presentasi perkuliahan Manajemen Kinerja operasi bab LengkapManagingInventoryEOQ

magister manajemen LengkapManagingInventoryEOQ

1. 12 -1
Managing Inventory
PowerPoint presentation to accompany
Heizer and Render
Operations Management, Global Edition, Eleventh Edition
Principles of Operations Management, Global Edition, Ninth Edition
PowerPoint slides by Jeff Heyl
12
© 2014 Pearson Education

2. 12 -2© 2011 Pearson Education, Inc. publishing as Prentice Hall
Outline
1.Types of Inventory
2.Functionsof Inventory
3.ABC Analysis
4.Record Accuracy
5.Cycle Counting
6.Independent vs. Dependent
DemandInventory Control
Systems

3. 12 -3© 2011 Pearson Education, Inc. publishing as Prentice Hall
Outline –Continued
7.Multi-PeriodDeterministicInventory
Models
I.Fixed-OrderQuantityModels
Economic OrderQuantity(EOQ)
Model.
ProductionOrderQuantity(POQ)
Model.
QuantityDiscountModel.
II.Fixed-TimePeriodModels
8.ProbabilisticModelsandSafetyStock
9.Single-PeriodInventoryModel

4. 12 -4© 2011 Pearson Education, Inc. publishing as Prentice Hall
Amazon.com
Amazon.com started as a “virtual”
retailer –no inventory, no
warehouses, no overhead; just
computers taking orders to be filled
by others
Growth has forced Amazon.com to
become a world leader in
warehousing and inventory
management

5. 12 -5© 2011 Pearson Education, Inc. publishing as Prentice Hall
Inventory Management
Tujuanmanajemenpersediaan
adalahuntukmencapai
keseimbanganantarainvestasi
persediaandanpelayanan
pelanggan

6. 12 -6
Inventory
Process
stage
Demand
Type
Number
& Value
Other
Raw Material
WIP
Finished Goods
Independent
Dependent
A Items
B Items
C Items
Maintenance
Repair
Operating
Inventory Classifications

7. 12 -7© 2011 Pearson Education, Inc. publishing as Prentice Hall
Functions of Inventory
1.Untuk memisahkanberbagai bagian
dari proses produksi dengan
mengcover penundaan
2.Untuk melindungiperusahaan dari
fluktuasi permintaan
3.Untuk memberikan pilihan bagi
pelanggan
4.Untuk memanfaatkandiskon kuantitas
5.Untuk lindung nilai (hedge) terhadap
inflasi

8. 12 -8
Problems Caused by Inventory
Persediaan mengikat modal
kerja
Persediaan memakan ruang
Persediaan rentan terhadap:
Kerusakan, Pencurian, dan
Keusangan
Persediaan menyembunyikan
masalah

9. 12 -9© 2011 Pearson Education, Inc. publishing as Prentice Hall
The Material Flow Cycle
Figure 12.1
InputWait for Wait toMoveWait in queueSetupRun Output
inspectionbe moved timefor operatortimetime
Cycle time
95% 5%

10. 12 -10© 2011 Pearson Education, Inc. publishing as Prentice Hall
ImportantIssuesin
Inventory Management
1.Classifying inventory
items
2.Keepingaccurate
inventory records

11. 12 -1112-11
ABC Classification System
Classifying inventory according to
some measure of importance and
allocating control efforts accordingly.
A-very important
B-mod. important
C-least important
Annual
$ value
of items
A
B
C
High
Low
Low High
Percentage of Items

12. 12 -12
ABC Worked Example
Item Usage and Value

13. 12 -13
ABC Worked Example
Annual Usage Values

14. 12 -14
ABC Worked Example
Ascending Usage Values

15. 12 -15
ABC Worked Example
ABC Chart Showing Classifications

16. 12 -16© 2011 Pearson Education, Inc. publishing as Prentice Hall
ABC Classification System
Policies employed for A items
may include
More emphasis on supplier
development
Tighter physical inventory
control
More care in forecasting

17. 12 -17© 2011 Pearson Education, Inc. publishing as Prentice Hall
Inventory Record Accuracy&Cycle
Counting
Items are counted and records are
updated on a periodic basis
Often used with ABC analysis
to determine thecycle
(frequencyof counting)
Eliminates shutdowns and interruptions
Maintainsaccurate inventory records

18. 12 -18© 2011 Pearson Education, Inc. publishing as Prentice Hall
Cycle Counting Example2,
page516, Ch.12
5,000itemsininventory,500Aitems,1,750B
items,2,750Citems
PolicyistocountAitemseverymonth(20working
days),Bitemseveryquarter(60days),andC
itemseverysixmonths(120days)
Item
ClassQuantityCycle Counting Policy
Number of Items
Counted per Day
A 500 Each month 500/20 = 25/day
B 1,750Each quarter 1,750/60 = 29/day
C 2,750Every 6 months 2,750/120 = 23/day
Total 5000 77/day

19. 12 -19
RecordAccuracyandInventory Counting Systems
Periodic Inventory CountingSystem
Penghitunganfisikbarangdilakukan
denganinterval periodik(mingguan,
bulananatautahunan)
Perpetual (continual) Inventory
Counting System
Sistem Komputer yang melacak
pemindahan dari persediaansecara terus
menerus, sehingga memantau level saat ini
dari setiap item(Bar code Technology)

20. 12 -20© 2011 Pearson Education, Inc. publishing as Prentice Hall
Independent andDependent Demand
Inventory Management Systems
Independent demand-permintaan
untukitem tersebuttidak
tergantungpadapermintaanuntuk
item lain dalampersediaan
Dependent demand-permintaan
untukitem tergantungpada
permintaanuntukbeberapaitem
lain dalampersediaan

21. 12 -2121
ExamplesforIndependent Versus
Dependent Demand
Independent demand –finished goods,
items that are ready to be soldsuch as
computers, cars.
Forecasts are used to develop production and
purchase schedules for finished goods.
Dependent demand –components of
finished products(computers, cars) such
as chips, tires and engine
Dependent demand inventory control
techniques utilize material requirements
planning (MRP) logic to develop production
and purchase schedules(Ch14)

22. 12 -2222
Independent Demand
A
B(4) C(2)
D(2) E(1)D(3) F(2)
Dependent Demand
Independent demand is uncertain. That is why it is forecasted.
Dependent demand is certainand it is calculated.
Inventory

23. 12 -2323
How Muchto Order?
Whento order?
Regardless of the nature of demand
(independent, dependent) two
fundamental issues underlie all
inventory planning:

24. 12 -24
IndependentDemandInventory Modelsto
AnswerTheseQuestions
1)Single-Period Inventory Model:One time
orderingdecision suchas selling t-shirts at a
football game, newspapers, fresh bakery
products. Objectiveis to balance the costof
running out of stock with thecostof
overstocking.The unsold items, however, may
have some salvage values.
2)Multi-Period Inventory Models
Fixed-Order Quantity Models: Eachtime a fixed
amountof orderis placed.
EconomicOrderQuantity(EOQ) Model
ProductionOrderQuantity(POQ) Model
QuantityDiscountModels
Fixed-Time Period Models:Ordersare placed at
specific timeintervals.

25. 12 -25
Lead time:time interval between ordering and receiving
the order
Holding (carrying) costs:cost to carry an item in
inventory for a length of time, usually a year (heat, light,
rent, security, deterioration, spoilage, breakage,
depreciation, opportunity cost,…, etc.,)
Ordering costs:costs of ordering and receiving
inventory (shipping cost, preparing invoices, cost of
inspecting goods upon arrival for quality and quantity,
moving the goods to temporary storage)
Set-up Cost: cost to prepare a machine or process for
manufacturing an order
Shortage costs:costs when demand exceeds supply,
the opportunity cost of not making a sale
Key Inventory Terms

26. 12 -26© 2011 Pearson Education, Inc. publishing as Prentice Hall
Basic EOQ Model
1.Demand is known, constant, and
independent
2.Lead time is known and constant
3.Receipt of inventory is instantaneous and
complete
4.Quantity discounts are not possible
5.Only variable costs are orderingand
holding
6.Stockouts can be completely avoided
Important assumptions

27. 12 -27© 2011 Pearson Education, Inc. publishing as Prentice Hall
Inventory Usage Over Time
Figure 12.3
Order
quantity = Q
(maximum
inventory
level)
Usage rateAverage
inventory
on hand
Q
2
Minimum
inventory
Inventory level
Time
0

28. 12 -28
The Inventory Cycle
Quantity
on hand
(maximum
İnventory)
Q
Receive
order
Place
order
Receive
order
Place
order
Receive
order
Lead time
Reorder
point
Usage
rate
Time

29. 12 -29© 2011 Pearson Education, Inc. publishing as Prentice Hall
Minimizing Costs
Objective is to minimize total costs
Table 12.4(c)
Annual cost
Order quantity
Total cost of
holding and
setup (order)
Holding cost
Setup (or order)
cost
Minimum
total cost
Optimal order
quantity (Q*)

30. 12 -30© 2011 Pearson Education, Inc. publishing as Prentice Hall
The EOQ Model
Q= Order Quantity
Q*= Optimal number of pieces per order (EOQ)
D= Annual demand in units for the inventory item
S= Setup or ordering cost for each order
H= Holding or carrying cost per unit per year
Annual setup cost =(Number of orders placed per year)
x (Setup or order cost per order)
Annual demand
Order Quantity
Setup or order
cost per order
=
Annual setup cost = S
D
Q
= (S)
D
Q

31. 12 -31© 2011 Pearson Education, Inc. publishing as Prentice Hall
The EOQ Model
Q= Order Quantity
Q*= Optimal number of pieces per order (EOQ)
D= Annual demand in units for the inventory item
S= Setup or ordering cost for each order
H= Holding or carrying cost per unit per year
Annual holding cost =(Average inventory level)
x (Holding cost per unit per year)
Order quantity
2
= (Holding cost per unit per year)
= (H)
Q
2
Annual setup cost = S
D
Q
Annual holding cost = H
Q
2

32. 12 -32© 2011 Pearson Education, Inc. publishing as Prentice Hall
The EOQ Model
Q= Order Quantity
Q*= Optimal number of pieces per order (EOQ)
D= Annual demand in units for the inventory item
S= Setup or ordering cost for each order
H= Holding or carrying cost per unit per year
Optimal order quantity is found when annual setup cost
equals annual holding costor we take the derivative of
the total cost function and set the derivative (slope)
equal to zero and solve for Q
Annual setup cost = S
D
Q
Annual holding cost = H
Q
2
D
Q
S= H
Q
2
Solving for Q*
2DS= Q
2
H
Q
2
= 2DS/H
Q* = 2DS/H

33. 12 -33© 2011 Pearson Education, Inc. publishing as Prentice Hall
An EOQ Example
Determine optimal number of needles to order(Q)
D= 1,000 unitsper year
S= $10 per order
H= $.50 per unit per year
Q* =
2DS
H
Q* =
2(1,000)(10)
0.50
= 40,000 = 200 units

34. 12 -34© 2011 Pearson Education, Inc. publishing as Prentice Hall
An EOQ Example
Determine expected number orders per year (N)
D= 1,000 units Q*= 200 units
S= $10 per order
H= $.50 per unit per year
= N= =
Expected
number of
orders
Demand
Order quantity
D
Q*
N= = 5 orders per year
1,000
200

35. 12 -35© 2011 Pearson Education, Inc. publishing as Prentice Hall
An EOQ Example
Determine expected time between orders (T)
D= 1,000 units Q*= 200 units
S= $10 per order N= 5 orders per year
H= $.50 per unit per year
= T=
Expected
time between
orders
Number of working
days per year
N
T= = 50 days between orders
250
5

36. 12 -36© 2011 Pearson Education, Inc. publishing as Prentice Hall
An EOQ Example
Determine total annual cost:
D= 1,000 units Q*= 200 units
S= $10 per order N= 5 orders per year
H= $.50 per unit per yearT= 50 days
Total annual cost = Setup cost + Holding cost
TC= S+ H
D
Q
Q
2
TC= ($10) + ($.50)
1,000
200
200
2
TC= (5)($10) + (100)($.50) = $50 + $50 = $100

37. 12 -37© 2011 Pearson Education, Inc. publishing as Prentice Hall
Robust Model
The EOQ model is robust
It works even if all parameters
and assumptions are not met
Becausethe total cost
curve is relatively flat in
the area of the EOQ

38. 12 -38© 2011 Pearson Education, Inc. publishing as Prentice Hall
Minimizing Costs
Objective is to minimize total costs
Table 12.4(c)
Annual cost
Order quantity
Total cost of
holding and
setup (order)
Holding cost
Setup (or order)
cost
Minimum
total cost
Optimal order
quantity (Q*)

39. 12 -39© 2011 Pearson Education, Inc. publishing as Prentice Hall
An EOQ Example
Suppose Management underestimatesdemand by 50%
D= 1,000 units Q*= 200 units
S= $10 per order N= 5 orders per year
H= $.50 per unit per yearT= 50 days
TC= S+ H
D
Q
Q
2
TC= ($10) + ($.50) = $75 + $50 = $125
1,500
200
200
2
1,500 units

40. 12 -40© 2011 Pearson Education, Inc. publishing as Prentice Hall
An EOQ Example
Actual EOQ for new demand is 244.9 units
D= 1,000 units Q*= 244.9 units
S= $10 per order N= 5 orders per year
H= $.50 per unit per yearT= 50 days
TC= S+ H
D
Q
Q
2
TC= ($10) + ($.50)
1,500
244.9
244.9
2
1,500 units
TC= $61.24 + $61.24 = $122.48
Only 2% less
than the total
cost of $125
when the
order quantity
was 200

41. 12 -41© 2011 Pearson Education, Inc. publishing as Prentice Hall
Production Order Quantity (POQ)
Model
The third assumption of EOQ model
is relaxed: Receipt of inventory is
not instantaneous and complete
Units are produced and used/or
sold simultaneously
Production is done in batches or
lots
Capacity to produce a part exceeds
the part’s usage or demand rate
Hence, inventory builds up over a
period of time after an order is
placed

42. 12 -42© 2011 Pearson Education, Inc. publishing as Prentice Hall
Production Order Quantity
Model
Inventory level
Time
Demand part of cycle
with no production
Part of inventory cycle during
which production (and usage)
is taking place
t
Maximum
inventory
Figure 12.6

43. 12 -43© 2011 Pearson Education, Inc. publishing as Prentice Hall
Production Order Quantity
Model
Q=Order Quantity p=Daily production rate
H=Holding cost per unit per yeard=Daily demand/usage rate
t=Length of the production run in days
= (Average inventory level) x
Annual inventory
holding cost
Holding cost
per unit per year
= (Maximum inventory level)/2
Annual inventory
level
= –
Maximum
inventory level
Total produced during
the production run
Total used during
the production run
= pt–dt

44. 12 -44© 2011 Pearson Education, Inc. publishing as Prentice Hall
Production Order Quantity
Model
Q=Order Quantity p=Daily production rate
H=Holding cost per unit per yeard=Daily demand/usage rate
t=Length of the production run in days
= –
Maximum
inventory level
Total produced during
the production run
Total used during
the production run
= pt–dt
However, Q= total produced = pt; thus t= Q/p
Maximum
inventory level
= p –d = Q1 –
Q
p
Q
p
d
p
Holding cost = (H) = 1 – H
d
p
Q
2
Maximum inventory level
2

45. 12 -45© 2011 Pearson Education, Inc. publishing as Prentice Hall
Production Order Quantity
Model
Q=Order Quantity p=Daily production rate
H=Holding cost per unit per yeard=Daily demand/usage rate
D=Annual demand
Q
2
=
2DS
H[1 -(d/p)]
Q* =
2DS
H[1 -(d/p)]
p
Setup cost =(D/Q)S
Holding cost =HQ[1 -(d/p)]
1
2
(D/Q)S= HQ[1 -(d/p)]
1
2

46. 12 -46© 2011 Pearson Education, Inc. publishing as Prentice Hall
Production Order Quantity Example
D=1,000 units p=8 units per day
S=$10 d=4 units per day
H=$0.50 per unit per year# of days plant is open=250
Q* =
2DS
H[1 -(d/p)]
= 282.8 or 283 hubcaps
Q* = = 80,000
2(1,000)(10)
0.50[1 -(4/8)]

47. 12 -47© 2011 Pearson Education, Inc. publishing as Prentice Hall
Production Order Quantity
Model
When annual data are used the equation becomes
Q* =
2DS
annual demand rate
annual production rate
H1 –
Note:
d= 4 = =
D
Number of days the plant is in operation
1,000
250

48. 12 -48© 2011 Pearson Education, Inc. publishing as Prentice Hall
Quantity Discount Models
These models are used where the price of
the item ordered varies with the order size.
Reduced prices are often available when
larger quantities are ordered.
The buyer must weigh the potential
benefits of reduced purchase price and
fewer orders that will result from buying in
large quantities against the increase in
carrying cost caused by higher average
inventories.
Hence, three is trade-off is between
reducedpurchasing and orderingcost
and increased holding cost

49. 12 -49
Total Costs with Purchasing Cost
Annual
carrying
cost
Purchasing
cost
TC = +
Q
2
H
D
Q
STC = +
+
Annual
ordering
cost
PD+
Where P is the unit price.
Rememberthat the basic EOQ modeldoesnot take into
consideration the purchasing cost. Because this model works
under the assumption of no quantity discounts, price per unit is
the same for all order size. Note that including purchasing cost
would merely increase the total cost by the amount P times the
demand (D). See the following graph.

50. 12 -50
Total Costs with Purchasing Cost
Cost
EOQ
TC with PD
TC without PD
PD
0 Quantity
Adding Purchasing cost
doesn’t change EOQ

51. 12 -51
Quantity Discount Models
There are two general cases of
quantity discount models:
1.Carrying costs are constant(e.g.
$2 per unit).
2.Carrying costs are stated as a
percentage of purchase price
(20% of unit price)
© 2011 Pearson Education, Inc. publishing as Prentice Hall

52. 12 -52
Total Cost with Constant Carrying Costs
OC
EOQ
Quantity
Total Cost
TC
a
TC
c
TC
b
Decreasing
Price
CC
a,b,c
In this case there is a
single minimum point;
all curves will have
their minimum point at
the same quantity

53. 12 -53
EOQ when carrying cost is constant
1.Hitungtitikminimum umumdenganmenggunakan
model kuantitaspesananekonomidasar.
2.Hanyasatudarihargasatuanyang akanmemilikititik
minimum dalamrentangyang layakkarenarentang
tersebuttidaktumpangtindih. Identifikasirentangitu:
a) jikatitikminimum yang layakberadapadakisaranharga
terendah, itulahkuantitaspesananyang optimal.
b) jikatitikminimum yang layakadalahrentanglain, hitung
biayatotal untuktitikminimum danuntukjedahargadari
semuabiayaunit yang lebihrendah. Bandingkantotal
biaya; kuantitasyang menghasilkanbiayaterendahadalah
kuantitaspesananyang optimal.

54. 54
Quantity Discount Model with
Constant Carrying Cost
QUANTITY PRICE
1 -49 $1,400
50 -89 1,100
90+ 900
S=$2,500
H=$190 per computer
D=200
Q
opt= = = 72.5 PCs
2SD
H
2(2500)(200)
190
TC= + + PD = $233,784
SD
Q
opt
H Q
opt
2
For Q= 72.5
TC= + + PD = $194,105
SD
Q
H Q
2
For Q= 90

55. 55
BiayaTotal denganBiayaPenyimpananyang bervariasi
Ketika biaya penyimpanan dinyatakan sebagai persentase dari harga satuan, setiap
kurva akan memiliki titik minimum yang berbeda.
TC
a
TC
b
TC
c
CC
a
CC
b
CC
c
Cost
Quantity
OC

56. 12 -56
EOQ when carrying cost is a percentage of
the unit price
1.Dimulai dengan harga satuan terendah, hitung
titik minimum untuk setiap rentang harga
hingga Anda menemukan titik minimum yang
layak (yaitu, hingga titik minimum berada
dalam kisaran kuantitas harganya).
2.Jika titik minimum untuk harga satuan terendah
layak, itu adalah jumlah pesanan yang optimal.
Jika titik minimum tidak layak dalam kisaran
harga terendah, bandingkan total biaya pada
jeda harga untuk semua harga yang lebih
rendah dengan total biaya titik minimum yang
layak. Kuantitas yang menghasilkan total biaya
terendah adalah yang optimal

57. 12 -57© 2011 Pearson Education, Inc. publishing as Prentice Hall
Quantity Discount Models
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
Table 12.2
A typical quantity discount schedule, Inventory
Carrying cost is 20% of unit price

58. 12 -58© 2011 Pearson Education, Inc. publishing as Prentice Hall
Whencarrying costs are specified as a percentage of
unitprice, thetotal costcurveis brokenintodifferent
total costcurvesforeachdiscountrange
1,000 2,000
Total cost $
0
Order quantity
Q* for discount 2 is below the allowable range at point a
and must be adjusted upward to 1,000 units at point b
a
b
1st price
break
2nd price
break
Total cost
curve for
discount 1
Total cost curve for discount 2
Total cost curve for discount 3
Figure 12.7

59. 12 -59© 2011 Pearson Education, Inc. publishing as Prentice Hall
Quantity Discount Example
Calculate Q* first forthe lowest
price range
Q* =
2DS
IP
Q
3* = = 718cars/order
2(5,000)(49)
(.2)(4.75)
Q
2* = = 714 cars/order
2(5,000)(49)
(.2)(4.80)
Q
1* = = 700cars/order
2(5,000)(49)
(.2)(5.00)

60. 12 -60© 2011 Pearson Education, Inc. publishing as Prentice Hall
Quantity Discount Example
Q* =
2DS
IP
Q
1* = = 700 cars/order
2(5,000)(49)
(.2)(5.00)
Q
2* = = 714 cars/order
2(5,000)(49)
(.2)(4.80)
Q
3* = = 718 cars/order
2(5,000)(49)
(.2)(4.75)
1,000 —adjusted
2,000 —adjusted

61. 12 -61© 2011 Pearson Education, Inc. publishing as Prentice Hall
Quantity Discount Example
Discount
Number
Unit
Price
Order
Quantity
Annual
Product
Cost
Annual
Ordering
Cost
Annual
Holding
Cost Total
1 $5.00 700 $25,000 $350 $350$25,700
2 $4.801,000 $24,000 $245 $480$24,725
3 $4.752,000 $23.750$122.50 $950$24,822.50
Table 12.3
Choose the price and quantity that gives
the lowest total cost
Buy 1,000 units at $4.80 per unit

62. 12 -62
When to Reorder with EOQ Ordering
Model EOQ menjawab persamaan berapa banyak yang
harus dipesan, tetapi bukan pertanyaan kapan harus
memesan. Titik pemesanan ulang terjadi ketika jumlah
yang ada turun ke jumlah yang telah ditentukan
sebelumnya.
Jumlah itu umumnya termasuk permintaan yang
diharapkan selama waktu tunggu.
Untuk mengetahui kapan titik pemesanan ulang telah
tercapai, diperlukan persediaan perpetual.
Tujuan pemesanan adalah melakukan pemesanan
ketika jumlah persediaan yang ada cukup untuk
memenuhi permintaan selama waktu yang dibutuhkan
untuk menerima pesanan tersebut. (i.e., lead time)

63. 12 -63© 2011 Pearson Education, Inc. publishing as Prentice Hall
WhentoOrder: Reorder Points(Makesure
demandandleadtime areexpressedin the
same time units)
If the demand and lead time are both
constant, the reorder point (ROP) is
simply:
ROP =
Lead time for a
new order in days
Demand
per day
= dx L
d=
D
Number of working days in a year

64. 12 -64© 2011 Pearson Education, Inc. publishing as Prentice Hall
Reorder Point Curve
Q*
ROP
(units)Inventory level (units)
Time (days)
Figure 12.5
Lead time = L
Slope = units/day = d
Resupply takes place as order arrives

65. 12 -65© 2011 Pearson Education, Inc. publishing as Prentice Hall
Reorder Point Example
Demand = 8,000 iPods per year
250 working day year
Lead time for orders is 3 working days
ROP = dx L
d=
D
Number of working days in a year
= 8,000/250 = 32 units
= 32 units per day x 3 days = 96 units

66. 12 -66
When to reorder
Ketika variabilitas hadir dalam permintaan atau
lead time, itu menciptakan kemungkinan bahwa
permintaan aktual akan melebihi permintaan
yang diharapkan.
Konsekuensinya, perlu membawa persediaan
tambahan, yang disebut “safety stock”, untuk
mengurangi risiko kehabisan stok selama lead
time. Titik pemesanan kembali kemudian
meningkat dengan jumlah persediaan
pengaman:ROP = expected demand during
lead time + safety stock (SS)

67. 67
Safety Stock
LT Time
Expected demand
during lead time
Maximum probable demand
during lead time
ROP
Quantity
Safety stock
Safety stock reduces risk of
stockout during lead time

68. 68
Safety stock
•Karena menyimpan persediaan pengaman memerlukan
biaya, seorang manajer harus dengan hati-hati
mempertimbangkan biaya membawa persediaan
pengaman terhadap pengurangan risiko kehabisan
persediaan yang ditimbulkannya.
•Tingkat layanan pelanggan meningkat karena risiko
kehabisan stok berkurang.
•Siklus pesanan "tingkat layanan" dapat didefinisikan
sebagai probabilitas bahwa permintaan tidak akan
melebihi pasokan selama waktu tunggu. Tingkat layanan
95% menyiratkan probabilitas 95% bahwa permintaan
tidak akan melebihi pasokan selama waktu tunggu.

69. 69
Safety Stock
•The “risk of stockout” is the complement of
“service level”
Service level = 1 -Probability of stockout
•Higher service level means more safety
stock
•More safety stock means higher ROP
ROP = expected demand during lead time + safety stock (SS)

70. 70
Reorder Point witha Safety Stock
Reorder
point, R
Q
LT
Time
LT
Inventory level
0
Safety Stock

71. 12 -71
Probabilistic Models toDetermineROP and
Safety Stock(WhenStockoutCost/Unitis
known)
▶Use safety stock to achieve a desired
service level and avoid stockouts
ROP = dx L+ ss
Annual stockout costs = the sum of the
units short foreachdemandlevelxthe probability
of thatdemandlevelxthe stockout cost/unit
xthe number of orders per year(Equation12-12)

72. 12 -72
EXAMPLE 10 (pg.531): Probabilisticdemand,
constantleadtime, stockoutcost/unitis known
© 2011 Pearson Education, Inc. publishing as Prentice Hall

73. 12 -73
EXAMPLE 10 (pg.531): Probabilisticdemand,
constantleadtime, stockoutcost/unitis known
© 2011 Pearson Education, Inc. publishing as Prentice Hall

74. 12 -74
Safety Stock Example
(Stochasticdemandandconstantleadtime)
NUMBER OF UNITS PROBABILITY
30 .2
40 .2
ROP 50 .3
60 .2
70 .1
1.0
ROP = 50 units Stockout cost = $40 per frame
Opt. # of Orders per year(N)= 6
Carrying cost = $5 per frame per year(SS ???)

75. 12 -75
Safety Stock Example
ROP = 50 units Stockout cost = $40 per frame
Orders per year = 6 Carrying cost = $5 per frame per year
SAFETY
STOCK
ADDITIONAL
HOLDING COST STOCKOUT COST
TOTAL
COST
20 (20)($5) = $100 $0 $100
10 (10)($5) = $ 50(10)(.1)($40)(6) =$240 $290
0 $ 0(10)(.2)($40)(6) + (20)(.1)($40)(6)=$960 $960
A safety stock of 20 frames gives the lowest total cost
ROP = 50 + 20 = 70 frames

76. 12 -76
Probabilistic Models to Determine ROP
and Safety Stock (whenthecostof
stockoutscannot be determined)
Desiredservicelevelsareusedto
setsafetystock
ROP = demand during lead time + Zs
dLT
where Z=Number of standard deviations
below (or above) the mean
s
dLT=Standard deviation of demand
during lead time

77. 12 -77
From non-standard normal to
standard normal
X is a normal random variable with
mean μ,and standard deviation σ
Set Z=(X–μ)/σ
Z=standard unit or z-score of X
Then Z has a standard normal
distribution with mean 0 and
standard deviation of 1.

78. 12 -78© 2011 Pearson Education, Inc. publishing as Prentice Hall

79. 12 -79© 2011 Pearson Education, Inc. publishing as Prentice Hall

80. 12 -80© 2011 Pearson Education, Inc. publishing as Prentice Hall
Probabilistic Demand
Safety
stock
Probability of
no stockout
95% of the time
Mean
demand
350
ROP = ? kits Quantity
Number of standard
deviationsbelow or
above the mean
0 z
Risk of a stockout
(5% of area of
normal curve)

81. 12 -81
Probabilistic Example
m=Average demand during lead time = 350
resuscitation kits
s
dLT=Standard deviation of demand during lead
time = 10 kits
Z=5% stockout policy (service level = 95%)
Using Appendix I, for an area under the curve of
95%, the Z= 1.65
Safety stock = Zs
dLT= 1.65(10) = 16.5 kits
Reorder point=Expected demand during lead time +
Safety stock
=350 kits + 16.5 kits of safety stock
=366.5 or 367 kits

82. 12 -82© 2011 Pearson Education, Inc. publishing as Prentice Hall
Safety stock16.5 units
ROP 
Place
order
Probabilistic Demand
Inventory level
Time
0
Minimum demand during lead time
Maximum demand during lead time
Mean demand during lead time
Normal distribution probability of
demand during lead time
Expected demand during lead time (350 kits)
ROP = 350 + safety stock of 16.5 = 366.5
Receive
order
Lead
time
Figure 12.8

83. 12 -83
Other Probabilistic Models
todetermineSS andROP
▶When data on demand during lead
time is not available, there are other
models available
1.When demand per day is variable and
lead time (in days) is constant
2.When lead time (in days) is variable
and demand per day is constant
3.When both demand per day and lead
time (in days) are variable

84. 12 -84
Demandper day is variable and
lead time (in days) is constant
ROP =(Averagedaily demand)
*Lead time in days) + Zs
dLT
wheres
dLT= s
dLead time
s
d= standard deviation of demand per day

85. 12 -85
Example
Average daily demand (normally distributed) = 15
Lead time in days (constant) = 2
Standard deviation of daily demand = 5
Service level = 90%
Zfor 90% = 1.28
From Appendix I
ROP= (15 units x 2 days) + Zs
dLT
= 30 + 1.28(5)( 2)
= 30 + 9.02 = 39.02 ≈ 39
Safety stock is about 9 computers

86. 12 -86
Lead time (in days) is variable
and demand perdayis constant
ROP =(Daily demand *Averagelead time in
days) +Z*(Daily demand) *s
LT
wheres
LT= Standard deviation of lead time in days

87. 12 -87
Example
Daily demand (constant) = 10
Average lead time = 6 days
Standard deviation of lead time = s
LT= 1
Service level = 98%, so Z(from Appendix I) = 2.055
ROP= (10 units x 6 days) + 2.055(10 units)(1)
= 60 + 20.55 = 80.55
Reorder point is about 81 cameras

88. 12 -88
Both demand perdayand lead
time (in days) are variable
ROP =(Average daily demand
x Average lead time) + Zs
dLT
wheres
d=Standard deviation of demand per day
s
LT=Standard deviation of lead time in days
s
dLT=(Average lead time x s
d
2
)
+ (Average daily demand)
2
s
2
LT

89. 12 -89
Example
Average daily demand (normally distributed) = 150
Standard deviation = s
d= 16
Average lead time 5 days (normally distributed)
Standard deviation = s
LT= 1 day
Service level = 95%, so Z= 1.65 (from Appendix I)ROP=(150 packs´5 days)+1.65s
dLT
s
dLT
=5 days´16
2
( )+150
2
´1
2
( )=5´256( )+22,500´1( )
=1,280( )+22,500( )=23,780@154
ROP =(150´5)+1.65(154)@750+254=1,004 packs

90. 12 -90
Used to handle ordering of
perishables(fresh fruits,
flowers)and other items with
limited useful lives
(newspapers, spare parts for
specialized equipment).
Single-Period Inventory Model

91. 12 -91
Single-PeriodInventory
Model
In a single-period model, items are
received in the beginning of a period and
sold during the same period. The unsold
items are not carried over to the next
period.
The unsold items may be a total waste, or
sold at a reduced price, or returned to the
producer at some price less than the
original purchase price.
The revenue generated by the unsold
items is called the salvage value.

92. 12 -92© 2011 Pearson Education, Inc. publishing as Prentice Hall
Single Period Model
Only one order is placed for a product
Units have little or no value at the end of
the sales period
C
s= Cost of shortage = Cost of understocking
= Sales price/unit –Cost/unit= lost profit
C
o= Cost of overage = Cost of overstocking
= Cost/unit –Salvage value
Service level =
C
s
C
s+ C
o

93. 12 -93
Single Period
Example 15, pg.536
© 2011 Pearson Education, Inc. publishing as Prentice Hall

94. 12 -94© 2011 Pearson Education, Inc. publishing as Prentice Hall
Single Period
Example15, pg.536
Average demand = m=120 papers/day
Standard deviation = s= 15 papers
C
s= cost of shortage = $1.25 -$.70 = $.55
C
o= cost of overage = $.70 -$.30 = $.40
Service level =
C
s
C
s+ C
o
.55
.55 + .40
.55
.95
=
= = .578
Service
level
57.8%
Optimal stocking level
m= 120

95. 12 -95© 2011 Pearson Education, Inc. publishing as Prentice Hall
Single Period Example
From Appendix I, for the area .578, Z.20
The optimal stocking level
= 120 copies + (.20)(s)
= 120 + (.20)(15) = 120 + 3 = 123 papers
The stockout risk = 1 –service level
= 1 –.578 = .422 = 42.2%

96. 12 -96
Fixed-Period (P) Systems
▶Orders placed at the end of a fixed
period
▶Inventory counted only at the end of
period
▶Order brings inventory up to target
level
▶Only relevant costs are ordering and
holding
▶Lead times are known and constant
▶Items are independent of one another

97. 12 -97© 2011 Pearson Education, Inc. publishing as Prentice Hall
Fixed-Period (P) Systems, also
calledPeriodicReviewSystem
On
-
hand inventory
Time
Q
1
Q
2
Target quantity (T)
P
Q
3
Q
4
P
P
Figure 12.9

98. 12 -98
Fixed-Period Systems
▶Inventory is only counted at each
review period
▶May be scheduled at convenient
times
▶Appropriate in routine situations
▶May result in stockouts between
periods
▶May require increased safety stock