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Inventory Models

Inventory Models. Inventory models. Help to decide How much to order When to order Basic EOQ model POQ model. Basic EOQ model. Assumptions Known and constant demand Known and constant lead time Instantaneous receipt of material No quantity discounts

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Inventory Models

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  1. Inventory Models

  2. Inventory models • Help to decide • How much to order • When to order • Basic EOQ model • POQ model

  3. Basic EOQ model • Assumptions • Known and constant demand • Known and constant lead time • Instantaneous receiptof material • Noquantitydiscounts • Onlyorder (setup) costand holding cost • Nostockouts

  4. Basic EOQ model • Receive an order • Use the inventory at a constant rate • Reorder same amount • Instantaneously receive the order

  5. On-hand inventory (units) Time Economic Order Quantity

  6. On-hand inventory (units) Time Economic Order Quantity

  7. Receive order Q On-hand inventory (units) Time Economic Order Quantity

  8. Receive order Q On-hand inventory (units) 1 cycle Time Economic Order Quantity

  9. Receive order Q On-hand inventory (units) 1 cycle Time Economic Order Quantity

  10. Receive order Inventory depletion (demand rate) Q On-hand inventory (units) 1 cycle Time Economic Order Quantity

  11. Receive order Inventory depletion (demand rate) Q On-hand inventory (units) 1 cycle Time Economic Order Quantity

  12. Receive order Inventory depletion (demand rate) Q Q — 2 On-hand inventory (units) Average cycle inventory 1 cycle Time Economic Order Quantity

  13. Total Cost = Holding Cost + Order Cost

  14. Annual cost (dollars) Lot Size (Q) Total Cost = Holding Cost + Order Cost

  15. Annual cost (dollars) Holding cost (HC) Lot Size (Q) Total Cost = Holding Cost + Order Cost

  16. Purchase Order Purchase Order Description Qty. Description Qty. Microwave 1 Microwave 1000 Order quantity Order quantity Why Holding Costs Increase • More units must be stored if more are ordered

  17. Annual cost (dollars) Holding cost (HC) Ordering cost (OC) Lot Size (Q) Total Cost = Holding Cost + Order Cost

  18. Order cost $10 PurchaseOrder Description Qty. 1 Microwave Order Cost $10 PurchaseOrder Description Qty. Microwave 10 Why Order Costs Decrease • If we order more when we place an order, then we order fewer times over the year. • Example: You expect to order 10 microwave ovens over a year for a retail store like Sears. It cost $10 to place an order. • If you order 1 microwave, how many orders will you place over the year? what is the ordering cost? What is the ordering cost per microwave? • If you order 10 microwaves, how many orders will you place over the year? What is the ordering cost? What is the ordering cost per microwave?

  19. Total cost = HC + OC Annual cost (dollars) Holding cost (HC) Ordering cost (OC) Lot Size (Q) Total Cost = Holding Cost + Order Cost

  20. Gift Shop • A museum of natural history is having problems managing their inventories. Low inventory turnover is squeezing profit margins and causing cash-flow problems. • A Class A item, a birdfeeder is also a top-selling item. • Sales: 18 units/week • Purchase cost: $60 • Order cost: $45 • Annual holding cost: 25% of purchase cost • 52-week year • Management has been ordering in lots of 390 units.

  21. Q Time What is the annual cost of the current policy? • Q – order quantity • TC – Total cost • Annual • Monthly • ??

  22. Holding Cost

  23. Q 2 3000 — 2000 — 1000 — 0 — Holding cost Annual cost (dollars) Holding cost = (H) | | | | | | | | 50 100 150 200 250 300 350 400 Lot Size (Q)

  24. Ordering cost

  25. Q 2 D Q 3000 — 2000 — 1000 — 0 — Holding & Ordering Cost Annual cost (dollars) Holding cost = (H) Ordering cost = (S) | | | | | | | | 50 100 150 200 250 300 350 400 Lot Size (Q)

  26. 3000 — 2000 — 1000 — 0 — Q 2 D Q Total cost = (H) + (S) Q 2 Holding cost = (H) D Q Ordering cost = (S) | | | | | | | | 50 100 150 200 250 300 350 400 Lot Size (Q) Total Cost Annual cost (dollars)

  27. Total cost:

  28. What is the annual cost of the current policy? D – Total demand Q – Order quantity S – Setup/order cost H – Holding cost

  29. What is the annual cost of the current policy? D – Total demand 936/year Q – Order quantity 390/order S – Setup/order cost $45/order H – Holding cost = 0.25*60 = $15/unit/year

  30. Q 2 D Q Q 2 D Q Current cost 3000 — 2000 — 1000 — 0 — Total Cost for Q = 390 Total cost = (H) + (S) Annual cost (dollars) Holding cost = (H) Ordering cost = (S) | | | | | | | | 50 100 150 200 250 300 350 400 Current Q Lot Size (Q)

  31. Q 2 D Q Q 2 D Q Current cost 3000 — 2000 — 1000 — 0 — Can the gift shop do better? Total cost = (H) + (S) Annual cost (dollars) Holding cost = (H) Ordering cost = (S) | | | | | | | | 50 100 150 200 250 300 350 400 Current Q Lot Size (Q)

  32. 3000 — 2000 — 1000 — 0 — Annual cost (dollars) | | | | | | | | 50 100 150 200 250 300 350 400 Q* Lot Size (Q) Economic Order Quantity – Q* Setup cost = Holding Cost

  33. Economic Order Quantity (EOQ) – Q*

  34. Total Cost of Economic Order Quantity (EOQ) – Q* When Q = 390

  35. When to order? • Reorder point (ROP) • Lead time – amount of time from order placement to receipt of goods • Lead time demand – the demand the occurs during the lead time

  36. Reorder point Order received On-hand inventory OH

  37. Reorder point Order received On-hand inventory OH Time between orders TBO

  38. Reorder point Order received On-hand inventory OH L Lead time TBO

  39. Reorder point Order received On-hand inventory OH R Order placed L TBO

  40. Gift shop reorder point • Demand: 18 birdfeeders/week • Lead time: 2 weeks • Lead time demand: 36 birdfeeders • ROP: 36 birdfeeders

  41. Gift shop order policy • Place order when the on-hand inventory is 36 birdfeeders. • Order 75 birdfeeders • Order received in 2 weeks • Place next order when the on-hand inventory is 36 birdfeeders

  42. Gift shop order policy Order received 75 On-hand inventory OH 36 Order placed 2 wks

  43. Distribution Game • What is the EOQ for the central warehouse in the distribution game? • Order cost: S = • Holding cost: H = • Demand: D = $200 $14.70/unit/year 2190

  44. Distribution Game

  45. Production Order Quantity

  46. Production Order Quantity On-hand inventory Time

  47. Production Order Quantity Production quantity Q On-hand inventory Time

  48. Production Order Quantity Production quantity Q Demand during production interval On-hand inventory p – d Time

  49. Production quantity Q Demand during production interval On-hand inventory p – d Time Production Order Quantity

  50. Production quantity Q Demand during production interval On-hand inventory p – d Time Production and demand Demand only TBO Production Order Quantity

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