1 / 23

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)

ignatius
Download Presentation

Inventory Control: Part 2 - Lot-Size Inventories

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related