quantity
% o
f V
alu
e%
of
Val
ue
AA
BBCC
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Example 1
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독립재고 대 종속재고Independent vs. Dependent Demand
독립재고 , Independent demand - demand for item is independent of demand for any other item (e.g. Finished goods)
종속재고 , Dependent demand - demand for item is dependent upon the demand for some other item
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Item Materials WithIndependent Demand
Materials WithDependent Demand
DemandSource Company Customers Parent Items
MaterialType Finished Goods WIP & Raw Materials
Method ofEstimatingDemand
Forecast & BookedCustomer Orders
Calculated
PlanningMethod EOQ & ROP MRP
독립재고 대 종속재고
It makes no sense to independently forecast dependent demands.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 비용일반적으로 재고 수량과 비례적 관계
Obsolescence ( 열화 ) Insurance ( 보험 ) Extra staffing ( 관리 ) Interest ( 이자 ) Pilferage ( 도난 ) Damage ( 손상 ) Warehousing ( 보관 ) Etc.
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주문비 (Ordering Cost)
물건을 주문하고 수령하는데 드는 비용일반적으로 제품의 수량과 관련이 없다
Supplies ( 공급관련 비용 ) Forms ( 양식 ) Order processing ( 주문처리 ) Clerical support ( 사무적 지원 ) 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 모델Fixed order-quantity models
경제적 주문 수량Economic order quantity (EOQ)
경제적 생산 수량Production order quantity (POQ)
대량할인Quantity discount
확률적 모델Probabilistic models
정기발주 모델Fixed order-period models
Help answer the inventory planning questions!
Help answer the inventory planning questions!
재고모델(Inventory Models)
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EOQ 모델의 가정 고정적이고 이미 알고 있는 수요
Known and constant demand 고정적이고 이미 알고 있는 리드타임 ( 배송시간 )
Known and constant lead time 순간적인 물자 입고
Instantaneous receipt of material 대량할인이 없다
No quantity discounts 주문비 ( 혹은 준비비 ) 와 보관비만 고려
Only order (setup) cost and holding cost 제품 품절은 없다
No stockouts
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재고 주문 사이클
Figure 10.1Figure 10.1
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주문량과 재고수준과의 관계
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EOQ 모델얼마를 주문해야 하는가 ?
Order quantity
Annual Cost
Holding Cost CurveTotal Cost Curve
Order (Setup) Cost Curve
Optimal Order Quantity (Q*)
Minimum total cost
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More units must be stored if more are ordered
Purchase OrderDescription Qty.Microwave 1
Order quantity
Purchase OrderDescription Qty.Microwave 1000
Order quantity
Why Holding Costs Increase
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Cost is spread over more units
Example: You need 1000 microwave ovens
Purchase OrderDescription Qty.Microwave 1
Purchase OrderDescription Qty.Microwave 1
Purchase OrderDescription Qty.Microwave 1
Purchase OrderDescription Qty.Microwave 1
1 Order (Postage $ 0.33) 1000 Orders (Postage $330)
Order quantity
Purchase OrderDescription Qty.Microwave 1000
Why Order Costs Decrease
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EOQ 구하는 법1. 주문비 ( 혹은 준비비 ) 에 대한 식을 구한다
Develop an expression for setup or ordering costs2. 보관비에 대한 식을 구한다
Develop an expression for holding cost3. 준비비와 보관비가 동일하게 수식을 세운다
Set setup cost equal to holding cost4. 수식을 풀면 , EOQ 가 계산 된다
Solve the resulting equation for the best order quantity
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계산 Holding Cost:
Ordering Costs: s per order, so
Calculation
D
hQ
hQ
Q
2cost holdingunit
2cost holding annual
2inventory average
Q
s
Q
Ds
cost setupunit
cost setup annual
?Q
Cost Setup Annual2
cost holding Annual
Q
Ds
D
hQ
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예제 ) Demand, D = 1000 racks per year
Price, P = $250
Ordering Cost, s = $500 (estimated from
supplier’s pricing)
Holding Cost, h = $35 per unit per year, or
H = IP, I = annual interest rate for
inventory carrying cost. Then, I = 1.4 %
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EOQ 모델의 비용 그래프
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
20.00
0 100 200 300 400 500
Order Quantity (Q)
Co
st
($/u
nit
)
hQ/2D
A/Qc
Y(Q)
Q* =169
S/QP
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Optimal Order Quantity
Expected Number of Orders
Expected Time Between Orders Working Days / Year
Working Days / Year
= =× ×
= =
= =
=
= ×
Q* D SH
ND
Q*
TN
dD
ROP d L
2
D = Demand per year
S = Setup (order) cost per order
H = Holding (carrying) cost
d = Demand per day
L = Lead time in days
EOQ Model Equations
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재발주점과 리드타임 The Reorder Point (ROP) Curve
Q*
ROP (Units)
Slope = units/day = d
Lead time = LTime (days)
Inve
ntor
y le
vel (
units
)
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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
timesQ
DN
IPH
DSQ
205250
1000
505
250
5200
1000
2001005.0
1010002
)(
2
*
*
**
*
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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?
24595.2445.0
10150022
100$5.02
20010
200
1000
2)(
*
H
DSQ
HQ
SQ
DQTC
125$5.02
20010
200
1500)200( TC
47.122$5.02
24510
245
1500)245( TC
%247.122
47.122125
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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 EOQ 와는 다른 가정
경제적 제품생산량을 결정하는데 유용하다Suited for production environment
Material produced, used immediately Provides production lot size
EOQ 모델 보다 재고 보관비용이 적게 나타난다Lower holding cost than EOQ model
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EOQ POQ (or EPQ) ModelWhen To Order
Time
Inve
ntor
y Le
vel
생산과 소비가 동시에 이루어
진다 소비만 이루어 진다Maximum
inventory level
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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* dp
Q
D
QS
p*
1
(
0.5 * H * Q -d
p1
)-d
p1
( )
2*D*S
( )Maximum inventory level
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Solution to POQ Model
Annual Cost Function:
Solution (by taking derivative and setting equal to zero):
DcQPDH
Q
SDQTC
2
)/1()(
setup holding production
)/1(
2*
PDH
SDQ
• tends to EOQ as P
• otherwise larger than EOQ because replenishment takes longer
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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*
PDH
DSPOQ
71.70$2
283)2000/10001(5.0
283
100010)283(
TC
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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 quantities
Other EOQ assumptions apply 가격할인과 재고보관 비용에 대한 절충
Trade-off is between lower price & increased holding cost
대량할인 모델Quantity Discount Model
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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 $4.75
D = 5000 units/yr, S=49$/order, I = 20%,
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대량할인 문제 푸는 방법1. 각각의 할인에 대해서 EOQ 를 사용하여 각각의 최적 주문량을 구한다 .
For each discount, calculate a value for optimal order size Q*, using EOQ formula
2. 만약 최적 주문량이 할인을 허용하는 최초치 보다 더 작을 경우 , 할인이 가능한 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 b
e the quantity that will minimize the total inventory cost
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Quantity Discount – How Much to Order
PDQH
SQ
DTC
2
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해답 – Price Discount ModelDiscount 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 $3
D = 5000 units/yr, S=49$/order, I = 20%,
unitsPI
SDQ
unitsPI
SDQ
unitsPI
SDQ
7182.0*3
5000*49*22
7142.0*8.4
5000*49*22
7002.0*5
5000*49*22
*3$
*8.4$
*5$
adjusting
50.822,24$,2000
725,24$,1000
700,25$,700
*3$
*8.4$
*5$
TCunitsQ
TCunitsQ
TCunitsQ
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다른 예제 ..Quantity Discount Example
QUANTITYQUANTITY PRICEPRICE
1 - 491 - 49 $1,400$1,400
50 - 8950 - 89 1,1001,100
90+90+ 900900
SS = = $2,500 $2,500
HH = = $190 per computer $190 per computer
DD = = 200200
QQ** = = = 72.5 PCs = = = 72.5 PCs22SDSD
HH2(2500)(200)2(2500)(200)
190190
TCTC = + + = + + PDPD = $233,784 = $233,784 SDSD
QQ**
HQHQ**
22
For For QQ = 72.5 = 72.5
TCTC = + + = + + PDPD = $194,105= $194,105SDSD
HQHQ
22
For For QQ = 90 = 90
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재발주점 계산 예제
년간수요 년간수요 , D = 10,000 units/year, D = 10,000 units/year
년간 작업일수년간 작업일수 , Store open , Store open 311311 days/year days/year
일간수요일간수요 , d = 10,000 / 311 = 32.154 units/day, d = 10,000 / 311 = 32.154 units/day
리드타임리드타임 , L = 10 days, L = 10 days
R = dL = (32.154)(10) = 321.54 unitsR = dL = (32.154)(10) = 321.54 units
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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 고려한다Consider service level & safety stock
봉사수준 , Service level = 1 - Probability of stockout ( 품절확률 )
더 높은 봉사수준을 위해서는 더 많은 안전재고가 필요하다Higher service level means more safety stock
더 많은 안전재고는 더 높은 재발주점을 의미한다 .More safety stock means higher ROP
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Probabilistic ModelsWhen to Order?
Reorder Point
(ROP)
Optimal Order
Quantity X
Safety Stock (SS)
Time
Inventory Level
Lead Time
SSROP
Service Level P(Stockout)
Place order
Receive order
Frequency
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안전재고 (Safety Stocks)
Safety stock (Safety stock ( 안전재고안전재고 )) 제품의 품절을 줄이기 위해제품의 품절을 줄이기 위해 , , 리드타임 동안의 수요에 대비한 리드타임 동안의 수요에 대비한
추가적인 재고추가적인 재고buffer added to on hand inventory during lead timebuffer added to on hand inventory during lead time
Stockout (Stockout ( 품절품절 )) 재고 부족 재고 부족 (an inventory shortage)(an inventory shortage)
Service level (Service level ( 봉사 봉사 or or 서비스 수준서비스 수준 )) 리드타임 동안의 재고가 부족하지 않을 확률리드타임 동안의 재고가 부족하지 않을 확률
probability that the inventory available during lead probability that the inventory available during lead time will meet demandtime will meet demand
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Variable Demand with a Reorder Point
ReorderReorderpoint, point, RR
LTLT
TimeTimeLTLT
Inve
nto
ry le
vel
Inve
nto
ry le
vel
00
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Reorder Point with a Safety Stock
Figure 10.6Figure 10.6
ReorderReorderpoint, point, RR
LTLT
TimeTimeLTLT
Inve
nto
ry le
vel
Inve
nto
ry le
vel
00
Safety Stock
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예제 10
재발주점 계산 ROP = d*L + SS, SS=Safety Stock (ROP = d*L + SS, SS=Safety Stock ( 안전재고안전재고 )) d*L=50 units H=$5/ 년 , 품절비용 (C)=$40/ 개 , 년간 발주수 =6
Number of Units Probability
3040506070
0.20.20.30.20.1
Demand for reorder period
Safety StockInventory Holding
CostStockout Cost Total Cost
20100
20*$5=10010*$5=50
0
010*0.1*$40*6=240
10*0.2*$40*6+20*0.1*$40*6=960
$100$290$960
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얼마나 주문할 것인가에 대해 답변Answers how much to order
주문을 일정한 간격으로 한다Orders placed at fixed intervals
적정재고 수준까지 주문Inventory 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
고정발주시스템Fixed Period Model
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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 targ
et maximum
pp pp pp
QQ11 QQ22
QQ33
QQ44
Target maximum
TimeTime
On-
Hand
Inve
ntor
yO
n-Ha
nd In
vent
ory
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Example고정발주시스템에서 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
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Announcement
Next Week 2nd Exam (LP), Queueing, Supply Chain, Inventory
HW Review Examples Review Solved Problems
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Good Bye!