1 / 21

EOQ

EOQ. Answers the Question “How Much to Order?” Assumptions : Instantaneous production Immediate delivery Deterministic demand Constant demand: D units/year Constant setup cost: A $/setup Independent products. EOQ view of Inventory. Order Quantity Q. Inventory. Time. Costs.

saki
Download Presentation

EOQ

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. EOQ Answers the Question “How Much to Order?” Assumptions: • Instantaneous production • Immediate delivery • Deterministic demand • Constant demand: D units/year • Constant setup cost: A $/setup • Independent products

  2. EOQ view of Inventory Order Quantity Q Inventory Time

  3. Costs • Setup Costs • A $/setup • How many setups if we make Q each time? • Why not just make D units in one setup?

  4. Inventory Cost • Usually billed as a “holding cost” • Essentially interest on the money tied up in inventory • h $/unit/year • Example: Holding 100 units for 6 months costs: ? • Inventory holding Cost • h*Average Inventory

  5. A Model Lot Size or Order Quantity: Q units Average Inventory Level: Q/2units Annual Demand: D units/year Order Frequency: every D/Q times per year Average Variable Cost/Year: TVC = h*Q/2 +A*D/Q

  6. The EOQ • Use Calculus to find the value of Q that minimizes TVC(Q) • Or...

  7. The Economic Order Quantity h Q/2 = A D/Q Q2 = 2 A D/h Q = SQRT(2 A D/h) CAVEAT: Make sure you use commensurate units!

  8. An Example • Raw Material X • Quarterly demand: 6,000 units • Cost per unit: ~ $25/unit • Holding Cost: say 10% per year • Transaction Cost: $100/order EOQ = SQRT(2 CT D/ CI) = SQRT(2 * 100 * 6,000/(0.025*25)) ~ 1,385 units per shipment

  9. Robustness of the EOQ

  10. Robustness

  11. EPQ Answers the Question “How Much to Produce?” Assumptions: • Instantaneous production • Constant production rate: P > D units/year • Immediate delivery • Deterministic demand • Constant demand: D units/year • Constant setup cost: A$/setup • Independent products

  12. EPQ view of Inventory Inventory Production Quantity Q Max Inv. Level Length of Prod. Run Time

  13. A Model Lot Size or Production Quantity: Q units Average Inventory Level • Production run lasts: Q/P • Inventory grows at rate: (P-Q) • So, max inventory is: (P-D)Q/P = (1-D/P)Q • Average inventory is: (1-D/P)Q/2 Order Frequency: every D/Q times per year Average Variable Cost/Year: TVC = h*(1-D/P)Q/2 +A*D/Q

  14. The EPQ • Use Calculus to find the value of Q that minimizes TVC(Q) • Or use the previous answer... • TVC = h*(1-D/P)Q/2 +A*D/Q = h’Q/2 +A*D/Q So, Q = SQRT(2 A D/h’) = SQRT(2AD/h(1-D/P))

  15. An Example • Raw Material X • Quarterly demand: 6,000 units • Cost per unit: ~ $25/unit • Holding Cost: say 10% per year • Transaction Cost: $100/order • Quarterly Production Rate: 8,000 units EOQ = SQRT(2 CT D/ CI) = SQRT(2*100*6,000/(0.025*25*(1-6/8))) ~ 2,771 units per run

  16. A Model • Divide the planning horizon into time buckets t = 1, 2, ..., T • Dt = units of demand in period t • ct = unit production cost in period t • At = setup cost in period t • ht = inventory holding cost in period t • Qt = the lot size in period t • It = units in inventory at the end of period t

  17. Heuristics • Lot-for-lot: Make what is required each period. • Fixed Order Quantity: Order the EOQ • Period Order Quantity: Calculate the EOQ, Q. Convert to order frequency: T = Q/D. Orders sized to last for time T.

More Related