COORDINATED INVENTORY
MANAGEMENT
CONTENTS
General Introduction to Inventory
Management
Inventory Models for Smooth Demand:
With and without coordination
Inventory Models for Seasonal Demand:
With and Without Coordination
Inventory Exists In Many Places
Throughout The Supply Chain
Supplier
Manufacture
Distributor
Distributor
There are a number of reasons
why inventory exists:
•
To obtain economies of scale
•
To prevent for uncertainty / to
achieve higher service level
FUNGSI PERSEDIAAN :
•
Mengurangi ketergantungan antar tahap dalam mata
rantai sistem produksi
–
distribusi.
•
Mempertahankan stabilitas penggunaan tenaga kerja
karena fluktuasi
demand
.
•
Mengantisipasi kemungkinan terjadinya gangguan
yang berupa keterlambatan pasokan atau
berhentinya aktivitas dalam sistem produksi.
•
Mengambil keuntungan dng memanfaatkan potongan
harga untuk pembelian dlm jumlah besar.
•
Mengantisipasi tejadinya kenaikan harga barang
karena inflasi.
•
Mengantisipasi terjadinya
stock out
karena
permintaan melebihi perkiraan.
Types of Inventory
•
Based on their status:
•
Raw Material
•
Finished Part
•
Component Part
•
Subassembly Material
•
Work In-Process
(
WIP
)
•
Finished Goods
•
Based on their functions:
•
Pipeline / in-transit inventory
•
Cycle stock
Types of Inventory (2)
•
Berdasarkan Sifat Ketergantungan Kebutuhan
•
Independent Demand → kebutuhan akan suatu item barang
tidak tergantung item yang lain.
Misalnya kebutuhan barang untuk memenuhi permintaan
pembeli di sebuah toko, kebutuhan bahan baku utama dari
produk yang kebutuhannya ditentukan berdasarkan
demand forecasting.
•
Dependent Demand → kebutuhan akan item tertentu
tergantung/terkait pada kebutuhan terhadap item yang lain.
Ketergantungan antar item bisa berbentuk :
•
ketergantungan vertikal : mis. kebutuhan dari komponen
penyusun subrakitan/ produk jadi.
•
ketergantungan horizontal : mis. kebutuhan dr komponen
pelengkap (bahan pembantu) yang menyertai produk.
People often behave conservatively when
making inventory decision.
This is due to, as stated by Ballou (1999, pp.
310), criticism for being overstocked is much
more defensible than being short of supply.
The major portion of inventory holding costs is
of an opportunity cost nature and therefore
goes unidentified in normal accounting system.
Inventory Models For Items
With Stable Demand
Models without
coordination
Models with
coordination
between buyer and
supplier
Finding Optimal Order Quantity
•
When a type of item is consumed quite continuously
in almost a constant rate, there is a simple model to
apply to determine the optimal order quantity such
that the total inventory cost is minimum. Total
inventory costs consist of ordering cost and inventory
holding cost.
•
If ordering cost is high, people tend to order less
frequently to reduce total order cost. If inventory
holding cost is high, order smaller quantity so that
lower average inventory is held.
How Large Should Your Orders
Be?
•
If your orders are too large, you’ll have excess
inventory and high holding costs
•
If your orders are too small, you will have to place
more orders to meet demand, leading to high ordering
costs
Order Size
Holding Costs
Ordering Costs
Too LARGE
High
Low
Too SMALL
Low
High
•
Ordering cost
perperioda = frekuensi pemesanan
dalam 1 perioda x C =
•
Purchase cost
perperioda = jumlah kebutuhan
perperioda x P = DP
•
Holding cost
perperioda = rata-rata banyaknya barang
yang disimpan perperioda x H =
•
Total cost inventory
: TC =
+ DP +
•
TC akan minimum jika : = dan
C
Q
D
H
Q
2
C
Q
D
H
Q
2
0
dQ
dTC
0
2
2
Q
d
The model:
Total cost = Order cost + Holding cost
h
Q
Co
Q
D
Q
TC
2
)
(
h
CoD
Q
*
2
Where D = annual demand
Co = order cost
h = inventory holding cost
An Example
A baking company produces bread using
flour as main raw material. The company
on average uses 200 kg flours a day
(1 year = 365 days). Costs for placing an
order is about Rp. 100.000. The price for
10 kg flour is Rp. 25.000,- Annual
inventory holding cost is about 25% of
the inventory value. Determine optimal
order quantity.
Reorder Point
•
When there is a lead time, EOQ should be
applied under a reorder point scheme.
Reorder point is an inventory position where a
company should place an order. When lead
time is l periods and demand per period is d
then the reorder point is demand during lead
time, that is:
d x l
•
For example, if lead time for ordering flour is
one week, determine reorder point.
16
Z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.05.00E-01 4.96E-01 4.92E-01 4.88E-01 4.84E-01 4.80E-01 4.76E-01 4.72E-01 4.68E-01 4.64E-01
0.14.60E-01 4.56E-01 4.52E-01 4.48E-01 4.44E-01 4.40E-01 4.36E-01 4.33E-01 4.29E-01 4.25E-01
0.24.21E-01 4.17E-01 4.13E-01 4.09E-01 4.05E-01 4.01E-01 3.97E-01 3.94E-01 3.90E-01 3.86E-01
0.33.82E-01 3.78E-01 3.75E-01 3.71E-01 3.67E-01 3.63E-01 3.59E-01 3.56E-01 3.52E-01 3.48E-01
0.43.45E-01 3.41E-01 3.37E-01 3.34E-01 3.30E-01 3.26E-01 3.23E-01 3.19E-01 3.16E-01 3.12E-01
0.53.09E-01 3.05E-01 3.02E-01 2.98E-01 2.95E-01 2.91E-01 2.88E-01 2.84E-01 2.81E-01 2.78E-01
0.62.74E-01 2.71E-01 2.68E-01 2.64E-01 2.61E-01 2.58E-01 2.55E-01 2.51E-01 2.48E-01 2.45E-01
0.72.42E-01 2.39E-01 2.36E-01 2.33E-01 2.30E-01 2.27E-01 2.24E-01 2.21E-01 2.18E-01 2.15E-01
0.82.12E-01 2.09E-01 2.06E-01 2.03E-01 2.01E-01 1.98E-01 1.95E-01 1.92E-01 1.89E-01 1.87E-01
0.91.84E-01 1.81E-01 1.79E-01 1.76E-01 1.74E-01 1.71E-01 1.69E-01 1.66E-01 1.64E-01 1.61E-01
1.01.59E-01 1.56E-01 1.5 39E01 1.52E-01 1.49E-01 1.47E-01 1.45E-01 1.42E-01 1.40E-01 1.38E-01
1.11.36E-01 1.34E-01 1.31E-01 1.29E-01 1.27E-01 1.25E-01 1.23E-01 1.21E-01 1.19E-01 1.17E-01
1.21.15E-01 1.13E-01 1.11E-01 1.09E-01 1.08E-01 1.06E-01 1.04E-01 1.02E-01 1.00E-01 9.85E-02
1.39.68E-02 9.51E-02 9.34E-02 9.18E-02 9.01E-02 8.85E-02 8.69E-02 8.53E-02 8.38E-02 8.23E-02
1.48.08E-02 7.93E-02 7.78E-02 7.64E-02 7.49E-02 7.35E-02 7.21E-02 7.08E-02 6.94E-02 6.81E-02
1.56.68E-02 6.55E-02 6.43E-02 6.30E-02 6.18E-02 6.06E-02 5.94E-02 5.82E-02 5.71E-02 5.59E-02
1.65.48E-02 5.37E-02 5.26E-02 5.16E-02 5.05E-02 4.95E-02 4.85E-02 4.75E-02 4.65E-02 4.55E-02
1.74.46E-02 4.36E-02 4.27E-02 4.18E-02 4.09E-02 4.01E-02 3.92E-02 3.84E-02 3.75E-02 3.67E-02
1.83.59E-02 3.52E-02 3.44E-02 3.36E-02 3.29E-02 3.22E-02 3.14E-02 3.07E-02 3.01E-02 2.94E-02
1.92.87E-02 2.81E-02 2.74E-02 2.68E-02 2.62E-02 2.56E-02 2.50E-02 2.44E-02 2.39E-02 2.33E-02
2.02.28E-02 2.22E-02 2.17E-02 2.12E-02 2.07E-02 2.02E-02 1.97E-02 1.92E-02 1.88E-02 1.83E-02
2.11.79E-02 1.74E-02 1.70E-02 1.66E-02 1.62E-02 1.58E-02 1.54E-02 1.50E-02 1.46E-02 1.43E-02
2.21.39E-02 1.36E-02 1.32E-02 1.29E-02 1.26E-02 1.22E-02 1.19E-02 1.16E-02 1.13E-02 1.10E-02
2.31.07E-02 1.04E-02 1.02E-02 9.90E-03 9.64E-03 9.39E-03 9.14E-03 8.89E-03 8.66E-03 8.42E-03
2.48.20E-03 7.98E-03 7.76E-03 7.55E-03 7.34E-03 7.14E-03 6.95E-03 6.76E-03 6.57E-03 6.39E-03
2.56.21E-03 6.04E-03 5.87E-03 5.70E-03 5.54E-03 5.39E-03 5.23E-03 5.09E-03 4.94E-03 4.80E-03
2.64.66E-03 4.53E-03 4.40E-03 4.27E-03 4.15E-03 4.02E-03 3.91E-03 3.79E-03 3.68E-03 3.57E-03
2.73.47E-03 3.36E-03 3.26E-03 3.17E-03 3.07E-03 2.98E-03 2.89E-03 2.80E-03 2.72E-03 2.64E-03
2.82.56E-03 2.48E-03 2.40E-03 2.33E-03 2.26E-03 2.19E-03 2.12E-03 2.05E-03 1.99E-03 1.93E-03
2.91.87E-03 1.81E-03 1.75E-03 1.70E-03 1.64E-03 1.59E-03 1.54E-03 1.49E-03 1.44E-03 1.40E-03
3.01.35E-03 1.31E-03 1.26E-03 1.22E-03 1.18E-03 1.14E-03 1.11E-03 1.07E-03 1.04E-03 1.00E-03
3.19.68E-04 9.35E-04 9.04E-04 8.74E-04 8.45E-04 8.16E-04 7.89E-04 7.62E-04 7.36E-04 7.11E-04
3.26.87E-04 6.64E-04 6.41E-04 6.19E-04 5.98E-04 5.77E-04 5.57E-04 5.38E-04 5.19E-04 5.01E-04
3.34.84E-04 4.67E-04 4.50E-04 4.34E-04 4.19E-04 4.04E-04 3.90E-04 3.76E-04 3.63E-04 3.50E-04
3.43.37E-04 3.25E-04 3.13E-04 3.02E-04 2.91E-04 2.80E-04 2.70E-04 2.60E-04 2.51E-04 2.42E-04
3.52.33E-04 2.24E-04 2.16E-04 2.08E-04 2.00E-04 1.93E-04 1.86E-04 1.79E-04 1.72E-04 1.66E-04
3.61.59E-04 1.53E-04 1.47E-04 1.42E-04 1.36E-04 1.31E-04 1.26E-04 1.21E-04 1.17E-04 1.12E-04
3.71.08E-04 1.04E-04 9.97E-05 9.59E-05 9.21E-05 8.86E-05 8.51E-05 8.18E-05 7.85E-05 7.55E-05
3.87.25E-05 6.96E-05 6.69E-05 6.42E-05 6.17E-05 5.92E-05 5.68E-05 5.46E-05 5.24E-05 5.03E-05
3.94.82E-05 4.63E-05 4.44E-05 4.26E-05 4.09E-05 3.92E-05 3.76E-05 3.61E-05 3.46E-05 3.32E-05
4.03.18E-05 3.05E-05 2.92E-05 2.80E-05 2.68E-05 2.57E-05 2.47E-05 2.36E-05 2.26E-05 2.17E-05
4.12.08E-05 1.99E-05 1.91E-05 1.82E-05 1.75E-05 1.67E-05 1.60E-05 1.53E-05 1.47E-05 1.40E-05
4.21.34E-05 1.29E-05 1.23E-05 1.18E-05 1.13E-05 1.08E-05 1.03E-05 9.86E-06 9.43E-06 9.01E-06
4.38.62E-06 8.24E-06 7.88E-06 7.53E-06 7.20E-06 6.88E-06 6.57E-06 6.28E-06 6.00E-06 5.73E-06
4.45.48E-06 5.23E-06 5.00E-06 4.77E-06 4.56E-06 4.35E-06 4.16E-06 3.97E-06 3.79E-06 3.62E-06
4.53.45E-06 3.29E-06 3.14E-06 3.00E-06 2.86E-06 2.73E-06 2.60E-06 2.48E-06 2.37E-06 2.26E-06
4.62.15E-06 2.05E-06 1.96E-06 1.87E-06 1.78E-06 1.70E-06 1.62E-06 1.54E-06 1.47E-06 1.40E-06
4.71.33E-06 1.27E-06 1.21E-06 1.15E-06 1.10E-06 1.05E-06 9.96E-07 9.48E-07 9.03E-07 8.59E-07
4.88.18E-07 7.79E-07 7.41E-07 7.05E-07 6.71E-07 6.39E-07 6.08E-07 5.78E-07 5.50E-07 5.23E-07
4.94.98E-07 4.73E-07 4.50E-07 4.28E-07 4.07E-07 3.87E-07 3.68E-07 3.50E-07 3.32E-07 3.16E-07
Probabilitas terjadi
stockout = 0.0495
Z=1.65
Dealing with Demand Uncertainty
•
When demand and or lead time is
uncertain, extra inventory is usually
provided to cope with demand
uncertainty. Thus, reorder point
should include safety stock as
follows:
s
dxl
ROP
Safety Stock
•
If demand variability follows a normal distribution
around the average level, demand uncertainty is
represented by the standard deviation of demand.
Furthermore, safety stock affects the service level.
Thus, when setting a safety stock level, a service level
target should be determined. Safety stock is the
determined by the following formula:
•
where k (SL) is a number in a standard normal
distribution representing that there is a probability of
SL that demand is less than or equal to k, while is
the standard deviation of demand. The values of k for
different SL can be obtained in a normal inverse table.
For example, if k = 1.645, SL = 95%.
x
SL
k
s
(
)
•
Lead Time Pengiriman berdistribusi
normal dengan rata-rata 5 hari dan
standard deviasi 0,5 hari dan
permintaan per hari rata2 1 ton
dengan standard deviasi 0,1 ton.
Manajemen menetapkan service
level 95%.Hitung safety stock dan
nilai ROP nya..
EOQ WITH COORDINATION
The weakness of the traditional EOQ is
that it views cost from the perspective of
the buyer only.
If there is cost incurred to the supplier
associated with each order placed by the
buyer, an integrated model can be
developed.
The Model
Optimal order quantity from both sides is:
Where:
As
= fixed order processing cost incurred to the
supplier
Ab
= fixed order cost incurred to the buyer
D = annual demand
hs
= inventory holding cost to the supplier
hb
= inventory holding cost to the buyer
)
(
)
(
2
b
s
b
s
h
h
D
A
A
Q
Joint Ordering Policies: An Example
For Products With Stable Demand
Demand in a year = 10000
(Buyer) Order cost = 200
(Buyer) Inventory holding cost = 4
(Supplier) Order processing cost = 800
(Supplier) Inventory holding cost = 3
Tentukan berapa optimal order quantity
dan ongkos-ongkos yang ditanggung oleh
buyer, supplier, maupun total keduanya
bila:
1.
Tidak ada integrasi
2.
Ada integrasi antara buyer dan supplier
Solution
TRADITIONAL MODEL
INTEGRATED MODEL
EOQ = 1000
EOQ = 1690
4000
9500
13500
4563
7269
11832
0
2000
4000
6000
8000
10000
12000
14000
16000
Buyer's
Supplier's
TC
Non integrated
Integrated
INVENTORY MODELS FOR ITEMS WITH
SEASONAL DEMAND AND/OR LIMITED LIFE
Model without coordination
Model with coordination between
Examples of Inventory with Seasonal Demand or
Inventory with Limited Lifetime
•
Newspapers and Magazines
•
Vegetables, fresh milk, fresh foods, etc.
•
Fashion products
•
Innovative high tech products: digital
camera, mobile phone, computers
Tradeoff
•
Here, unlike for products with stable
demand, the tradeoff is not between
ordering and inventory holding costs,
but between: overstocking and shortage
costs.
•
Overstocking
products sold with
markdown costs or even disposed
•
Shortage
lost of opportunity and
lost of future customers
BASIC MODEL:
NEWSBOY INVENTORY PROBLEM
•
For items with limited life, in
determining purchasing or production
decisions, we balance the overstocking
and understocking costs. Overstocking
cost is not just inventory holding cost,
but could also be costs due to very low
or zero selling price for the products.
Understocking cost is cost associated
with the lost of selling opportunity.
Newsboy Model
Ritel
c = harga
per unit dari
supplier
p = harga jual
normal per
unit
s = harga
jual diskon
per unit
If the overstocking cost is Co and understocking
cost is Cu then the optimal service level is:
Co = c-s dan Cu = p-c
•
Q < D
(p-c) Q atau Cu*Q
•
Q > D
(p-c) D - (c-s) (Q-D)
•
Secara umum :
P(b)=Cu Min (Q,D)
–
max (0, [Q-D] Co)
Kentungan perusahaan
Optimal Order Quantity
•
If demand is normally distributed with mean
and standard deviation then the optimal order
or production quantity is:
•
If the overstocking cost is Co and
understocking cost is Cu then the optimal
service level is:
•
Where k(SL*) is the inverse normal
distribution, can be found in normal table.
(
*)
*
k
SL
Q
Co
Cu
Cu
SL
Joint Ordering Policies
Principle:
•
Consider costs more broadly. The overstocking
cost is the real cost incurred, from the supply
chain perspective, for stocking one unit of
extra inventory.
•
The understocking cost is the opportunity cost
incurred for one unit shortage from the
perspective of the supply chain.
Example
•
Garment distributor in USA is determining how many
shirts are to be ordered from Indonesia for a selling
season in Summer 2002. The selling price for a shirt is
$35 if sold during the summer. If not, the shirts have to
be sold in a discount price of $10. The distributor has
to pay $17.5 for one shirt to the manufacturer. The
cost already includes delivery. Demand for the shirts is
estimated to follow a normal distribution with mean
1000 and standard deviation 300.
•
Determine:
•
The optimal service level for the distributor
•
The optimal number of shirts to be ordered.
MODEL FOR JOINT ORDERING
POLICIES
SUPPLIER
RETAILER
v = 15
c = 17.5
p = 35
s = 10
For Retailer:
Co = c-s = 7.5
Cu = p-c = 17.5
For Supply Chain:
Co = v-s = 5
Cu = p-v = 20
Optimal service level = Cu/(Co+Cu)
For retailer alone, SL*= 17.5/25 = 70%
For supply chain, SL* = 20/25 = 80%
Suppose that the costs associated with producing one
unit of item at the manufacturer is $15.
Optimal Order for Different
Situation
Tanpa
Koordinasi
Dengan
Koordinasi
Perubahan
SL*
70%
80%
10%
Q
1157
1253
96
Keuntungan Ritel
(Ekspektasi)
14858
14758
-101
Keuntungan pabrik
2893
3133
240
Keuntungan Total
17751
17890
139
Steps Dalam Melakukan Simulasi
(Silakan dicoba)
•
Generate demand (D) yang berdistribusi normal
dengan mean 1000 dan standar deviasi 200. Pada
Excell ini bisa dilakukan dengan perintah:
=Round(NORMINV(Rand(), 1000, 200),0).
•
Profit supplier (SP) yang besarnya = Q * 2 dimana Q
adalah order quantity dari buyer.
•
Profit untuk buyer (BP) adalah Q * 5 kalau Q kurang
dari permintaan dan D * 5
–
(Q-D)*3 kalau Q lebih
dari D. Pada EXCELL formulasinya adalah:
=Min(Q,D)*5
–
Max(0,(Q-D))*3
•
Hitung total profit = BP + SP.
•
Lakukan untuk Q = 1066 maupun 1235.
What is required to make the
models work?
Willingness to share costs data
Quick Response: Reducing inventory
mismatch
Ukuran batch
kecil
Ekspektasi awal
Zara menghentikan produksi kalau
signal awal menunjukkan
Pasar kurang agresif
Vendor Managed Inventory (VMI)
Barilla Spa
Cortese
Informasi POS dan data
persediaan secara real time
Membuat
keputusan
pengiriman ke
Cortese
Suppliers are given more roles.
They make decisions on delivery schedule.
Results :
-Pengurangan stockout dari 6-7 %
menjadi hampir 0%
- Persediaan berkurang sekitar 46%
