Inventory Exists In Many Places Throughout The Supply Chain

  CONTENTS General Introduction to Inventory Management

COORDINATED INVENTORY

  Inventory Models for Smooth Demand: MANAGEMENT With and without coordination

  Inventory Models for Seasonal Demand: With and Without Coordination Inventory Exists In Many Places Throughout The Supply Chain

  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 : Types of Inventory

• Supplier Manufacture Distributor Distributor
• Mengurangi ketergantungan antar tahap dalam mata Based on their status:
• Raw Material rantai sistem produksi – distribusi.

  Finished Part Mempertahankan stabilitas penggunaan tenaga kerja

• Component Part karena fluktuasi demand.
• Subassembly Material
• Mengantisipasi kemungkinan terjadinya gangguan
• Work In-Process (WIP)

  yang berupa keterlambatan pasokan atau

• Finished Goods berhentinya aktivitas dalam sistem produksi.
• Based on their functions:
>Mengambil keuntungan dng memanfaatkan potongan
• Pipeline / in-transit inventory harga untuk pembelian dlm jumlah besar.
• Cycle s
• Mengantisipasi tejadinya kenaikan harga barang
>Safety stock karena inflasi.
• Anticipation s
• Mengantisipasi terjadinya stock out karena permintaan melebihi perkiraan.

  Types of Inventory (2)

• Berdasarkan Sifat Ketergantungan Kebutuhan

  People often behave conservatively when Independent Demand → kebutuhan akan suatu item barang • making inventory decision. tidak tergantung item yang lain.

  Misalnya kebutuhan barang untuk memenuhi permintaan pembeli di sebuah toko, kebutuhan bahan baku utama dari This is due to, as stated by Ballou (1999, pp. produk yang kebutuhannya ditentukan berdasarkan demand forecasting. 310), criticism for being overstocked is much

  Dependent Demand → kebutuhan akan item tertentu • more defensible than being short of supply. tergantung/terkait pada kebutuhan terhadap item yang lain. Ketergantungan antar item bisa berbentuk :

• ketergantungan vertikal : mis. kebutuhan dari komponen

  The major portion of inventory holding costs is penyusun subrakitan/ produk jadi.

• ketergantungan horizontal : mis. kebutuhan dr komponen of an opportunity cost nature and therefore pelengkap (bahan pembantu) yang menyertai produk.

  goes unidentified in normal accounting system.

  Inventory Models For Items Finding Optimal Order Quantity

  With Stable Demand

• 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

  Models with holding cost. Models without coordination coordination between buyer and

• If ordering cost is high, people tend to order less

  supplier 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
• Ordering cost perperioda = frekuensi pemesanan

  inventory and high holding costs D C dalam 1 perioda x C =

  Q

  If your orders are too small, you will have to place Purchase cost perperioda = jumlah kebutuhan more orders to meet demand, leading to high ordering perperioda x P = DP costs

• Holding cost perperioda = rata-rata banyaknya barang

  Order Size Holding Costs Ordering Costs Q H yang disimpan perperioda x H =

  2 Too LARGE High Low D Q

• C

  Total cost inventory : TC = + DP + H Q

  2 Too SMALL Low High

  2 dTC d TC

• TC akan minimum jika : = dan  

  2 dQ d Q

•  Where D = annual demand Co = order cost h = inventory holding cost
• 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:

  4.19E-04

  5.01E-04

  3.3

  4.84E-04

  4.67E-04

  4.50E-04

  4.34E-04

  4.04E-04

  5.38E-04

  3.90E-04

  3.76E-04

  3.63E-04

  3.50E-04

  3.4

  3.37E-04

  5.19E-04

  5.57E-04

  3.13E-04

  7.36E-04

  9.04E-04

  8.74E-04

  8.45E-04

  8.16E-04

  7.89E-04

  7.62E-04

  7.11E-04

  5.77E-04

  3.2

  6.87E-04

  6.64E-04

  6.41E-04

  6.19E-04

  5.98E-04

  3.25E-04

  3.02E-04

  9.68E-04

  1.21E-04

  1.53E-04

  1.47E-04

  1.42E-04

  1.36E-04

  1.31E-04

  1.26E-04

  1.17E-04

  3.6

  1.12E-04

  3.7

  1.08E-04

  1.04E-04

  9.97E-05

  9.59E-05

  1.59E-04

  1.66E-04

  2.91E-04

  2.33E-04

  2.80E-04

  2.70E-04

  2.60E-04

  2.51E-04

  2.42E-04

  3.5

  2.24E-04

  1.72E-04

  2.16E-04

  2.08E-04

  2.00E-04

  1.93E-04

  1.86E-04

  1.79E-04

  9.35E-04

  3.1

  8.86E-05

  3.57E-03

  4.27E-03

  4.15E-03

  4.02E-03

  3.91E-03

  3.79E-03

  3.68E-03

  2.7

  4.53E-03

  3.47E-03

  3.36E-03

  3.26E-03

  3.17E-03

  3.07E-03

  2.98E-03

  4.40E-03

  4.66E-03

  2.80E-03

  5.87E-03

  6.76E-03

  6.57E-03

  6.39E-03

  2.5

  6.21E-03

  6.04E-03

  5.70E-03

  2.6

  5.54E-03

  5.39E-03

  5.23E-03

  5.09E-03

  4.94E-03

  4.80E-03

  2.89E-03

  2.72E-03

  1.00E-03

  1.31E-03

  1.54E-03

  1.49E-03

  1.44E-03

  1.40E-03

  3.0

  1.35E-03

  1.26E-03

  1.64E-03

  1.22E-03

  1.18E-03

  1.14E-03

  1.11E-03

  1.07E-03

  1.04E-03

  1.59E-03

  1.70E-03

  2.64E-03

  2.19E-03

  2.8

  2.56E-03

  2.48E-03

  2.40E-03

  2.33E-03

  2.26E-03

  2.12E-03

  1.75E-03

  2.05E-03

  1.99E-03

  1.93E-03

  2.9

  1.87E-03

  1.81E-03

  9.21E-05

  8.51E-05

  7.14E-03

  1.70E-06

  4.6

  2.15E-06

  2.05E-06

  1.96E-06

  1.87E-06

  1.78E-06

  1.62E-06

  2.37E-06

  1.54E-06

  1.47E-06

  1.40E-06

  4.7

  1.33E-06

  1.27E-06

  2.26E-06

  2.48E-06

  1.15E-06

  3.62E-06

  4.77E-06

  4.56E-06

  4.35E-06

  4.16E-06

  3.97E-06

  3.79E-06

  4.5

  2.60E-06

  3.45E-06

  3.29E-06

  3.14E-06

  3.00E-06

  2.86E-06

  2.73E-06

  1.21E-06

  1.10E-06

  5.23E-06

  3.32E-07

  4.50E-07

  4.28E-07

  4.07E-07

  3.87E-07

  3.68E-07

  3.50E-07

  3.16E-07

  4.98E-07

  Probabilitas terjadi stockout = 0.0495 Z=1.65

  Dealing with Demand Uncertainty

  ROP s dxl  

  Safety Stock

  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%.

   SL x k s ) (

  4.73E-07

  4.9

  1.05E-06

  7.79E-07

  9.96E-07

  9.48E-07

  9.03E-07

  8.59E-07

  4.8

  8.18E-07

  7.41E-07

  5.23E-07

  7.05E-07

  6.71E-07

  6.39E-07

  6.08E-07

  5.78E-07

  5.50E-07

  5.00E-06

  5.48E-06

  8.18E-05

  4.0

  4.09E-05

  3.92E-05

  3.76E-05

  3.61E-05

  3.46E-05

  3.32E-05

  3.18E-05

  4.44E-05

  3.05E-05

  2.92E-05

  2.80E-05

  2.68E-05

  2.57E-05

  2.47E-05

  4.26E-05

  4.63E-05

  2.26E-05

  6.42E-05

  7.85E-05

  7.55E-05

  3.8

  7.25E-05

  6.96E-05

  6.69E-05

  6.17E-05

  4.82E-05

  5.92E-05

  5.68E-05

  5.46E-05

  5.24E-05

  5.03E-05

  3.9

  2.36E-05

  2.17E-05

  4.4

  7.88E-06

  9.86E-06

  9.43E-06

  9.01E-06

  4.3

  8.62E-06

  8.24E-06

  7.53E-06

  1.08E-05

  7.20E-06

  6.88E-06

  6.57E-06

  6.28E-06

  6.00E-06

  5.73E-06

  1.03E-05

  1.13E-05

  4.1

  1.60E-05

  2.08E-05

  1.99E-05

  1.91E-05

  1.82E-05

  1.75E-05

  1.67E-05

  1.53E-05

  1.18E-05

  1.47E-05

  1.40E-05

  4.2

  1.34E-05

  1.29E-05

  1.23E-05

  6.95E-03

  7.34E-03

   

  2.42E-01

  2.58E-01

  2.55E-01

  2.51E-01

  2.48E-01

  2.45E-01

  0.7

  2.39E-01

  2.64E-01

  2.36E-01

  2.33E-01

  2.30E-01

  2.27E-01

  2.24E-01

  2.21E-01

  2.61E-01

  2.68E-01

  2.15E-01

  2.95E-01

  3.12E-01

  0.5

  3.09E-01

  3.05E-01

  3.02E-01

  2.98E-01

  2.91E-01

  2.71E-01

  2.88E-01

  2.84E-01

  2.81E-01

  2.78E-01

  0.6

  2.74E-01

  2.18E-01

  0.8

  3.19E-01

  1.49E-01

  1.64E-01

  1.61E-01

  1.0

  1.59E-01

  1.56E-01 1.5 39E01

  1.52E-01

  1.47E-01

  1.69E-01

  1.45E-01

  1.42E-01

  1.40E-01

  1.38E-01

  1.1

  1.36E-01

  1.66E-01

  1.71E-01

  2.12E-01

  1.92E-01

  2.09E-01

  2.06E-01

  2.03E-01

  2.01E-01

  1.98E-01

  1.95E-01

  1.89E-01

  1.74E-01

  1.87E-01

  0.9

  1.84E-01

  1.81E-01

  1.79E-01

  1.76E-01

  3.16E-01

  3.23E-01

  1.31E-01

  4.80E-01

  0.0

  5.00E-01

  4.96E-01

  4.92E-01

  4.88E-01

  4.84E-01

  4.76E-01

  0.08

  4.72E-01

  4.68E-01

  4.64E-01

  0.1

  4.60E-01

  4.56E-01

  0.09

  0.07

  4.48E-01

  Reorder Point

  The model: Total cost = Order cost + Holding cost h Q

  Co Q D Q TC

  2 ) (   h CoD

  Q

  2

  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.

  d x l

  0.06

  16 Z

  0.01

  0.02

  0.03

  0.04

  0.05

  4.52E-01

  4.44E-01

  3.26E-01

  3.52E-01

  3.75E-01

  3.71E-01

  3.67E-01

  3.63E-01

  3.59E-01

  3.56E-01

  3.48E-01

  3.82E-01

  0.4

  3.45E-01

  3.41E-01

  3.37E-01

  3.34E-01

  3.30E-01

  3.78E-01

  0.3

  4.40E-01

  4.17E-01

  4.36E-01

  4.33E-01

  4.29E-01

  4.25E-01

  0.2

  4.21E-01

  4.13E-01

  3.86E-01

  4.09E-01

  4.05E-01

  4.01E-01

  3.97E-01

  3.94E-01

  3.90E-01

  1.34E-01

  1.29E-01

  7.55E-03

  2.12E-02

  2.39E-02

  2.33E-02

  2.0

  2.28E-02

  2.22E-02

  2.17E-02

  2.07E-02

  2.50E-02

  2.02E-02

  1.97E-02

  1.92E-02

  1.88E-02

  1.83E-02

  2.1

  2.44E-02

  2.56E-02

  1.74E-02

  3.07E-02

  3.52E-02

  3.44E-02

  3.36E-02

  3.29E-02

  3.22E-02

  3.14E-02

  3.01E-02

  2.62E-02

  2.94E-02

  1.9

  2.87E-02

  2.81E-02

  2.74E-02

  2.68E-02

  1.79E-02

  1.70E-02

  3.67E-02

  9.14E-03

  1.07E-02

  1.04E-02

  1.02E-02

  9.90E-03

  9.64E-03

  9.39E-03

  8.89E-03

  1.10E-02

  8.66E-03

  8.42E-03

  2.4

  8.20E-03

  7.98E-03

  7.76E-03

  2.3

  1.13E-02

  1.66E-02

  2.2

  1.62E-02

  1.58E-02

  1.54E-02

  1.50E-02

  1.46E-02

  1.43E-02

  1.39E-02

  1.16E-02

  1.36E-02

  1.32E-02

  1.29E-02

  1.26E-02

  1.22E-02

  1.19E-02

  3.59E-02

  3.75E-02

  1.27E-01

  8.53E-02

  9.51E-02

  9.34E-02

  9.18E-02

  9.01E-02

  8.85E-02

  8.69E-02

  8.38E-02

  1.3

  8.23E-02

  1.4

  8.08E-02

  7.93E-02

  7.78E-02

  7.64E-02

  9.68E-02

  9.85E-02

  7.35E-02

  1.15E-01

  1.25E-01

  1.23E-01

  1.21E-01

  1.19E-01

  1.17E-01

  1.2

  1.13E-01

  1.00E-01

  1.11E-01

  1.09E-01

  1.08E-01

  1.06E-01

  1.04E-01

  1.02E-01

  7.49E-02

  7.21E-02

  3.84E-02

  1.7

  5.05E-02

  4.95E-02

  4.85E-02

  4.75E-02

  4.65E-02

  4.55E-02

  4.46E-02

  5.26E-02

  4.36E-02

  4.27E-02

  4.18E-02

  4.09E-02

  4.01E-02

  3.92E-02

  5.16E-02

  5.37E-02

  7.08E-02

  6.30E-02

  6.94E-02

  6.81E-02

  1.5

  6.68E-02

  6.55E-02

  6.43E-02

  6.18E-02

  5.48E-02

  6.06E-02

  5.94E-02

  5.82E-02

  5.71E-02

  5.59E-02

  1.6

• For example, if lead time for ordering flour is one week, determine reorder point.
• 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
• 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:

EOQ WITH COORDINATION

  Lead Time Pengiriman berdistribusi that it views cost from the perspective of normal dengan rata-rata 5 hari dan the buyer only. standard deviasi 0,5 hari dan permintaan per hari rata2 1 ton

• The weakness of the traditional EOQ is

  If there is cost incurred to the supplier dengan standard deviasi 0,1 ton. associated with each order placed by the

  Manajemen menetapkan service buyer, an integrated model can be level 95%.Hitung safety stock dan developed. nilai ROP nya..

  Joint Ordering Policies: An Example The Model

  For Products With Stable Demand Demand in a year = 10000 Optimal order quantity from both sides is:

  (Buyer) Order cost = 200 s b

  (Buyer) Inventory holding cost = 4 Q 

  

( h s  h b ) (Supplier) Order processing cost = 800

Where:

  (Supplier) Inventory holding cost = 3 A s = fixed order processing cost incurred to the supplier

  Tentukan berapa optimal order quantity dan ongkos-ongkos yang ditanggung oleh A b = fixed order cost incurred to the buyer buyer, supplier, maupun total keduanya

  D = annual demand bila: h s = inventory holding cost to the supplier

  1. Tidak ada integrasi

  2. Ada integrasi antara buyer dan supplier h b = inventory holding cost to the buyer

  INVENTORY MODELS FOR ITEMS WITH SEASONAL DEMAND AND/OR LIMITED LIFE Solution

TRADITIONAL MODEL

   Model without coordination

  EOQ = 1000 EOQ = 1690 

  Model with coordination between buyer and supplier 16000 13500 14000 11832 12000 9500 10000 7269

  8000 6000 4563 4000 4000

  2000 Buyer's Supplier's TC Non integrated Integrated

  Examples of Inventory with Seasonal Demand or Inventory with Limited Lifetime

• Newspapers and Magazines • Vegetables, fresh milk, fresh foods, etc.
• 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
• Fashion products
• Innovative high tech products: digital
• Shortage  lost of opportunity and
• For items with limited life, in
• If demand is normally distributed with mean and standard deviation then the optimal order or production quantity is:
• Q < D  (p-c) Q atau Cu*Q
• Q > D  (p-c) D - (c-s) (Q-D)
• Secara umum :
• ) ( *
• – max (0, [Q-D] Co)

• 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.
• Garment distributor in USA is determining how many

  camera, mobile phone, computers Tradeoff

  markdown costs or even disposed

  lost of future customers BASIC MODEL: NEWSBOY INVENTORY PROBLEM

  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

  P(b)=Cu Min (Q,D)

  Kentungan perusahaan Optimal Order Quantity

   

  SL k Q  

  Co Cu Cu SL

    *

• 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.
• Determine:
• The optimal service level for the distributor • The optimal number of shirts to be ordered.

  Optimal Order for Different Situation Tanpa Koordinasi Dengan Koordinasi Perubahan

  What is required to make the models work?  Willingness to share costs data 

  dari permintaan dan D * 5

  dengan mean 1000 dan standar deviasi 200. Pada Excell ini bisa dilakukan dengan perintah: =Round(NORMINV(Rand(), 1000, 200),0).

  (Silakan dicoba)

  Keuntungan Total 17751 17890 139 Steps Dalam Melakukan Simulasi

  96 Keuntungan Ritel (Ekspektasi) 14858 14758 -101 Keuntungan pabrik 2893 3133 240

  SL* 70% 80% 10% Q 1157 1253

  Suppose that the costs associated with producing one unit of item at the manufacturer is $15.

  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%

  Co = c-s = 7.5 Cu = p-c = 17.5 For Supply Chain: Co = v-s = 5

  MODEL FOR JOINT ORDERING POLICIES SUPPLIER RETAILER v = 15 c = 17.5 p = 35 s = 10 For Retailer:

  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.

  Example

  Joint Ordering Policies Principle:

• Generate demand (D) yang berdistribusi normal

  Willingness to work together to establish joint plan

• Profit supplier (SP) yang besarnya = Q * 2 dimana Q adalah order quantity dari buyer.
• Profit untuk buyer (BP) adalah Q * 5 kalau Q kurang
• – (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.

  Quick Response: Reducing inventory Vendor Managed Inventory (VMI) mismatch Suppliers are given more roles.

  Zara menghentikan produksi kalau They make decisions on delivery schedule. signal awal menunjukkan Pasar kurang agresif

  Informasi POS dan data persediaan secara real time Cortese Barilla Spa

  Results : Membuat Ukuran batch Ekspektasi awal

• Pengurangan stockout dari 6-7 % keputusan

  kecil menjadi hampir 0% pengiriman ke

• Persediaan berkurang sekitar 46% Cortese - 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