Inventory Management I

Definitions Inventory-A physical resource that a firm holds in stock with the intent of selling it or transforming it into a more valuable state. Inventory System- A set of policies and controls that monitors levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be

Inventory management Responsible for planning and controlling inventory from the raw material stage to the customer and for production support. Usually represent from 20% to 60% of total assets.

Inventory Def. - A physical resource that a firm holds in stock with the intent of selling it or transforming it into a more valuable state. Raw Materials Works-in-Process Finished Goods Maintenance, Repair and Operating (MRO)

Reasons for Inventories Improve customer service Economies of purchasing Economies of production Transportation savings Hedge against future Unplanned shocks (labor strikes, natural disasters, surges in demand, etc.) To maintain independence of supply chain

Reasons for Inventories Low cost plan operation Minimum investment

Inventory Costs Costs associated with inventory: Item cost / purchasing cost = c Carrying cost / Holding cost = h Ordering cost / Set up cost = k Cost of having too much / disposal Cost of not having enough (shortage)

Inventory Holding Costs Category% of Value Housing (building) cost6% Material handling3% Labor cost3% Opportunity/investment11% Pilferage/scrap/obsolescence3% Total Holding Cost26%

Inventory Holding Costs Capital cost Storage cost Risk cost - Obsolescence - Damage - Pilferage, goods lost, strayed, stolen - Deterioration

ABC Analysis Divides on-hand inventory into 3 classes A class, B class, C class Basis is usually annual $ volume $ volume = Annual demand x Unit cost Policies based on ABC analysis Develop class A suppliers more Give tighter physical control of A items Forecast A items more carefully

Classifying Items as ABC % of Inventory Items % Annual $ Usage A B C

ABC Classification Solution Stock #Vol.Cost$ Vol.%ABC 20626,000$ 36$936, , , , ,000480, , ,000 Total1,316,000

ABC Classification Solution

Order Quantities How much should be ordered at one time ? When should an order be placed ?

Order Quantities Static : - EOQ ( Economic Order Quantity ) - POQ ( Period- Order Quantity ) - EPQ ( Economic Production Quantity ) Dynamic : - EOQ - Warner – Within ( dynamic prog.) - Silver- meal

Economic Order Quantity Assumptions Demand rate is known and constant No order lead time Shortages are not allowed Costs: k - setup cost per order h - holding cost per unit time

EOQ Time Inventory Level Q* Optimal Order Quantity Decrease Due to Constant Demand

EOQ Time Inventory Level Q* Optimal Order Quantity Instantaneous Receipt of Optimal Order Quantity

EOQ Time Inventory Level Q* Optimal Order Quantity Lead Time

EOQ Time Inventory Level Q* Lead Time Reorder Point (ROP)

EOQ Time Inventory Level Q* Lead Time Reorder Point (ROP) Average Inventory Q/2

Total Costs Average Inventory = Q/2 Annual Holding costs = H * Q/2 # Orders per year = D / Q Annual Ordering Costs = k * D/Q Annual Total Costs = Holding + Ordering

How Much to Order? Annual Cost Order Quantity Holding Cost = H * Q/2

How Much to Order? Annual Cost Order Quantity Holding Cost = H * Q/2 Ordering Cost =k* D/Q

How Much to Order? Annual Cost Order Quantity Total Cost = Holding + Ordering

How Much to Order? Annual Cost Order Quantity Total Cost = Holding + Ordering Optimal Q

Optimal Quantity Total Costs =

Optimal Quantity Total Costs = Take derivative with respect to Q =

Optimal Quantity Total Costs = Take derivative with respect to Q = Set equal to zero

Optimal Quantity Total Costs = Take derivative with respect to Q = Solve for Q: Set equal to zero

Optimal Quantity Total Costs = Take derivative with respect to Q = Solve for Q: Set equal to zero

A Question: If the EOQ is based on so many horrible assumptions that are never really true, why is it the most commonly used ordering policy?

Benefits of EOQ Profit function is very shallow Even if conditions don’t hold perfectly, profits are close to optimal Estimated parameters will not throw you off very far

Quantity Discounts How does this all change if price changes depending on order size? Explicitly consider price: v = price, r = discount price

Discount Example D = 10,000k= $20 r = 20% PriceQuantityEOQ v = 5.00Q < Q >=

Discount Pricing Total Cost Order Size 500 1,000 Price 1Price 2Price 3 X 633 X 666 X 716

Discount Pricing Total Cost Order Size 500 1,000 Price 1Price 2Price 3 X 633 X 666 X 716

Discount Example Order 666 at a time: Hold 666/2 * 4.50 * 0.2=$ Order10,000/666 * 20 =$ Mat’l10,000*4.50 =$45, , =$ Order 1,000 at a time: Hold 1,000/2 * 3.90 * 0.2=$ Order10,000/1,000 * 20 =$ Mat’l10,000*3.90 =$39, ,590.00

Discount Model 1.Compute EOQ for each price 2.Is EOQ ‘realizeable’? (is Q in range?) If EOQ is too large, use lowest possible value. If too small, ignore. 3.Compute total cost for this quantity 4.Select quantity/price with lowest total cost.

Period-Order Quantity Minimize the total cost of ordering and carrying inventory and is based on assumption that demand is uniform. POQ = EOQ / average weekly usage

Period-Order Quantity Example : EOQ = 2800 units, and the annual usage is 52,000 units. What is POQ ? Average weekly usage = / 52 = 1000 per week POQ = 2800/ 1000 = 2.8 weeks -  = 3 weeks.

EPQ Persediaan diterima secara bertahap sepanjang suatu perioda waktu t 2t Tingkat persediaan Max Persediaan diisi kembali Persediaan dikosongkan waktu RO/XVI/14

R = jumlah produksi per tahun r = jumlah produksi per hari = R/365 D = jumlah permintaan per tahun d = jumlah permintaan per hari = d = D / 365 Agar persediaan mencapai Q, dibutuhkan Q/r hari Selama Q/r hari, jumlah permintaan = Q/r. d Persediaan maksimal = Q - Q/r. d Rata rata persediaan maksimal = ½ ( Q – Q/ r d )= Q/2 ( 1 – d/r )

Total biaya pemeliharaan = Cc. Q/2 ( 1 – d/r ) Total biaya persediaan tahunan = Tc= Co D/Q + Cc Q/2 ( 1- d/r ) Q optimal : Total biaya persediaan tahunan :

Model Dinamis EOQ Model EOQ statis didasarkan pada asumsi tingkat permintaan diketahui dan relatif konstan. Jika permintaan tidak konstan (bervariasi) maka bisa dengan pendekatan EOQ, Wagner-Within, atau Silver-Meal.

Pendekatan EOQ Bulan Jumlah Permintaan Pers Awal Pembelian Pers Akhir Biaya Pesan Biaya Simpan Biaya total persediaan832

Pendekatan Wagner-Within Bulan Jumlah Permintaan Pers Awal Pembelian Pers Akhir Biaya Pesan Biaya Simpan Biaya total persediaan584

Ukuran Persediaan Inventory turnover rate, seberapa cepat produk mengalir relatif terhadap jumlah yang tersimpan sebagai persediaan Misal perusahaan menjual 150 jenis produk, nilai persediaan rata-rata Rp. 3 milyar. Penjualan setahun Rp. 40 milyar dengan margin 25%. Berarti persediaan yang terjual dalam setahun Rp. 30 milyar, sehingga tingkat perputaran adalah 10 kali dalam setahun.

Ukuran Persediaan Inventory days of supply, rata-rata jumlah hari suatu perusahaan bisa beroperasi dengan jumlah persediaan yang dimiliki. Misal perusahaan beroperasi 300 hari dalam setahun, maka nilai persediaan yang terjual perhari = 30 milyar / 300 hari = 0.1 milyar. Jadi persediaan senilai Rp. 3 milyar dapat digunakan selama 3/0.1 = 30 hari kerja.

Ukuran Persediaan Fill rate, persentase jumlah item yang tersedia saat diminta pelanggan. Fill rate 97% berarti kemungkinan 3% dari item yang diminta oleh pelanggan tidak tersedia.