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Inventory Control: Part 2 - Lot-Size Inventories

Inventory Control: Part 2 - Lot-Size Inventories. Types of Inventories. By Function - Lot-Size (Cycle or Replenishment) - Instantaneous (Purchase) - Non-Instantaneous (Produce) - Safety (Fluctuation or Buffer) - Anticipation (Seasonal) - Transportation (Pipeline)

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Inventory Control: Part 2 - Lot-Size Inventories

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  1. Inventory Control:Part 2 - Lot-Size Inventories

  2. Types of Inventories • By Function - Lot-Size(Cycle or Replenishment) - Instantaneous (Purchase) - Non-Instantaneous (Produce) - Safety (Fluctuation or Buffer) - Anticipation (Seasonal) - Transportation (Pipeline) - Hedge (Beyond Scope of Class)

  3. Lot-Size Stocks: Instantaneous Receipts

  4. Lot-Size Stocks: Instantaneous • Let Q = Order Quantity A = Usage (Forecast Demand) S = Order (Setup) Cost per Order c = Purchase Price per Item i = Cost as % of Purchase H = Holding Cost per Unit = ic • TC = Order + Holding = S(A/Q) + ic(Q/2)

  5. Lot-Size Stocks: Instantaneous, Example Joe the plumber has gone into the designer plunger business. He buys basic plungers from a well-known supplier in Washington D.C. and customizes them. He maintains a huge raw materials plunger inventory in Defiance, Ohio. Demand averages about 1,000 items per month; holding costs per month are 50% of purchase costs; and order costs are $30. Joe buys plungers for $12. How much and how often should Joe order? Determine total relevant costs.

  6. Lot-Size Stocks: Instantaneous, Example • A = 1000 Plungers per Month S = $ 30 per Order c = $ 12 per Item i = 50% of Purchase Costs H = (.50)($12) = $ 6 per Unit per Month • TC = Order + Holding = (30000/Q) + (6)(Q/2)

  7. Lot Size Stocks: Instantaneous, Example Q Order Holding Total (TC) 50 $600 $150 $750 100 300 300 600 150 200 450 650 200 150 600 750 Best Q or Q* is Apparently 100

  8. Lot Size Stocks: Instantaneous, Example

  9. Lot Size Stocks: Instantaneous Let Holding = Order Cost at Best Answer (ic)Q/2 = S(A/Q) Q2 ic = 2AS Q* = (2AS/ic)0.5 = EOQ(1) TC* = (2ASic)0.5 (2) N* = A/Q* = # of Orders (3) T* = 1/N* = Reorder Time (4)

  10. Cycle Stocks: Instantaneous Example • A = 1000 Items per Month S = $30 per Order c = $12 per Item i = 50% of Purchase Costs H = (.50)($12) = $6 per Unit per Month • Q*(EOQ) = (2AS/ic)0.5=(2x1000x30/6)0.5= 100 • TC* = (2ASic)0.5 = (2x1000x30x6)0.5= $600 • N* = A/Q* = 1000/100 = 10

  11. Lot-Size Stocks: Instantaneous, Price Discounts A distributor buys an average of 1,600 Snortoff Vodka bottles a year. Bottles cost $0.98 if orders are at least 800 bottles; otherwise bottles cost $1.00. Order costs are $5.00 and holding costs are 10% of purchase per year. Determine the economic order quantity.

  12. Lot-Size Stocks: Price (or Quantity) Discounts • Let x = Price Break Point • If Q < x, We Have Regular Price c1 Q  x, We Have Discounted Price c2 • Example Problem If Q < 800, Regular Price c1=$1.00 Q  800, Discounted Price c2 = $0.98 Also: A = 1600 per Year, S = $5, i = 10%

  13. Lot-Size Stocks: Price Discounts • TC = Order + Holding + Purchase TC = S(A/Q) + ic(Q/2) + cA (1) • Q* = (2AS/ic)0.5 (2) • TC* = (2ASic)0.5 + cA (3)

  14. Lot-Size Stocks, Price Discount Rules 1. Compute Q* Using Equation (2) and c2. If Answer is  x, Stop. You Have Answer. 2. Calculate TC* Using Equation (3) and c1. Calculate TCx Using Equation (1), c2, and Q = x. 3. If TCx TC*, Q* = x. 4. If TC* < TCx, Calculate Q* from Equation (2) Using c1.

  15. Lot-Size Stocks, Quantity Discount Example (1) Q* = (2AS/ic)0.5 = [(2x1600x5)/(.10x.98)]0.5 = 404 404 < 800, So Go On! (2) TC* = (2ASic)0.5 + cA = [(2x1600x5x.1x1)]0.5+(1x1600)=$1640 TCx = S(A/Q) + ic(Q/2) + cA = (5)(1600)/800) + (.1x.98)x(800/2) + (.98)(1600) = $1617 (3) $1617 < $1640, So Q* = x = 800

  16. Lot-Size Stocks: Non-Instantaneous Receipts

  17. Lot-Size Stocks:Non-Instantaneous • Let Q = Run Size A = Forecast Demand (or Usage Rate = d) S = Setup Cost per Order H = Holding Cost per Item p = Production/Delivery Rate Tp= Time Machine On IMAX is Maximum Inventory • TC = Setup + Holding

  18. Lot-Size Stocks:Non-Instantaneous • Suppose p = 100 per Hour, d = 50 per Hour, Tp = 2 Hours • What is Q? What is IMAX? • Note that Q = pTp (100x2) or Tp (Time On) = Q/p • Also, IMAX = (p - d)Tp (50x2) = (p - d)(Q/p) = [1-(d/p)]Q

  19. Lot-Size Stocks:Non-Instantaneous • TC = Setup + Holding • TC = S(A/Q) + H(IMAX/2) TC = S(A/Q) + (1-(d/p)) (HQ/2) (1) • Q* = [(2AS/H)(p/(p-d))]0.5 (2) • TC* = [2ASH (1-(d/p))]0.5(3) • N* = (A/Q*) (4)

  20. Incorporating Q* (Or EOQ) into MRP We Can Use EOQ as Lot Size in MRP Creates Excessive Inventory Due to “Lumpy” Demand Let Q* = EOQ = 250 20

  21. Period Order Quantity (POQ) POQ = Q* / A = T* A is Often in Weeks POQ Normally Reduces Inventory and Number of Orders When Compared with EOQ Ordering E.g. POQ = 250 / 89 = 2.81  3 Weeks 21

  22. POQ Example POQ Reduces Inventory and Number of Orders. 22

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