Inventory Management I

1. Inventory Management I

2. 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

3. 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.

4. 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)

5. 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

6. Reasons for Inventories • Low cost plan operation • Minimum investment

7. 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)

8. Inventory Holding Costs Category% of Value Housing (building) cost 6% Material handling 3% Labor cost 3% Opportunity/investment 11% Pilferage/scrap/obsolescence 3% Total Holding Cost 26%

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

10. 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

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

12. ABC Classification Solution Stock # Vol. Cost $ Vol. % ABC 206 26,000 $ 36 $936,000 105 200 600 120,000 019 2,000 55 110,000 144 20,000 4 80,000 207 7,000 10 70,000 Total 1,316,000

13. ABC Classification Solution

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

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

16. 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

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

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

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

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

21. 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

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

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

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

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

26. Optimal Quantity Total Costs =

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

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

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

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

31. 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?

32. 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

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

34. Discount Example D = 10,000 k= $20 r = 20% Price Quantity EOQ v = 5.00 Q < 500 633 4.50 501-999 666 3.90 Q >= 1000 716

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

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

37. Discount Example Order 666 at a time: Hold 666/2 * 4.50 * 0.2= $ 299.70 Order 10,000/666 * 20 = $ 300.00 Mat’l 10,000*4.50 =$45,000.00 45,599.70 =$45.599.00 Order 1,000 at a time: Hold 1,000/2 * 3.90 * 0.2= $390.00 Order 10,000/1,000 * 20 = $200.00 Mat’l 10,000*3.90 = $39,000.00 39,590.00

38. 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.

39. 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

40. Period-Order Quantity Example : EOQ = 2800 units, and the annual usage is 52,000 units. What is POQ ? Average weekly usage = 52000 / 52 = 1000 per week POQ = 2800/ 1000 = 2.8 weeks - = 3 weeks.

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

42. 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 )

43. 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 :

44. 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.

47. 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.

48. 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.

49. 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.