Inventory Management :
MODEL PERSEDIAAN

TUJUAN
Mengetahui model-model pengelolaan
persediaan
MODEL PERSEDIAAN

Tujuan

Ukuran persediaan berhubungan dengan
ukuran pesanan, frekuensi pesan

1.
2.
menentukan ukuran persediaan
Item dengan permintaan atau kebutuhan
yang relatif stabil dalam jangka panjang,
ukuran pesanan berdampak pada
frekuensi pesan
rata-rata persediaan.
TRADE OFF
Menentukan ukuran pesanan
Makin besar ukuran pesanan :
 frekuensi pesan lebih kecil
 rata-rata persediaan besar
 biaya pesan kecil
 biaya simpan besar
Sebaliknya untuk ukuran pesan kecil.
Model
Pengelolaan Persediaan
Item dengan pasokan relatif stabil :
 dapat menggunakan model EOQ untuk
menentukan ukuran pesanan yang ekonomis.
 Ketidakpastian diakomodasi dengan
menentukan reorder point dan safety stock
Model Persediaan
Item bersifat musiman :
 Penting mempertimbangkan trade off antara
biaya kelebihan dan kekurangan persediaan.
 Resiko kelebihan dapat dikurangi dengan
(1) mengurangi harga jual di musim jual,
(2) mengurangi lead time sehingga responsif
terhadap pasar
VENDOR MANAGED INVENTORY
Vendor Managed Inventory (VMI)
 Model pengelolaan persediaan dimana
keputusan waktu dan ukuran pengiriman
ditentukan supplier.

Pembeli memberikan informasi yang up to
date tentang kondisi persediaan dan
kebutuhan
•Biaya pesan dan simpan
•Demand is known and constant D units
per time.
•No stock-outs!
•Leadtime=0!
Costs:
K: order cost
c: Unit variable cost
h: inventory holding cost
Q : order size (decision var.)
Inventory
Q
-D
Time
T
Deriving EOQ




Total cost at every cycle:
C(Q)=K+cQ
Average inventory holding cost in a cycle: Q/2
Cycle time T =Q/D
G(Q)=(K+cQ)/T + hQ/2 = KD/Q + Dc + hQ/2
2 KD
Q* 
h
EOQ: Costs
G(Q)
Ordering Cost
Holding cost
Total cost
G(Q)
hQ
2
KD
Q
Q
Q*
Stochastic Demand

Usually the demand has a variable component
D=Dconstant+Dvariable
Inventory Policy
Continuous Periodic
Type A
(s,S)
(R,s,S)
Type B
(s,Q)
(R,S)
Continuous review,
reorder policy
m – demand rate
L – replenishment lead time
S: inventory reorder level; Q: reorder size
inventory
+Q
+Q
S
dL=mL
Safety stock: S-dL
L
place
order
order arrives
time
Periodic Review, Orderup-to Policy
Define:
Inventory Position = Quantity
on hand
+
Quantity
on order
S - Base stock level/Order-up-to Point
R- Review period
L- Replenishment lead time
m - Demand per unit time
Q - Order quantity
ss - Safety stock
Ordering Rule:
Place an order every R periods so as to bring your
inventory position to the Base Stock Level, S.
Periodic review with no
demand variability
Inventory position
Inventory Level
On-hand inventory
m(R+L)
mR
mL
0
R
L
2R
R+L
3R
2R+L
4R
3R+L
time
Periodic review with no
demand variability
Order Quantity, Q = mR
Average Cycle stock = Q/2 = mR / 2
Pipeline stock = m L
Order-up-to point, S = m (R+L)
Periodic review with
variable demand
Order-up-to point (S) = m (R+L) + Safety Stock (ss)
Average Order Quantity (Q) = mR
Average Pipeline stock = m L
Average Cycle stock = Q/2 = mR / 2
Average Safety Stock = ss = ?
Determination of the
Safety Stock
Inventory Level
Inventory position
On-hand inventory
mR+mL+ss
mR+ss
mL+ss
ss
0
R
L
2R
R+L
3R
2R+L
4R
3R+L
time
Inventory Level
Freq
Inventory
On-hand
X
Place
order
Lead Time
Receive
order
Time
Inventory Level
Freq
Inventory
On-hand
X
m ( R  L) + SS  z R L
=S
Safety Stock (SS)
Place
order
Lead Time
Receive
order
Time
Given R, L, m, and :
Safety Stock (ss) =
z R  L
Choose z such that:
L( z )   R  L
Fill Rate (p) = 1 
mR
Expected standard
loss (shortage)
Demand variability
over R + L units time
Average demand filled
per period
So:
L( z )  1  p 
where L(z) is the standard loss function
Base Stock Level (S) =mR  mL  z R  L
mR
 RL
Example #1
Given:
Solve:
L z   1  p 
R = 2 weeks
L= 1 week
m = 150 units per week
 = 10 units per week
Target fill rate, p=99%
mR
 RL
 .01
150  2
 0.173 so from table, z = 0.58
10 2  1
Safety stock = ss  z R  L  0.58 10 3  10
Base stock level = S  mR  mL  z
R  L  150  2  150 1  10  460
Example #2
Given:
R = 2 weeks
L= 1 week
m = 150 units per week
 = 10 units per week
Target fill rate, p=95%
Solve:
L z   1  p 
mR
 RL
 .05
150  2
 0.866 so from table, z = -0.73
10 2  1
Safety stock = ss  z R  L  0.73 10 3  12
Base stock level =
S  mL  mR  z R  L  150  2  150 1  12  438