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CONTENTS General Introduction to Inventory Management
COORDINATED 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
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.
There are a number of reasons why inventory exists: • To obtain economies of scale • To prevent for uncertainty / to achieve higher service level
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 Safety stock Anticipation stock
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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.
Inventory Models For Items With Stable Demand
Models with coordination between buyer and supplier
Models without coordination
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.
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
• Ordering cost perperioda = frekuensi pemesanan
• If your orders are too small, you will have to place more orders to meet demand, leading to high ordering costs
• Purchase cost perperioda = jumlah kebutuhan
Order Size
Holding Costs
Ordering Costs
Too LARGE
High
Low
Too SMALL
Low
High
dalam 1 perioda x C =
D C Q
perperioda x P = DP
• Holding cost perperioda = rata-rata banyaknya barang Q
yang disimpan perperioda x H = 2 H D Q • Total cost inventory : TC = C + DP + H Q
2
dTC d 2TC • TC akan minimum jika : = 0 dan 0 dQ d 2Q
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TC (Q)
D Q Co h Q 2
Q*
2CoD h
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.
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
5.00E-01 4.60E-01 4.21E-01 3.82E-01 3.45E-01 3.09E-01 2.74E-01 2.42E-01 2.12E-01 1.84E-01
4.96E-01 4.56E-01 4.17E-01 3.78E-01 3.41E-01 3.05E-01 2.71E-01 2.39E-01 2.09E-01 1.81E-01
4.92E-01 4.52E-01 4.13E-01 3.75E-01 3.37E-01 3.02E-01 2.68E-01 2.36E-01 2.06E-01 1.79E-01
4.88E-01 4.48E-01 4.09E-01 3.71E-01 3.34E-01 2.98E-01 2.64E-01 2.33E-01 2.03E-01 1.76E-01
4.84E-01 4.44E-01 4.05E-01 3.67E-01 3.30E-01 2.95E-01 2.61E-01 2.30E-01 2.01E-01 1.74E-01
4.80E-01 4.40E-01 4.01E-01 3.63E-01 3.26E-01 2.91E-01 2.58E-01 2.27E-01 1.98E-01 1.71E-01
4.76E-01 4.36E-01 3.97E-01 3.59E-01 3.23E-01 2.88E-01 2.55E-01 2.24E-01 1.95E-01 1.69E-01
4.72E-01 4.33E-01 3.94E-01 3.56E-01 3.19E-01 2.84E-01 2.51E-01 2.21E-01 1.92E-01 1.66E-01
4.68E-01 4.29E-01 3.90E-01 3.52E-01 3.16E-01 2.81E-01 2.48E-01 2.18E-01 1.89E-01 1.64E-01
4.64E-01 4.25E-01 3.86E-01 3.48E-01 3.12E-01 2.78E-01 2.45E-01 2.15E-01 1.87E-01 1.61E-01
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
1.59E-01 1.36E-01 1.15E-01 9.68E-02 8.08E-02 6.68E-02 5.48E-02 4.46E-02 3.59E-02 2.87E-02
1.56E-01 1.34E-01 1.13E-01 9.51E-02 7.93E-02 6.55E-02 5.37E-02 4.36E-02 3.52E-02 2.81E-02
1.5 39E01 1.31E-01 1.11E-01 9.34E-02 7.78E-02 6.43E-02 5.26E-02 4.27E-02 3.44E-02 2.74E-02
1.52E-01 1.29E-01 1.09E-01 9.18E-02 7.64E-02 6.30E-02 5.16E-02 4.18E-02 3.36E-02 2.68E-02
1.49E-01 1.27E-01 1.08E-01 9.01E-02 7.49E-02 6.18E-02 5.05E-02 4.09E-02 3.29E-02 2.62E-02
1.47E-01 1.25E-01 1.06E-01 8.85E-02 7.35E-02 6.06E-02 4.95E-02 4.01E-02 3.22E-02 2.56E-02
1.45E-01 1.23E-01 1.04E-01 8.69E-02 7.21E-02 5.94E-02 4.85E-02 3.92E-02 3.14E-02 2.50E-02
1.42E-01 1.21E-01 1.02E-01 8.53E-02 7.08E-02 5.82E-02 4.75E-02 3.84E-02 3.07E-02 2.44E-02
1.40E-01 1.19E-01 1.00E-01 8.38E-02 6.94E-02 5.71E-02 4.65E-02 3.75E-02 3.01E-02 2.39E-02
1.38E-01 1.17E-01 9.85E-02 8.23E-02 6.81E-02 5.59E-02 4.55E-02 3.67E-02 2.94E-02 2.33E-02
2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9
2.28E-02 1.79E-02 1.39E-02 1.07E-02 8.20E-03 6.21E-03 4.66E-03 3.47E-03 2.56E-03 1.87E-03
2.22E-02 1.74E-02 1.36E-02 1.04E-02 7.98E-03 6.04E-03 4.53E-03 3.36E-03 2.48E-03 1.81E-03
2.17E-02 1.70E-02 1.32E-02 1.02E-02 7.76E-03 5.87E-03 4.40E-03 3.26E-03 2.40E-03 1.75E-03
2.12E-02 1.66E-02 1.29E-02 9.90E-03 7.55E-03 5.70E-03 4.27E-03 3.17E-03 2.33E-03 1.70E-03
2.07E-02 1.62E-02 1.26E-02 9.64E-03 7.34E-03 5.54E-03 4.15E-03 3.07E-03 2.26E-03 1.64E-03
2.02E-02 1.58E-02 1.22E-02 9.39E-03 7.14E-03 5.39E-03 4.02E-03 2.98E-03 2.19E-03 1.59E-03
1.97E-02 1.54E-02 1.19E-02 9.14E-03 6.95E-03 5.23E-03 3.91E-03 2.89E-03 2.12E-03 1.54E-03
1.92E-02 1.50E-02 1.16E-02 8.89E-03 6.76E-03 5.09E-03 3.79E-03 2.80E-03 2.05E-03 1.49E-03
1.88E-02 1.46E-02 1.13E-02 8.66E-03 6.57E-03 4.94E-03 3.68E-03 2.72E-03 1.99E-03 1.44E-03
1.83E-02 1.43E-02 1.10E-02 8.42E-03 6.39E-03 4.80E-03 3.57E-03 2.64E-03 1.93E-03 1.40E-03
3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9
1.35E-03 9.68E-04 6.87E-04 4.84E-04 3.37E-04 2.33E-04 1.59E-04 1.08E-04 7.25E-05 4.82E-05
1.31E-03 9.35E-04 6.64E-04 4.67E-04 3.25E-04 2.24E-04 1.53E-04 1.04E-04 6.96E-05 4.63E-05
1.26E-03 9.04E-04 6.41E-04 4.50E-04 3.13E-04 2.16E-04 1.47E-04 9.97E-05 6.69E-05 4.44E-05
1.22E-03 8.74E-04 6.19E-04 4.34E-04 3.02E-04 2.08E-04 1.42E-04 9.59E-05 6.42E-05 4.26E-05
1.18E-03 8.45E-04 5.98E-04 4.19E-04 2.91E-04 2.00E-04 1.36E-04 9.21E-05 6.17E-05 4.09E-05
1.14E-03 8.16E-04 5.77E-04 4.04E-04 2.80E-04 1.93E-04 1.31E-04 8.86E-05 5.92E-05 3.92E-05
1.11E-03 7.89E-04 5.57E-04 3.90E-04 2.70E-04 1.86E-04 1.26E-04 8.51E-05 5.68E-05 3.76E-05
1.07E-03 7.62E-04 5.38E-04 3.76E-04 2.60E-04 1.79E-04 1.21E-04 8.18E-05 5.46E-05 3.61E-05
1.04E-03 7.36E-04 5.19E-04 3.63E-04 2.51E-04 1.72E-04 1.17E-04 7.85E-05 5.24E-05 3.46E-05
1.00E-03 7.11E-04 5.01E-04 3.50E-04 2.42E-04 1.66E-04 1.12E-04 7.55E-05 5.03E-05 3.32E-05
4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9
3.18E-05 2.08E-05 1.34E-05 8.62E-06 5.48E-06 3.45E-06 2.15E-06 1.33E-06 8.18E-07 4.98E-07
3.05E-05 1.99E-05 1.29E-05 8.24E-06 5.23E-06 3.29E-06 2.05E-06 1.27E-06 7.79E-07 4.73E-07
2.92E-05 1.91E-05 1.23E-05 7.88E-06 5.00E-06 3.14E-06 1.96E-06 1.21E-06 7.41E-07 4.50E-07
2.80E-05 1.82E-05 1.18E-05 7.53E-06 4.77E-06 3.00E-06 1.87E-06 1.15E-06 7.05E-07 4.28E-07
2.68E-05 1.75E-05 1.13E-05 7.20E-06 4.56E-06 2.86E-06 1.78E-06 1.10E-06 6.71E-07 4.07E-07
2.57E-05 1.67E-05 1.08E-05 6.88E-06 4.35E-06 2.73E-06 1.70E-06 1.05E-06 6.39E-07 3.87E-07
2.47E-05 1.60E-05 1.03E-05 6.57E-06 4.16E-06 2.60E-06 1.62E-06 9.96E-07 6.08E-07 3.68E-07
2.36E-05 1.53E-05 9.86E-06 6.28E-06 3.97E-06 2.48E-06 1.54E-06 9.48E-07 5.78E-07 3.50E-07
2.26E-05 1.47E-05 9.43E-06 6.00E-06 3.79E-06 2.37E-06 1.47E-06 9.03E-07 5.50E-07 3.32E-07
2.17E-05 1.40E-05 9.01E-06 5.73E-06 3.62E-06 2.26E-06 1.40E-06 8.59E-07 5.23E-07 3.16E-07
Z
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:
dxl • For example, if lead time for ordering flour is one week, determine reorder point.
Probabilitas terjadi stockout = 0.0495
Z=1.65
0
Dealing with Demand Uncertainty
Safety Stock
• 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:
• 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:
ROP dxl s
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The model: Total cost = Order cost + Holding cost
s k ( SL) x • 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%.
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EOQ WITH COORDINATION • 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..
Optimal order quantity from both sides is:
2( As Ab) D (hs hb)
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
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
INVENTORY MODELS FOR ITEMS WITH SEASONAL DEMAND AND/OR LIMITED LIFE
Solution TRADITIONAL MODEL EOQ = 1000
INTEGRATED MODEL EOQ = 1690
16000
Model without coordination Model with coordination between buyer and supplier
13500 11832
14000 12000
9500
10000
7269
8000 6000
If there is cost incurred to the supplier associated with each order placed by the buyer, an integrated model can be developed.
Joint Ordering Policies: An Example For Products With Stable Demand
The Model Q
The weakness of the traditional EOQ is that it views cost from the perspective of the buyer only.
4000 4563
4000 2000 0 Buyer's
Non integrated
Supplier's
TC
Integrated
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Examples of Inventory with Seasonal Demand or Inventory with Limited Lifetime
Tradeoff
• Newspapers and Magazines • Vegetables, fresh milk, fresh foods, etc. • Fashion products • Innovative high tech products: digital camera, mobile phone, computers
• 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.
Kentungan perusahaan • 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)
Newsboy Model p = harga jual normal per unit
c = harga per unit dari supplier Ritel
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
Optimal Order Quantity • If demand is normally distributed with mean and standard deviation then the optimal order or production quantity is: Q* k ( SL*) • If the overstocking cost is Co and understocking cost is Cu then the optimal Cu service level is: SL* Cu Co • Where k(SL*) is the inverse normal distribution, can be found in normal table.
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Example
Joint Ordering Policies
• 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.
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.
Optimal Order for Different Situation
MODEL FOR JOINT ORDERING POLICIES Suppose that the costs associated with producing one unit of item at the manufacturer is $15. v = 15
SUPPLIER
c = 17.5
For Retailer: Co = c-s = 7.5 Cu = p-c = 17.5
p = 35 RETAILER
s = 10 For Supply Chain: Co = v-s = 5 Cu = p-v = 20
Tanpa Koordinasi
Dengan Koordinasi
Perubahan
SL*
70%
80%
Q
1157
1253
96
14858
14758
-101
2893
3133
240
17751
17890
139
Keuntungan Ritel (Ekspektasi) Keuntungan pabrik Keuntungan Total
10%
Optimal service level = Cu/(Co+Cu) For retailer alone, SL*= 17.5/25 = 70% For supply chain, SL* = 20/25 = 80%
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 Willingness to work together to establish joint plan
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Quick Response: Reducing inventory mismatch Zara menghentikan produksi kalau signal awal menunjukkan Pasar kurang agresif
Vendor Managed Inventory (VMI) Suppliers are given more roles. They make decisions on delivery schedule. Informasi POS dan data persediaan secara real time
Barilla Spa Ukuran batch kecil
Ekspektasi awal
Membuat keputusan pengiriman ke Cortese
Cortese Results : -Pengurangan stockout dari 6-7 % menjadi hampir 0% - Persediaan berkurang sekitar 46% - Pengiriman menjadi lebih konsisten
• Demand for Deskpro computer at Best Buy 1000 unit per month. Best Buy incurs a fixed order placement, transportation, and receiving cost of $4000 each time an order is placed. Each computer cost Best Buy $500 and the retailer has a holding cost of 20 percent . Evaluate the number of computer that the store manager should order in each replenishment lot
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