Contoh Perhitungan Log

7/30/2019 Contoh Perhitungan Log

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CONTOH PERHITUNGAN

MANAJEMEN LOGISTIK

Sekolah Tinggi Manajemen Bandung


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UMUR EKONOMIS

Umur ekonomis suatu aktiva tetap adalah suatu periode yang

memberikan Equivalent Uniform Annual Cost (EUAC) minimum.Untuk mencari umur ekonomis, kita harus menghitung Total EUAC

dimana k minimum, k = 1,2,3,4n

Rumus Umum Umur Ekonomis :

EUAC =

P(A/P,i%,k)-Sk(A/F,i%,k)+[SAOCj(P/F,i%,k)](A/P,i%,k)

Contoh :

Sebuah Sentral Telepon Digital dibeli dengan harga $ 1.000.000.-Dengan perkiraan nilai sisa dan biaya operasi tahunan seperti tabel

dibawah ini, jika diketahui MARR = 10 %, pada tahun berapa umur

ekonomis sentral tersebut dicapai?


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Year - k Salvage Value t Annual

thn ke-n operatingcost

1 900,000 100,000

2 850,000 120,000

3 800,000 120,000

4 750,000 120,000

5 700,000 125,000

6 650,000 130,000

7 600,000 140,000

8 550,000 150,0009 500,000 200,000

10 450,000 250,000


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n (A/P,10%,k) (A/F,10%,K) (P/F,10%,K)1 1.1000 1.0000 0.9091

2 0.5762 0.4762 0.8264

3 0.4021 0.3021 0.7513

4 0.3155 0.2155 0.68305 0.2638 0.1636 0.6209

6 0.2298 0.1296 0.5645

7 0.2054 0.1054 0.5132

8 0.1874 0.0874 0.4665

9 0.1736 0.0736 0.4241

10 0.1627 0.0627 0.3855

Factor bunga untuk membantu perhitungan


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Year EUAC EUAC TOTAL

k CAPITAL OPERA- EUAC

RECOVERY TIONS

1 200,000 100,001 300,001

2 171,430 104,758 276,188

3 160,420 102,713 263,133

4 153,875 99,124 252,999

5 149,280 95,819 245,099

6 145,560 92,751 238,311

7 142,160 90,127 232,287

8 139,330 87,859 227,189

9 136,800 88,717 225,51710 134,485 91,259 225,744

Jadi Umur Ekonomis Sentral Digital tersebut adalah = 9 tahun


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MODEL-MODEL PERSEDIAAN

Variabel Model - P Model - Q

Apa? Klasifikasi A-B-C

Berapa? Maks.Persediaan = S Besar Pesanan = QKapan? Lama Periode = T Titik Pesan = R

D = Besar pesanan setahun

B = Biaya tiap pesani = %, interewst tahunanS = Unit price


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Contoh :

D = Besar pesanan setahun= 36.000 YARDS, 1 hari = 100YardsB = Biaya tiap pesan = Rp 1.000 tiap kali pesani = %, interest tahunan, 25 % per tahunS = Unit price, Rp 800 per yardsLT = Lead time

DLT = Demand Lead Time, misal LT = 2 hari,DLT = 200 yards, makasetiap persedian mencapai200 yards harus segera dipesan sejumlah EOQ

80025.0

3600010002

x

xxEOQ

SiDBEOQ

.

..2

EOQ = 600 yards tiap kali pesan, kebutuhan 1 hari = 100 YardsT = Periode = 600/100 = 6 hariBiaya pesan minimum = (360 hari/ 6 hari) x Rp 1000= Rp 60.000,-


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A. LEAD TIME BERSIFAT POSITIF, DEMAND KONSTAN

LT = Lead time

DLT = Demand Lead Time, misal LT = 2 hari,DLT = 200 yards, makasetiap persedian mencapai 200 yardsharus segera dipesan sejumlah EOQ

B. LEAD TIME BERSIFAT POSITIF, DEMAND KONSTAN

Safety Stock = SS = DLT + ( Z X Standard Deviasi LT) D

Misal : LT (rata-rata) = 2 hariStandard Deviasi = 1 hari

Service level = 95 %

Z = 1.65Demand per hari = D = 100 yards

Maka SS = 200 + ( 1.65 x 100 ) = 365 yards.


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C. LEAD TIME KONSTAN, DEMAND PROBABILISTIK

Safety Stock = SS = DLT + ( Z X (LT X Standard Deviasi LT)Misal : Demand per hari (rata-rata) = D = 100 yards

Standard Deviasi = 80 yards

Lead Time = 2 hariService level = 95 % Z = 1.65

Maka SS = 200 + ( 1.65 x (2 X 80 ) = 387 yards.


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Diketahui : D = 10.000 unit per tahun

B = $ 24 per pesananS = $ 3 per unitK = $ 4 per unit kekuranganX = 40 unit per hari distribusi normal

dengan Standar Deviasi = 15 unitService level = 95 %

LT = 7 hari, 1 tahun = 250 kari kerja,

Dapat dihitung :a. Periode pesanan (T) = (2.B/D.S) = (2x24/10.000x3) = 0.04

tahun = 10 hari

b. Periode Perencanaan ( Y = T + TL ) = 10 + 7 = 17 haric. EOQ atau E = Y x X = 17 x 40 unit = 680 unitd. Sdy (SD Perencanaan) =( Y ) SDx = ( 17 ) x 15 = 62 unite. Maksimum Persediaan = S max = E + Z . (SDy)

= 680 + 1.65 x 62 = 782 unit

Contoh lain persediaan Model P


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SERVICE LEVELPROBABILITY

TOCK OUTPROBABILITY

M R

DISTRIBUSI PERMINTAAN SELAMA LEAD TIME


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Hubungan Z dengan % Stock Out

Z Service Level (%) Stock Out (%)

0.0 50.0 50.0

0.5 69.1 30.9

1.0 84.1 15.9

1.1 86.4 13.6

1.2 88.5 11.5

1.3 90.3 9.7

1.4 91.9 8.1

1.5 93.3 6.7

1.6 94.5 5.5

1.7 95.5 4.51.8 96.4 3.6

1.9 97.1 2.9

2.0 97.7 2.3

2.1 98.2 1.8

2.2 98.6 1.4

2.3 98.9 1.12.4 99.2 0.8

2.5 99.4 0.6

2.6 99.5 0.5

2.7 99.6 0.4

2.8 99.7 0.3

2.9 99.8 0.2

3.0 99.9 0.1


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Contoh Lain:

Diketahui : D = 4.000 unit per tahun

B = Rp 10.000,- per pesananS = Rp 10.000,-per unitOngkos penyimpanan = Rp 4000,- per th.=Cp

Lead Time = 7 hari, 1 tahun = 365 kari

Ditanya : Tentikan Reorder point, agar jumlah pemesanan (Q) minimal.

Dapat dihitung :

a. EoQ = (2.BD/Ongkos penyimpanan ) = (2x4000x10000)/4000 =141.4 unit =141 unit

b. Titik Pembelian kembali = (TLxD)/365 =76,7 unit = 77 unit

Jadi pemesanan sebanyak 141 unit bila inventory menurun sampai =77 unit

c. Berapa kali pesanan per tahun = D/Q =4000/141 kali = 28 kalid. Periode pesanan (lama antar pesanan) = 365 hari/jumlah pesanan

per tahun = 365/28 = 13 hari.

2BxDQ = ---------

Cp


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Manajemen Material ( MM )

Peranan MM :

Mengurangi biaya materal

Memperbaiki ROI :

Profit Sales

ROI = ------------ x --------------------------------------------

Sales Fixed Asset + Current Asset


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Fungsi Manajemen Material ( MM )

Perencanaan Materal

Pengadaan Material

Penyimpanan Material

Pendistribusian Material

Penghapusan Material

Pengendalian Material

Quality ( material yang tepat)Reasonable Cost (harga wajar)

Delivery ( Waktu/saat tepat)FlexibleService level


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Manajemen Material ( MM )

Persoalan Persediaan Tradisoional Persediaan KebutuhanMaterial

Objek Komponen Produk

Data Penglaman masa lalu Keterkaitan antar

komponenOrientasi Masa lalu Masa y.a.d

Metode Statistik Komputasi

Pemakaian Independent Demand Dependent demand

Asumsi Pemakaian uniform Pemakaian (bisa grdual)

Pesanan Reorder Point atau waktupesan tetap

Sesuai kebutuhan


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Persediaan Tradisional

Dasar Kebijakan

Pola permintaan : Probabilisti - Deterministik

Statis - Dinamis

Pola Pengadaan : Sekaligus Bertahap - Kontinu

Lead Time : Deterministik - Probabilistik

Kendala Fisik : Gudang

transportasi - dllStruktur Biaya : Biaya Pengadaan (B)

Biaya Penyimpanan (S)

Biaya Kekurangan Persediaan (K)

Pola Manajemen : Kebijakan Delivery, CaraPembayaran

Pencatatan Biaya, dll


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Logistical Management

CH.8 : INVENTORY STRATEGY &

CH.9 : INVENTORY MANAGEMENT


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Chapter. 8 :

INVENTORY STRATEGY

High risk and high impact

Sales lost and customer satisfaction declineOver stock may increase cost and reduce

profitability

Inventory type and characteristics

Basic inventory decision rules

Uncertainty


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Chapter. 8 :

INVENTORY STRATEGY


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Relation between formulating inventory andmanufacturing / marketing .Inventory as a % (percentages) of assetsOpportunity of increasing inventory productivity

vs. integrated supply chains ability to useinformation exchange and management focus toreduce uncertainty

Chapter. 8 :

INVENTORY STRATEGY


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1. Inventory functionality andprinciples

a. Inventory type and characteristicsb. Inventory functionalityc. Inventory related definitionsd. Cost of carrying inventory


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1. Inventory functionalityand principles

A. Inventory type and characteristicsInventory risk due to capital investment and

potential for obsolescenceI. Investment of inventory

II. Possibility of risk

Nature of risk is vary depend on an enterprises position inthe distribution channel. :a. Manufacturing long term dimension

b. Wholesalenarrow but deeper and longer duration

c. Retailer wide but not deep.


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1. Inventory functionality andprinciples

Inventory functionality

1) Geographical Specialization - resources vs. distance need

individual operating unit2) Decoupling - provide maximum operating efficiency, the process

permit each product to be manufactured and distribute in economical

lots size.

3) Balancing supply and demand - is concern with elapsedtime between consumption and manufacturing, its reconcile supply

availability with demand

4) Buffer uncertainty- the safety stock or buffer stock functionconcern short range variation in either demand or replenishment. Its

protect two type uncertainty : forecast and delay


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C. Inventory related definitionsInventory Policy - guide line what to purchase and manufacture, whenand what quantity

Service Levelis target specified by management.it defined theperformance objectivesAverage Inventory - consist of material, components, W-I-P, and finished

goods typically stocked in logistical facilities

Cycle inventoryis the portion of average inventory that result from

replenishment processSafety stock inventory - the second part of average inventoryheld to

protect against uncertainty on each facility

Transit inventorystock in moving or awaiting for transportation

Inventory functionality and principles


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Example of average inventory overperformance cycle

200

100

0 20 40 60

days

Averageinventory

Orderplacement

Orderarrival

inventory


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:Assume the following condition :i. Replenishment cycle20 days

ii. Sales rate during replenishment10 unitsiii. Ordering upon deliveryiv. Replenishment order quantity200 units

Figure 8.2 is called , rate sales is 10 units per day

and take 20 days to complete inventory replenishment,its mean that order 200 units every 20 days.Formulation :Reorder point is specified as 200units on hand whatever happened

Average inventory100 units, since stock on hand is 100 units.

Assume that work days is 240 days a year, so 12 time ofpurchase is needed during one year.Sales 10 units per day , so became 2400 per yearThus became 2400 divided by 100 unit =


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What happen if order more frequently than onceevery 20 days?Order 100 units every 10 days? Or 600 units every 60 days?

Assuming that inventory cycle is constant 20 days.The policy of ordering 600 units every 60 days would resultthat average inventory became 300 units and turn over

became 2400units/300units = 8

If the order 100 units per 10 days means that two orderbe outstanding. Thus reorder point remain 200 units

Average inventory became 50 units


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600

300

020 60 100

Days

Averageinventory

Orderarrival

inventory 400

200

40 80 120

Figure 8.3 : Alternative order quantity andaverage inventory


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100

50

0 20 40 60

Orderplacement

Orderarrival

invento

ry

Averageinventory

Figure 8.3 Alternative order quantityand

average inventory


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Inventory Carrying cost components :


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PLANNING THE INVENTORY RESOURCES

Basic reorder formula :

Where R = Reorder point in unitsD = Average daily demandT = Average performance cycle length

e.g Demand = 10 units per dayPerformance cycle = 20 days

R = 10 units /day X 20 days = 200units

With buffer stock or Safety Stock (SS)


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Determine Lots Size byEconomic Order Quantity (EOQ )Formulation

Remark :1) Co = cost per order2) Ci = annual inventory carrying cost3) D = annual sales volume, units

4) U = cost per unit


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Example using EOQ Formula

Annual demand volume = 2400 units Unit value at cost = $ 5.00 Inventory carrying cost percentage = 20 % annually

Ordering cost = $ 19.00 per order

By substituting from above , we have :

2 X 19 X 2400EOQ = ----------------------0.20 X 5.00


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EOQ extension :

EOQ formulation is straight forward, but there are some other factormust be considered in actual application : Volume transportation rates Quantity discountOther EOQ adjustment : (I) production lots size

(ii) Multiple item purchase(iii) Limited capital(iv) Private trucking

Discrete Lot SizingLot-for lot sizing

Period order quantity ( POQ) EOQ = 300 unitsForecast per year = 2400 unitsOrder per year = 2400/300 = 8 timesOrder interval = 12/8 = 1.5 months


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ACCOMMODATING UNCERTAINTY

Forecast vs. actual

Frequency demand

Normal distributionStandard deviation

Inventory policy can not assume consistent delivery

Table 8.11

Table 8.12

MRP Formulae


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Table 8-8 Typical Demand ExperienceDuring Replenishment Cycle

-------------------------------------------------------------------------------------------------------Forecast cycle 1 Stock out cycle Over stock cycle 3------------------------------ ------------------------------ ------------------------------Day Demand Accum. Day Demand Accum Day Demand Acumm

------------------------------------------------------------------------------------------------------1 9 9 11 0 0 21 5 52 2 11 12 6 6 22 5 103 1 12 13 5 11 23 4 144 3 15 14 7 18 24 3 175 7 22 15 10 28 25 4 21

6 5 27 16 7 35 26 1 227 4 31 17 6 41 27 2 248 8 39 18 9 50 28 8 329 6 45 19 so 50 29 3 3510 5 50 20 so 50 30 4 39--------------------------------------------------------------------------------------------------------


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Table 8-9 Frequency of Demand

----------------------------------------------------------------------------------------------------Demand/day Frequency (days) Demand Frequency (days)--------------------------------------------- ----------------------------------------------

Stockout 2 Five units 5Zero 1 Six units 3One unit 2 Seven units 3Two units 2 Eight units 2Three units 3 Nine Units 2

Four Units 4 Te units 1


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Historical analysis

ofdemand history


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Normal Distribution


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Calculation of standard deviationof daily demand

-------------------------------------------------------------------------------------Units Frequency Deviation Deviation

from Mean Squared(FJ) (Di) (Di) FiDi

------------------------------------------------------------------------------------

0 1 -5 25 251 2 -4 16 322 2 -3 9 183 3 -2 4 124 4 -1 1 45 5 0 0 0

6 3 1 1 37 3 2 4 128 2 3 9 189 2 4 16 3210 1 5 25 25------------------------------------------------------------------------------------


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s

s


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Chapter .9 :INVENTORY MANAGEMENT

a) Inventory Control

b) Reactive Method

c) Planning Method

d) Adaptive Logic

a) Strategy Development Process

b) Method of improvement Inventory Management


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Chapter .9 :INVENTORY MANAGEMENT

Chapter 8 focused on inventory decision for single item at a singlelocation, while chapter 9 discussed inventory management for a range ofSKUs (Stock Keeping Units) and at multiple location.

Inventory management is the integrated process that operationalizes thefirms and the value chains inventory policy.

Reactive approach or pull inventory approach, uses customer demandto pull product through the distribution channel

Planning approach, - proactively schedule product movement,according to the forecast.

Combination of two approach abov,respon to the product and marketenvironment


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Inventory ControlInventory control is a mechanical procedure for implementing aninventory policy. Accountability and tracking should be done eithermanually or computerized. The primary differential are : speed,accuracyand cost.Inventory control procedure can be characterized as perpetual

or periodic.A perpetual inventory control process reviews

inventory status daily to determine replenishment needs, implementedthrough and .

Order quantity determine using EOQ Formulation, EOQ extension oranother approach


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Example :Average daily demand = 20 units

Performance cycle = 10 daysOrder quantity = 200 unitsROP = D X T + SS SS = 0

= 20 X 10 + 0 = 200 unitsThere are two type inventory in this case,

on - order - inventory or inventory on order Qo and on - handinventory or inventory on hand I

Mathematically we can say that :

If I + Qo < ROP then order QAverage inventory can be calculate :

I = Q/2 + SS I = 200/2 + 0 = 100


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The formula for calculating periodic review reorder point :

ROP = Reorder PointD = Average Daily DemandT = Average performance cycle lengthP = review period in days

SS = Safety Staock

The Average Inventory Formula for periodic is

I = average inventory in units


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To accommodate specific situation, variations and combinationsof the basic periodic and perpetual control systems have beenDeveloped. Most common are :

The replenishment level system andThe optional replenishment system.

The target of replenishment can be calculated by using thefollowing formula :

Where : TGT = replenishment levelSS = Safety StockD = Average daily demandP = Review period in daysT = Average performance cycle length

The General reorder rule became


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The General reorder rule became

Where : Q = order quantityTGT = Replenishment LevelI = Inventory Status at review timeQo = Quantity on order

The Average Inventory became :

Replenishment order can be guarantee at least be equal to

the difference between max level (S) and min level (s)


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Example :

The minimum or (s) level is determined similarly to ROP,

where there is no uncertainty

When demand and performance-cycle uncertainty exist, the

Minimum stock level (s) must be incremented by an allowance forsafety stock.For example both maximum and minimum are definedin term of specific number say 100 units and 400 units respectively,The result is :

E.g : Quantity = 75 unitsQuantity on order = 0 unitsQuantity to order = 400750 = 325 units

Reactive Methods


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Reactive Methods

Replenishment era initiated when stock levels fall bellowminimum or order point. The review to anticipate these condition,

the following assuming and assumption should be discussed :i. The system should contribute equally profit.ii. Infinite availability at the source that means no constraints exist.iii. No constraint on facility capacity or inventory availability.iv. Performance cycle time can be predicted and independent.v. Demand pattern are relatively stable and consistent.

Figure 9.1 explained reactive inventory environment.

I 250ROP 200OQ 400 I 80

ROP 75OQ 200D 14

I 45ROP 50OQ 200

D 5

Resupply order for 200 units need for Ws A

I ( current inventory) above ROP for Ws B

Ws A more independentWs B will stock out because Inventory level

close to ROP


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Planning Method

Use common information base to coordinate inventory requirementacross multiple locations or stages in the value added chain,Two type of planning method are commonly used :

-> equitable inventory see Figure 9.2-> more sophisticated,

similar with MRP see. Figure 9.3


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Adaptive Logic

A combined inventory management system may be use to overcomesome of the problem s in Reactive or Planning method.Description

Adaptive decision factor

Use proactive logic Use reactive logic- Highly profitable segment - Cycle time uncertainty

- Dependent demand - Demand uncertainty- Economics of sales - Destination capacity limitations- Supply uncertainty- Source capacity limitations- Seasonal supply buildup


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FUNGSI INVENTORY

Menyelaraskan antara penyediaan dankebutuhan

Menyelaraskan kebutuhan konsumen

dengan barang jadiMenyelaraskan barang jadi dengankomponen pembentuknya

Menyelaraskan kebutuhan operasi denganoutput dari operasi sebelumnya

Menyelaraskan komponen dan bahan bakudengan supplier material


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DILIHAT DARI FUNGSI DANPERANNYA INVENTORY DAPATDIBAGI MENJADI :

Anticipation InventoryFluctuation Inventory

Lot Size Inventory

Transportation Inventory


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Tujuan Manajemen Persediaan(Inventory Management)

Maximum, customer service

Low cost plant operationMinimum Inventory Investment


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CUSTOMER SERVICE

Availability

Management effectiveness

- percentage order shipped on schedule

- percentage line items shipped on schedule

- days of out of stocks


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OPERATING EFFICIENCY

Mengembangkan Inventory Investment

dengan hal-hal berikut :1. Customer Service

2. Biaya untuk merubah tingkat produksi

: overtime, hiring, training, lay-off3. Ongkos pemesanan

4. Ongkos transportasi


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INVENTORY COST

Item cost

Carrying costOrdering cost

Stock-out cost

Capacity-Related cost


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PENENTUANECONOMIC ORDER QUANTITY,

RE ORDER POINT &SAFETY STOCK


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Fixed Order Quantity Inventory System (System-Q).

Diketahui :

Kebutuhan Material pertahun =3.000 unit (D) Order Cost = $500 Perkali pesan (O)

Harga Material = $ 30 per unit (M)

Storage Cost/Carrying Cost / Holding cost = $ 3 /unit.tahun

(C) 1 tahun terdiri dari 300 hari kerja

Lead time 10 hari


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Rata-rata kecepatan pemakaian material adalah10 unit perhari dengan simpangan baku(standard deviation)= 1,2 unit

Service level : Diinginkan kemungkinanterjadinya Stock -Out adalah 0,05 atau 5 %


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Ditanya :

a. Economic Order Quantity

b. Reorder Point

c. Safety Stock

d. Total Inventory Cost Pertahun


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QuantityOrderEconomic1000*Q

93,1251,12590,0002,000*T750*Q

93,0001,50090,0001,500*T1000*Q

93,2502,25090,0001,000*T1500*Q

95,0004,50090,000500

2

3000x3

30x30003000

3000x500

*T3000*

Q


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EOQ

$

Order Cost

Carrying Cost

Total Cost (T*)

Q*


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Jawab :

a. EOQ =

b. Kebutuhan material pertahun = 3000 unitjumlah hari kerja pertahun = 300 hari

jadi kebutuhan material rata-rata perhari

= 3000 =10 unit/hari

300

Lead Time = 10 hari

Reorder Point = kebutuhan selama lead time= 10 x 10 unit = 100 unit

1000

3

30005002..2 xx

C

DO


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c. Safety Stock = Z.SX

Z = Nilai koefisien distribusi normal untuksevice level tertentu. Bila diinginkanProbabilitas Stock Out = 0,05(Probabilitas dapat terpenuhi kebutuhan

material sebesar 0,95 ) maka Z= 1,65Sx = Deviasi standard pemakian material

perhari =1,2 unit

t = Lead time ( dalam hari ) = 10 hariSS= 1,65x1,2 x =6,26 unit

t

10


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d. Total Inventory Cost pertahun

=

= 500 x 3000 + (3000 x 30) + (3 x 1000)+(6,26x3)

1000 2

Lt = 1500 + 90000+1500 + 18,78 = 93018,78

OD x MD + CQ* + (SS). C

Q* 2

Fi d O d P i d i t t


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Fixed Order Period inventory system( system P)

Untuk soal yang sama dengan system Q, bila Rate

pemakaian material konstan, maka system P dan Qmenunjukkan karakteristik yang sama, kecuali dalam

penentuan safety stock nya. Dalam hal pemakaian material tidak sepenuhnya

konstant, maka Order Quantity (Order size) bergantugkepada persediaan di gudang (inventory on hand) padasaat perioda pemesanan tiba.

misalnya: Pada Suatu perioda pemesanan inventory onhand = 150 unit ( termasuk SS)


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Safety stock = Z.S x

Dimana t+r = waktu siklus = waktu rata-rata dari

suatu pemesanan ke pemesanannya berikutnyadalam contoh t+r = EOQ

kecepatan pemakaian perhari

= 1000 = 100 hari10

Dengan Faktor keamanan 0,95 maka diperoleh :

SS= 1,65 x 1,2 x = 19,8 unit unit

Order size = EOQ + SS - Inventroy on Hand +

Pemakaian selama lead time

= 1000 + 20 - 150 + 100 = 970 unit

t r

100 20

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