1. Inventory Management

2. Inventory management A subsystem of logistics A subsystem of logistics Inventory: a stock of materials or other goods to facilitate production or to satisfy customer demand Inventory: a stock of materials or other goods to facilitate production or to satisfy customer demand Main decisions: Main decisions: Which items should be carried in stock? Which items should be carried in stock? How much should be ordered? How much should be ordered? When should an order be placed? When should an order be placed?

3. The need to hold stocks 1 Buffer between Supply and Demand Buffer between Supply and Demand To keep down production costs: to achieve low unit costs, production have to run as long as possible (setting up machines is tend to be costly) To keep down production costs: to achieve low unit costs, production have to run as long as possible (setting up machines is tend to be costly) To take account of variable supply times: safety stock to cover delivery delays from suppliers To take account of variable supply times: safety stock to cover delivery delays from suppliers To minimize buying costs associated with raising an order To minimize buying costs associated with raising an order To accommodate variations (on the short run) in demand (to avoid stock-outs) To accommodate variations (on the short run) in demand (to avoid stock-outs) To account for seasonal fluctuations: To account for seasonal fluctuations: There are products popular only in peak times There are products popular only in peak times There are goods produced only at a certain time of the year There are goods produced only at a certain time of the year

4. Adaptation fo the fluctuation of demand with building up stocks DEMAND CAPACITY Inventory accumulation Inventory reduction

5. The need to hold stocks 2 To take advantage of quantity discounts (buying in bulk) To take advantage of quantity discounts (buying in bulk) To allow for price fluctuations/speculation: to buy large quantities when a good is cheaper To allow for price fluctuations/speculation: to buy large quantities when a good is cheaper To help production and distribution operations run smoothly: to increase the independence of these activities To help production and distribution operations run smoothly: to increase the independence of these activities To provide immediate service for customers To provide immediate service for customers To minimize production delays caused by lack of spare parts (for maintenance, breakdowns) To minimize production delays caused by lack of spare parts (for maintenance, breakdowns) Work-in-progress: facilitating production process by providing semi-finished stocks between different processes Work-in-progress: facilitating production process by providing semi-finished stocks between different processes

6. Types of Stock-holding/Inventory raw material, component and packaging stock raw material, component and packaging stock in-process stocks (work-in-progress; WIP) in-process stocks (work-in-progress; WIP) finished products (finished goods inventory; FGI) finished products (finished goods inventory; FGI) pipeline stocks: held in the distribution chain pipeline stocks: held in the distribution chain general stores: contains a mixture of products to support general stores: contains a mixture of products to support spare parts: spare parts: Consumables (nuts, bolts, etc.) Consumables (nuts, bolts, etc.) Rotables and repairables Rotables and repairables

7. Independent vs. dependent demand Independent demand: Independent demand: Influenced only by market conditions Influenced only by market conditions Independent from operations Independent from operations Example: finished goods Example: finished goods Dependent demand: Dependent demand: Related to the demand for another item Related to the demand for another item Example: product components, raw material Example: product components, raw material

8. Another typology of stocks working stock: reflects the actual demand working stock: reflects the actual demand cycle stock: follows the production (or demand) cycles cycle stock: follows the production (or demand) cycles safety stock: to cover unexpected fluctuations in demand safety stock: to cover unexpected fluctuations in demand speculative stock: built up on expectations speculative stock: built up on expectations seasonal stock: goods stockpiled before peaks seasonal stock: goods stockpiled before peaks

9. Inventory cost Item cost: the cost of buying or producing inventory items Item cost: the cost of buying or producing inventory items Ordering cost: does not depend on the number of items ordered. Form typing the order to transportation and receiving costs. Ordering cost: does not depend on the number of items ordered. Form typing the order to transportation and receiving costs. Holding (carrying) cost: Holding (carrying) cost: Capital cost: the opportunity cost of tying up capital Capital cost: the opportunity cost of tying up capital Storage cost: space, insurance, tax Storage cost: space, insurance, tax Cost of obsolescence, deterioration and loss Cost of obsolescence, deterioration and loss Sometimes designated by management rather than computed Sometimes designated by management rather than computed Stockout cost: economic consequences of running out of stock (lost profit and/or goodwill) Stockout cost: economic consequences of running out of stock (lost profit and/or goodwill)

10. Economic Order Quantity (EOQ) Assumptions of the model: Assumptions of the model: Demand rate is constant, recurring and known Demand rate is constant, recurring and known The lead time (from order placement and order delivery) is constant and known The lead time (from order placement and order delivery) is constant and known No stockouts are allowed No stockouts are allowed Goods are ordered and produced in lots, and the lot is placed into inventory all at one time Goods are ordered and produced in lots, and the lot is placed into inventory all at one time Unit item cost is constant, carrying cost is linear function of average inventory level Unit item cost is constant, carrying cost is linear function of average inventory level Ordering cost is independent of the number of items in a lot Ordering cost is independent of the number of items in a lot Marginal holding cost is constant Marginal holding cost is constant The item is a single product (no interaction with other products) The item is a single product (no interaction with other products)

11. The „SAW-TOOTH” Inventory level Time Order quantity (Q) Order inteval Average inventory level = Q/2

12. Total cost of inventory (tradeoff between ordering frequency and inventory level) Minimum cost Total cost ∙ Ordering cost (S ∙ D/Q) ∙ Holding cost (H ∙ Q/2) EOQ

13. Calculating the total cost of inventory Let… Let… S be the ordering cost (setup cost) per oder S be the ordering cost (setup cost) per oder D be demanded items per planning period D be demanded items per planning period H be the stock holding cost per unit H be the stock holding cost per unit H=i∙C, where C is the unit cost of an item, and i is the carrying rate H=i∙C, where C is the unit cost of an item, and i is the carrying rate Q be the ordered quantity per order (= lot) Q be the ordered quantity per order (= lot) TC = S ∙ (D/Q) + H ∙ (Q/2) TC = S ∙ (D/Q) + H ∙ (Q/2) (D/Q) is the number of orders per period (D/Q) is the number of orders per period (Q/2) is the average inventory level in this model (Q/2) is the average inventory level in this model

14. The minimum cost (EOQ) TC = S ∙ (D/Q) + H ∙ (Q/2) TC = S ∙ (D/Q) + H ∙ (Q/2) бTC/бQ = 0 бTC/бQ = 0 0 = - S ∙ (D/Q 2 ) + H/2 0 = - S ∙ (D/Q 2 ) + H/2 H/2 = S ∙ (D/Q 2 ) H/2 = S ∙ (D/Q 2 ) Q 2 = (2 ∙ S ∙ D)/H Q 2 = (2 ∙ S ∙ D)/H EOQ = √ (2 ∙ S ∙ D)/H EOQ = √ (2 ∙ S ∙ D)/H

15. Example D = 1000 units per year S = 100 euro per order H = 20 euro per unit Find the economic order quantity! (we assume a saw-tooth model) EOQ = √ (2 ∙ 1,000 units ∙ 100 euro )/20 euro/unit EOQ = √ 10,000 units 2 = 100 units

16. The EOQ zone

17. Reordering (or replenishment) point When to start the ordering process? When to start the ordering process? It depends on the… It depends on the… Stock position: stock on-hand (+ stock on-order) Stock position: stock on-hand (+ stock on-order) in a simple saw-tooth model it is Q, in a simple saw-tooth model it is Q, in some cases, there can be an initial stock (Q 0 ), that is different from Q. In this case the first order depends on Q 0 in some cases, there can be an initial stock (Q 0 ), that is different from Q. In this case the first order depends on Q 0 lead time (LT): the time interval from setting up order to the start of using up the ordered stock lead time (LT): the time interval from setting up order to the start of using up the ordered stock Average demand per day (d) Average demand per day (d) ROP = d (LT ) + safety stock ROP = d (LT ) + safety stock

18. Examples Q 0 = 600 tons Q 0 = 600 tons Q = 200 tons Q = 200 tons d = 10 tons per day d = 10 tons per day LT = 8 days LT = 8 days What is the ROP and when we reach that level? What is the ROP and when we reach that level? What is the time of the next reorder? What is the time of the next reorder? ROP = 80 tons (600 – 80)/10 = 52. day Q 0 = Q = 400 tons Q 0 = Q = 400 tons d = 16 tons per day d = 16 tons per day LT = 20 days LT = 20 days ROP = ? ROP = ? First rearder time? First rearder time? ROP = 16 ∙ 20 = 320 tons First reorder: (400 – 320)/16 = 5. day 52 + 8 + (200 – 80)/10 = 72. day

19. Examples D = 2,000 tons S = 100 euros per order H = 25 euros per order Initial stock = 1,000 tons LT = 12 days N = 250 days EOQ = √ (2 ∙ 2,000 ts ∙ 100 euro )/25 euro/ts = 126.49 ts d = 2,000 ts /250 ds = 8 ts/ds ; ROP = 12 ∙ 8 = 96 tons Reroder 1 = (1,000 – 96)/8 = 113 Reorder 2 = 113 + 12 + (126.49 – 96)/8 = 128.81 = 128 Calculate the following: EOQdROP first and second reorder time

20. The SAW-TOOTH with safety stock Inventory level Time Order quantity Continuous demand Safety stock or buffer stock b

21. Buffer stock depends Demand rate and lead time Demand rate and lead time Variability of demand and lead time Variability of demand and lead time Desired service level Desired service level

22. Service level The probability that demand will not exceed supply during lead time. The probability that demand will not exceed supply during lead time. Service level = 100 percent - stockout risk Service level = 100 percent - stockout risk

23. Buffer (safety) stock b = z ∙ σ where z = safety factor from the (normal) distribution σ = sandard deviation of demand over lead time Let z be 1,65 (95%), and the standard deviation of demand is 200 units/lead time. b = 1,65 ∙ 200 units = 330 units

25. Example Lead time = 10 days Lead time = 10 days Average demand over lead time: 300 tons Average demand over lead time: 300 tons Standard deviation over lead time: 20 tons Standard deviation over lead time: 20 tons Accepted risk level: 5% Accepted risk level: 5% Safety stock = ? Reorder quantity = ? Safety stock = ? Reorder quantity = ? b = z * σ = 1,65 * 20 = 33 tons b = z * σ = 1,65 * 20 = 33 tons ROP = 300 + 33 = 333 tons ROP = 300 + 33 = 333 tons

26. Examples Q 0 = 600 tons Q 0 = 600 tons Q = 200 tons Q = 200 tons d = 10 tons per day d = 10 tons per day LT = 8 days LT = 8 days b = 33 tons b = 33 tons ROP = 8 * 10 + 33 = 113 Q 0 = Q = 400 tons Q 0 = Q = 400 tons d = 16 tons per day d = 16 tons per day LT =20 days LT =20 days b = 66 tons b = 66 tons ROP = 386

27. Economic production quantity (EPQ) Production of spare parts /materials done in batches (lots) Production of spare parts /materials done in batches (lots) Only on item Only on item Annual demand is known Annual demand is known Usage rate (u) is constant Usage rate (u) is constant Usage occurs continually but production occurs periodically Usage occurs continually but production occurs periodically Production rate is constant (p) Production rate is constant (p) Lead time (LT) does not vary Lead time (LT) does not vary No quantity (Q) discounts No quantity (Q) discounts Setup cost instead of ordering cost Setup cost instead of ordering cost

28. EPQ with incremental inventory replenishment

29. Total cost in EPQ TC EPQ = carrying cost + setup cost = = (I max /2)H + (D/Q)S TC EPQ = carrying cost + setup cost = = (I max /2)H + (D/Q)S The economic run quantity: Q EPQ = (2DS/H) 0,5 ∙ [p/(p – u)] 0,5 The economic run quantity: Q EPQ = (2DS/H) 0,5 ∙ [p/(p – u)] 0,5 Cycle time = Q EPQ / u Cycle time = Q EPQ / u Run time = Q EPQ / p Run time = Q EPQ / p I max = (Q EPQ / p) (p – u) I max = (Q EPQ / p) (p – u) I average = I max / 2 I average = I max / 2

30. EOQ example

31. Quantity discounts Price reductions for large orders Price reductions for large orders Example: Example: The buyers total cost curve to minimze: The buyers total cost curve to minimze:

32. Advantages For the buyer For the buyer Fewer order set-ups (D*S/Q) Fewer order set-ups (D*S/Q) Cheaper price (P*D) Cheaper price (P*D) For the seller: For the seller: Decreased holding costs (I*H/2) Decreased holding costs (I*H/2) Decreased administrative costs (FC) Decreased administrative costs (FC) Lower opportunity cost Lower opportunity cost

33. A TC görbe, ha szerepeltetjük a beszerzési költséget is

34. Allowances and TC curves

35. Constant carrying costs

36. Carrying costs are stated as a percentage of unit price Cost Quantity

37. Finding EOQ with constant holding cost D = 816 pieces/year D = 816 pieces/year S = 12 dollars/order S = 12 dollars/order H = 4 dollars/piece/year H = 4 dollars/piece/year Prices: Prices: 20 dollars 1-49 pieces, 20 dollars 1-49 pieces, 18 dollars 50-79 pieces, 18 dollars 50-79 pieces, 17 dollars 80-99 pieces, 17 dollars 80-99 pieces, 16 dollars over 100 pieces 16 dollars over 100 pieces

38. Calculating EOQ

39. Solution Q EOQ = (2*816*12/4) 0,5 = 69.97 = 70 pieces Q EOQ = (2*816*12/4) 0,5 = 69.97 = 70 pieces TC 70 = (70/2)*4 + (816/70)*12 + 18*816 = = 14.968 dollars TC 70 = (70/2)*4 + (816/70)*12 + 18*816 = = 14.968 dollars TC 80 = 14.154 TC 80 = 14.154 TC 100 = 13.354 TC 100 = 13.354

40. With non-constant holding costs D = 4.000 pieces, S = 30 dollars, H = 0.4*P D = 4.000 pieces, S = 30 dollars, H = 0.4*P Prices: Prices: 1-499 pieces 0.9 dollar; 1-499 pieces 0.9 dollar; 500-999 0.85 dollar; 500-999 0.85 dollar; over 1.000 pieces 0.8 dollar. over 1.000 pieces 0.8 dollar.

41. Solution 1. Q EOQ(0,8) =866 pieces → not feasible 2. Q EOQ(0,85) =840 pieces → feasible 3. TC 840 =30*(4000/840)+0,4*0,85*(840/2)+4000*0,85= =3685,66 dollars→ is it profitable to order a greater lot? 4. TC 1000 =30*(4000/1000)+0,4*0,8*(1000/2)+4000*0,8= =3480 dollars→ yes, it is profitable.

42. Alternative models 1 Periodic review system: Stock level is examined at regular intervals Stock level is examined at regular intervals Size of the order depends on the quantity on stock. it should bring the inventory to a predetermined level Size of the order depends on the quantity on stock. it should bring the inventory to a predetermined level time Stock on hand L Q Q LL TTT Q

43. Alternative models 2 Fixed-order-quantity system: A predetermined stock level (reorder point) is given, at which the replenishement order will be placed A predetermined stock level (reorder point) is given, at which the replenishement order will be placed The order quantity is constant The order quantity is constant R Stock on hand L L L Q Q

44. Elements of demand patterns (forecasting) Actual demand: Actual demand: Trend line Trend line Seasonal fluctuacion Seasonal fluctuacion Weekly fluctuation Weekly fluctuation (Daily fluctuation) (Daily fluctuation) Random fluctuation Random fluctuation

45. Inventory decisions and Multiple Distribution Centres / warehouses The ‘square root law’: A rule of thumb A rule of thumb The total safety-stock holding in a distribution system is proportional to the square root of the number of depot locations The total safety-stock holding in a distribution system is proportional to the square root of the number of depot locations Example: If we reduce the number of DCs from 10 to 5, the savings in safety stock is: 1 – (√5 / √10) = 29% Example: If we reduce the number of DCs from 10 to 5, the savings in safety stock is: 1 – (√5 / √10) = 29% Pareto’s law or the ’80/20 rule’: A rule of thumb A rule of thumb Approximately 20% of storage items account for 80% of the inventory value measured in money. Approximately 20% of storage items account for 80% of the inventory value measured in money. ABC analysis (or Pareto analysis): ABC analysis (or Pareto analysis): ‘A’ lines: fast movers (20%) – 80% of money usage ‘A’ lines: fast movers (20%) – 80% of money usage ‘B’ lines: medium movers (30%) – 15% of money usage ‘B’ lines: medium movers (30%) – 15% of money usage ‘C’ lines: slow movers (C+D 50%) – 5% of money usage ‘C’ lines: slow movers (C+D 50%) – 5% of money usage ‘D’ lines: obsolete / dead stock ‘D’ lines: obsolete / dead stock

46. Example Initial number of warehouses: 6 Initial number of warehouses: 6 Initial sum of safety stocks: 6,000 Initial sum of safety stocks: 6,000 New number of warehouses: 2 New number of warehouses: 2 What is the new sum of safety stocks? What is the new sum of safety stocks? 6000*(2/6) 0.5 =3464.10

47. ABC analysis

49. ABC analysis exercise Item number Annual demand Price Annual dollar value 12.500360? 21.00070? 32.400500? 41.500100? 570070? 61.0001000? 7200210? 81.0004000? 98.00010? 10500200? ?

50. ABC analysis exercise Item number Annual demand Price Annual dollar value 12.500360900.000 21.0007070.000 32.4005001.200.000 41.500100150.000 57007049.000 61.00010001.000.000 720021042.000 81.00040004.000.000 98.0001080.000 10500200100.000 ∑ 7.591.000

51. Solution Item number Annual dollar Classification Percentage of items Percentage of annual dollar value 84.000.000 31.200.000 61.000.000 1900.000 4150.000 10100.000 980.000 270.000 549.000 742.000

52. Solution Item number Annual dollar Classification Percentage of items Percentage of annual dollar value 84.000.000A1052,7 31.200.000B 3040,8 61.000.000B 1900.000B 4150.000C 606,5 10100.000C 980.000C 270.000C 549.000C 742.000C ? ?

53. Data Capture Techniques and error rates (Rushton et al. 2006) Techniques and error rates (Rushton et al. 2006) Written entry – 25,000 in 3,000,000 Written entry – 25,000 in 3,000,000 Keyboard entry – 10,000 in 3,000,000 Keyboard entry – 10,000 in 3,000,000 Optical character recognition (OCR) – 100 in 3,000,000 Optical character recognition (OCR) – 100 in 3,000,000 labels that are both machine- and human-readable labels that are both machine- and human-readable for example: license plates for example: license plates Bar code (code 39) – 1 in 3,000,000 Bar code (code 39) – 1 in 3,000,000 fast, accurate and fairly robust fast, accurate and fairly robust reliable and cheap technique reliable and cheap technique Transponders (radio frequency tags) – 1 in 30,000,000 Transponders (radio frequency tags) – 1 in 30,000,000 a tag (microchip + antenna) affixed to the goods or container a tag (microchip + antenna) affixed to the goods or container receiver antenna receiver antenna reader reader host station that relays the data to the server host station that relays the data to the server can be passive or active can be passive or active

54. Thank you for listening