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Modul ke:
Fakultas
Program Studi
Manajemen Persediaan
04 FEB
Manajemen
Penentuan Jumlah Persediaan dengan Metode Deterministik
Jenis Sistem Pengendalian Persediaan
• Sistem tempat persediaan tunggal – Bak/ papan diisi secara periodik, co: toko, pabrik – Disebut dengan sistem P
• Sistem tempat persediaan ganda – Tempat pesediaan dibagi2 yakni: persediaan yang akan dikeluarkan
dan persediaan yang masih disegel – Disebut dengan sistem Q
• Sistem kartu file – Terdapat 1 kartu untuk setiap item persediaan – Saat item terjual dan terisi kembali kartu korespondensi diperbaharui – Perpaduan sistem p dan sistem Q
• Sistem Komputer – Setiap item, transaksi penerimaan dicatat, berisikan keputusan dari
sistem P dan Q, peramalan permintaan, pemantauan kinerja persediaan
Periode Persediaan
• Persediaan periode tunggal
– Item yang akan di stok 1 kali dan setelah habis tidak akan dilakukan pemesanan kembali
• Persediaan periode ganda
– Persediaan yang akan dipertahankan keberadaannya dan akan dilakukan pemesanan kembali setelah dipergunakan/ terjual
– Dibagi menjadi 2 kategori yakni permintaan dependen dan independen
EOQ
• EOQ cocok diterapkan untuk item yang dibeli dari perusahaan lain
• EOQ banyak diterapkan untuk permintaan independen
• Digunakan untuk menentukan ukuran lot pemesanan dengan biaya yang paling optimal
Syarat Model EOQ
• Tingkat penggunaan seragam dan diketahui • Harga item sama untuk setiap ukuran pemesanan • Semua pesanan dikirim pada waktu yang sama • Lead time konstan dan diketahui dengan baik • Item merupakan produk tunggal dan tidak ada
kaitannya dengan produk lain • Biaya penempatan dan penerimaan pesanan
diabaikan untuk sejumlah pesanan • Biaya item unit konstan dan tidak ada diskon
untuk pembelian dalam jumlah besar, tidak ada skala ekonomi dalam biaya penyimpanan item
Independent vs. Dependent Demand
• Independent demand items are finished goods or other items sold to someone outside the company
• Dependent demand items are materials or component parts used in the production of another item (e.g., finished product)
Types of Inventory: How Inventory is Used
• Anticipation or seasonal inventory
• Safety stock: buffer demand fluctuations
• Lot-size or cycle stock: take advantage of quantity discounts or purchasing efficiencies
• Pipeline or transportation inventory
• Speculative or hedge inventory protects against some future event, e.g. labor strike
• Maintenance, repair, and operating (MRO) inventories
Objectives of Inventory Management
• Provide acceptable level of customer service (on-time delivery)
• Allow cost-efficient operations
• Minimize inventory investment
Relevant Inventory Costs
Item Cost Cost per item plus any other direct costs associated with getting the item to the plant
Holding Costs
Capital, storage, and risk cost typically stated as a % of the unit value,
e.g. 15-25%
Ordering Cost
Fixed, constant dollar amount incurred for each order placed
Shortage Costs
Loss of customer goodwill, back order handling, and lost sales
Order Quantity Strategies
Lot-for-lot Order exactly what is needed for the next period
Fixed-order quantity
Order a predetermined amount each time an order is placed
Min-max system
When on-hand inventory falls below a predetermined minimum level, order enough to refill up to maximum level
Order n periods
Order enough to satisfy demand for the next n periods
Examples of Ordering Approaches
Lot for Lot Example
1 2 3 4 5 6 7 8
Requirements 70 70 65 60 55 85 75 85
Projected-on-Hand (30) 0 0 0 0 0 0 0
Order Placement 40 70 65 60 55 85 75 85
Fixed Order Quantity Example with Order Quantity of 200
1 2 3 4 5 6 7 8
Requirements 70 70 65 60 55 85 75 85
Projected-on-Hand (30) 160 90 25 165 110 25 150 65
Order Placement 200 200 200
Min-Max Example with min.= 50 and max.= 250 units
1 2 3 4 5 6 7 8
Requirements 70 70 65 60 55 85 75 85
Projected-on-Hand (30) 180 110 185 125 70 165 90 165
Order Placement 220 140 180 160
Order n Periods with n = 3 periods
1 2 3 4 5 6 7 8
Requirements 70 70 65 60 55 85 75 85
Projected-on-Hand (30) 135 65 0 140 85 0 85 0
Order Placement 175 200 160
Three Mathematical Models for Determining Order Quantity
• Economic Order Quantity (EOQ or Q System)
– An optimizing method used for determining order quantity and reorder points
– Part of continuous review system which tracks on-hand inventory each time a withdrawal is made
• Economic Production Quantity (EPQ)
– A model that allows for incremental product delivery
• Quantity Discount Model
– Modifies the EOQ process to consider cases where quantity discounts are available
Economic Order Quantity
• EOQ Assumptions: – Demand is known & constant - no
safety stock is required
– Lead time is known & constant
– No quantity discounts are available
– Ordering (or setup) costs are constant
– All demand is satisfied (no shortages)
– The order quantity arrives in a single shipment
EOQ: Total Cost Equation
cost setupor ordering
cost holding annual
ordered be oquantity t
demand annual
cost annual total
2
S
H
Q
D
TC
Where
HQ
SQ
DTCEOQ
When to Order: The Reorder Point
• Without safety stock:
• With safety stock:
days/weeksintimelead
unitsindemandlydaily/week
unitsinpointreorderwhere
L
d
R
dLR
unitsin stock safety where
SS
SSdLR
ROP = LxD
Receive
order
Time
Inven
tory
Order
Quantity
Q
Place
order
Lead Time
Reorder
Point
(ROP)
If demand is known exactly, place an order when inventory equals demand during lead time.
D: demand per period L: Lead time in periods
Q: When shall we order?
A: When inventory = ROP
Q: How much shall we order?
A: Q = EOQ
Example
10
365 D = R =
10
365 5000 = 137
So, when the number of cars on the lot reaches 137, order 548 more cars.
Since D is given in years, first convert: 10 days = 10/365yrs
Example:
Assume a car dealer that faces demand for 5,000 cars per year, and that it costs $15,000 to have the cars shipped to the dealership. Holding cost is estimated at $500 per car per year. How many times should the dealer order, and what should be the order size?
What if the lead time to receive cars is 10 days? (when should you place your order?)
548500
)000,5)(000,15(2* Q
TimeTime
Inventory Inventory
LevelLevel
OrderOrder
QuantityQuantity
But demand is rarely predictable!
Demand???
Receive
order
Place
order Lead Time
ROP = ???
XX
Inventory at time of receipt
Receive Receive
orderorder
TimeTime
Inventory Inventory
LevelLevel
OrderOrder
QuantityQuantity
PlacePlace
orderorder
Lead TimeLead Time
Actual Demand < Expected Demand
ROP
Lead Time Demand
Stockout
Point
Unfilled demand
Receive Receive
order order
Time Inven
tory
Order Order
Quantity Quantity
Place Place
order order
Lead Time Lead Time
If Actual Demand > Expected, we Stock Out
ROP = Expected Demand
Average
TimeTime
Inventory Inventory
LevelLevel
OrderOrder
QuantityQuantity
If ROP = expected demand, service level is
50%. Inventory left 50% of the time, stock
outs 50% of the time.
Uncertain Demand
To reduce stockouts we add safety stock
Receive Receive
order order
Time Time
Place Place
order order
Lead Time Lead Time
Inventory Level
ROP =
Safety
Stock +
Expected
LT Demand
Order Quantity Q = EOQ
Expected LT Demand
Safety Stock
Service level
Safety
Stock
Probability of stock-out
Decide what Service Level you want to provide (Service level = probability of NOT stocking out)
Service level
Safety
Stock
Probability of stock-out
Safety stock = (safety factor z)(std deviation in LT demand)
Read z from Normal table for a given service level
EOQ Example
• Weekly demand = 240 units
• No. of weeks per year = 52
• Ordering cost = $50
• Unit cost = $15
• Annual carrying charge = 20%
• Lead time = 2 weeks
EOQ Example Solution
yearunitsD /480,1224052
yearperunitperH 3$152.0
unitsH
DSQ 64598.644
3
50480,1222
unitsdLR
HQ
SQ
DTC
4802240
$1,934.945.96744.967
32
64550
645
480,12
2
EPQ (Economic Production Quantity) Assumptions
• Same as the EOQ except: inventory arrives in increments & is drawn down as it arrives
EPQ Equations
• Adjusted total cost:
• Maximum inventory:
• Adjusted order quantity:
H
IS
Q
DTC MAX
EPQ2
p
dQIMAX 1
p
dH
DSEPQ
1
2
EPQ Example
• Annual demand = 18,000 units
• Production rate = 2500 units/month
• Setup cost = $800
• Annual holding cost = $18 per unit
• Lead time = 5 days
• No. of operating days per month = 20
EPQ Example Solution
monthunitspmonthunitsd /2500;/150012
000,18
units
p
dH
DSQ 2000
2500
1500118
800000,182
1
2
unitsp
dQIMAX 800
2500
1500120001
400,14200,7200,7
182
800800
2000
000,18
2
H
IS
Q
DTC MAX
EPQ Example Solution (cont.)
• The reorder point:
• With safety stock of 200 units:
unitsSSdLR 575200520
1500
unitsdLR 375520
1500
Quantity Discount Model Assumptions
• Same as the EOQ, except:
– Unit price depends upon the quantity ordered
• Adjusted total cost equation:
PDHQ
SQ
DTCQD
2
Daftar Pustaka
• Richardus Eko Indrajit, (2005), Manajemen Persediaan, Grasindo, Jakarta
• Heizer Jay, B.Rander, (206), Manajemen Operasi, Salemba Empat, Jakarta
• Hani handoko, (2002), Manajemen Produksi dan Operasi, BPFE, Yogyakarta
• Siswanto, (2005), Riset Operasi, Erlangga, Jakarta
• M. Syamsul Ma’arif, (2003), Manajemen Operasi, Grasindo, Jakarta
• Sofyan Assauri, (2001), Manajemen Operasi, BPFE, Jakarta
• Martinich, (2003), Operation Manaement, Prenice hall, New Yory